15 puzzle solver
You are encouraged to solve this task according to the task description, using any language you may know.
Your task is to write a program that finds a solution in the fewest moves possible single moves to a random Fifteen Puzzle Game.
For this task you will be using the following puzzle:
15 14 1 6 9 11 4 12 0 10 7 3 13 8 5 2
Solution:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0
The output must show the moves' directions, like so: left, left, left, down, right... and so on.
There are two solutions, of fifty-two moves:
rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd
rrruldluuldrurdddluulurrrdlddruldluurddlulurruldrrdd
see: Pretty Print of Optimal Solution
Finding either one, or both is an acceptable result.
- Extra credit.
Solve the following problem:
0 12 9 13 15 11 10 14 3 7 2 5 4 8 6 1
- Related Task
11l
-V
nr = [3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3]
nc = [3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]
T Solver
n = 0
np = 0
n0 = [0] * 100
n2 = [UInt64(0)] * 100
n3 = [Char("\0")] * 100
n4 = [0] * 100
F (values)
.n0[0] = values.index(0)
UInt64 tmp = 0
L(val) values
tmp = (tmp << 4) [|] val
.n2[0] = tmp
F fI()
V n = .n
V g = (11 - .n0[n]) * 4
V a = .n2[n] [&] (UInt64(15) << g)
.n0[n + 1] = .n0[n] + 4
.n2[n + 1] = .n2[n] - a + (a << 16)
.n3[n + 1] = Char(‘d’)
.n4[n + 1] = .n4[n] + Int(:nr[Int(a >> g)] > .n0[n] I/ 4)
F fG()
V n = .n
V g = (19 - .n0[n]) * 4
V a = .n2[n] [&] (UInt64(15) << g)
.n0[n + 1] = .n0[n] - 4
.n2[n + 1] = .n2[n] - a + (a >> 16)
.n3[n + 1] = Char(‘u’)
.n4[n + 1] = .n4[n] + Int(:nr[Int(a >> g)] < .n0[n] I/ 4)
F fE()
V n = .n
V g = (14 - .n0[n]) * 4
V a = .n2[n] [&] (UInt64(15) << g)
.n0[n + 1] = .n0[n] + 1
.n2[n + 1] = .n2[n] - a + (a << 4)
.n3[n + 1] = Char(‘r’)
.n4[n + 1] = .n4[n] + Int(:nc[Int(a >> g)] > .n0[n] % 4)
F fL()
V n = .n
V g = (16 - .n0[n]) * 4
V a = .n2[n] [&] (UInt64(15) << g)
.n0[n + 1] = .n0[n] - 1
.n2[n + 1] = .n2[n] - a + (a >> 4)
.n3[n + 1] = Char(‘l’)
.n4[n + 1] = .n4[n] + Int(:nc[Int(a >> g)] < .n0[n] % 4)
F fY()
I .n2[.n] == 1234'5678'9ABC'DEF0
R 1B
I .n4[.n] <= .np
R .fN()
R 0B
F fN() -> Bool
V n = .n
I .n3[n] != ‘u’ & .n0[n] I/ 4 < 3 {.fI(); .n++; I .fY() {R 1B}; .n--}
I .n3[n] != ‘d’ & .n0[n] I/ 4 > 0 {.fG(); .n++; I .fY() {R 1B}; .n--}
I .n3[n] != ‘l’ & .n0[n] % 4 < 3 {.fE(); .n++; I .fY() {R 1B}; .n--}
I .n3[n] != ‘r’ & .n0[n] % 4 > 0 {.fL(); .n++; I .fY() {R 1B}; .n--}
R 0B
F run()
L !.fY()
.np++
print(‘Solution found with ’(.n)‘ moves: ’, end' ‘’)
L(g) 1 .. .n
print(.n3[g], end' ‘’)
print(‘.’)
V solver = Solver([15, 14, 1, 6,
9, 11, 4, 12,
0, 10, 7, 3,
13, 8, 5, 2])
solver.run()- Output:
Solution found with 52 moves: rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd.
AArch64 Assembly
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program puzzle15solvex64.s */
/* this program is a adaptation algorithme C++ and go rosetta code */
/* thanck for the creators */
/* 1 byte by box on game board */
/* create a file with nano */
/* 15, 2, 3, 4
5, 6, 7, 1
9, 10, 8, 11
13, 14, 12, 0 */
/* Run this programm : puzzle15solver64 <file name> */
/* wait several minutes for résult */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ TRUE, 1
.equ FALSE, 0
.equ SIZE, 4
.equ NBBOX, SIZE * SIZE
.equ TAILLEBUFFER, 100
.equ NBMAXIELEMENTS, 100
.equ CONST_I, 1
.equ CONST_G, 8
.equ CONST_E, 2
.equ CONST_L, 4
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessTitre: .asciz "File name : "
sMessResult: .ascii " "
sMessValeur: .fill 22, 1, ' ' // size => 21
szCarriageReturn: .asciz "\n"
szMessCounterSolution: .asciz "Solution in @ moves : \n"
szMessErreur: .asciz "Error detected.\n"
szMessImpossible: .asciz "!!! Impossible solution !!!\n"
szMessErrBuffer: .asciz "buffer size too less !!"
szMessSpaces: .asciz " "
qTabNr: .quad 3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3
qTabNc: .quad 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
.align 8
sZoneConv: .skip 24
qAdrHeap: .skip 8
tbBox: .skip SIZE * SIZE // game boxes
qAdrFicName: .skip 8
qTabN0: .skip 8 * NBMAXIELEMENTS // empty box
qTabN3: .skip 8 * NBMAXIELEMENTS // moves
qTabN4: .skip 8 * NBMAXIELEMENTS // ????
qTabN2: .skip 8 * NBMAXIELEMENTS // table game address
sBuffer: .skip TAILLEBUFFER
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // INFO: main
mov x0,sp // stack address for load parameter
bl traitFic // read file and store value in array
cmp x0,#-1
beq 100f // error ?
ldr x0,qAdrtbBox
bl displayGame // display array game
ldr x0,qAdrtbBox // control if solution exists
bl controlSolution
cmp x0,#TRUE
beq 1f
ldr x0,qAdrszMessImpossible // no solution !!!
bl affichageMess
b 100f
1:
ldr x0,qAdrtbBox
ldr x9,qAdrqTabN2
str x0,[x9] // N2 address global
mov x10,#0 // variable _n global
mov x12,#0 // variable n global
bl searchSolution
cmp x0,#TRUE
bne 100f // no solution ?
ldr x3,qAdrqTabN2
ldr x0,[x3,x12,lsl #3] // visual solution control
bl displayGame
mov x0,x12 // move counter
ldr x1,qAdrsZoneConv
bl conversion10 // conversion counter
ldr x0,qAdrszMessCounterSolution
bl strInsertAtCharInc
ldr x1,qAdrsZoneConv
bl affichageMess
ldr x5,qAdrqTabN3
ldr x3,qAdrsBuffer
mov x2,#1
mov x4,#0
2: // loop solution display
ldr x1,[x5,x2,lsl 3]
cmp x2,#TAILLEBUFFER
bge 99f
strb w1,[x3,x4]
add x4,x4,#1
add x2,x2,#1
cmp x2,x12
ble 2b
mov x1,#0
strb w1,[x3,x4] // zéro final
mov x0,x3
bl affichageMess
ldr x0,qAdrszCarriageReturn
bl affichageMess
b 100f
99:
ldr x0,qAdrszMessErrBuffer
bl affichageMess
100: // standard end of the program
mov x0, #0 // return code
mov x8, #EXIT // request to exit program
svc #0 // perform the system call
qAdrtbBox: .quad tbBox
qAdrqTabN0: .quad qTabN0
qAdrqTabN2: .quad qTabN2
qAdrqTabN3: .quad qTabN3
qAdrqTabN4: .quad qTabN4
qAdrszMessCounterSolution: .quad szMessCounterSolution
qAdrszMessImpossible: .quad szMessImpossible
qAdrszMessErrBuffer: .quad szMessErrBuffer
qAdrsZoneConv: .quad sZoneConv
/******************************************************************/
/* search Solution */
/******************************************************************/
searchSolution: // INFO: searchSolution
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
// address allocation place on the heap
mov x0,#0 // allocation place heap
mov x8,BRK // call system 'brk'
svc #0
cmp x0,#-1 // allocation error
beq 99f
ldr x1,qAdrqAdrHeap
str x0,[x1] // store heap address
bl functionFN
ldr x3,qAdrqTabN2
ldr x0,[x3,x12,lsl #3] // last current game
bl gameOK // it is Ok ?
cmp x0,#TRUE
beq 100f // yes --> end
ldr x1,qAdrqAdrHeap // free up resources
ldr x0,[x1] // restaur start address heap
mov x8,BRK // call system 'brk'
svc #0
cmp x0,#-1 // allocation error
beq 99f
add x10,x10,#1 // _n
mov x12,#0 // n
bl searchSolution // next recursif call
b 100f
99:
ldr x0,qAdrszMessErreur
bl affichageMess
100:
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
qAdrszMessErreur: .quad szMessErreur
qAdrqAdrHeap: .quad qAdrHeap
/******************************************************************/
/* Fonction FN */
/******************************************************************/
functionFN: // INFO: functionFN
stp x1,lr,[sp,-16]! // save registres
ldr x4,qAdrqTabN3
ldr x3,[x4,x12,lsl #3]
ldr x5,qAdrqTabN0 // load position empty box
ldr x6,[x5,x12,lsl #3]
cmp x6,#15 // last box
bne 2f
cmp x3,#'R'
bne 11f
mov x0,#CONST_G
bl functionFZ
b 100f
11:
cmp x3,#'D'
bne 12f
mov x0,#CONST_L
bl functionFZ
b 100f
12:
mov x0,#CONST_G + CONST_L
bl functionFZ
b 100f
2:
cmp x6,#12
bne 3f
cmp x3,#'L'
bne 21f
mov x0,#CONST_G
bl functionFZ
b 100f
21:
cmp x3,#'D'
bne 22f
mov x0,#CONST_E
bl functionFZ
b 100f
22:
mov x0,#CONST_E + CONST_G
bl functionFZ
b 100f
3:
cmp x6,#13
beq 30f
cmp x6,#14
bne 4f
30:
cmp x3,#'L'
bne 31f
mov x0,#CONST_G + CONST_L
bl functionFZ
b 100f
31:
cmp x3,#'R'
bne 32f
mov x0,#CONST_G + CONST_E
bl functionFZ
b 100f
32:
cmp x3,#'D'
bne 33f
mov x0,#CONST_E + CONST_L
bl functionFZ
b 100f
33:
mov x0,#CONST_L + CONST_E + CONST_G
bl functionFZ
b 100f
4:
cmp x6,#3
bne 5f
cmp x3,#'R'
bne 41f
mov x0,#CONST_I
bl functionFZ
b 100f
41:
cmp x3,#'U'
bne 42f
mov x0,#CONST_L
bl functionFZ
b 100f
42:
mov x0,#CONST_I + CONST_L
bl functionFZ
b 100f
5:
cmp x6,#0
bne 6f
cmp x3,#'L'
bne 51f
mov x0,#CONST_I
bl functionFZ
b 100f
51:
cmp x3,#'U'
bne 52f
mov x0,#CONST_E
bl functionFZ
b 100f
52:
mov x0,#CONST_I + CONST_E
bl functionFZ
b 100f
6:
cmp x6,#1
beq 60f
cmp x6,#2
bne 7f
60:
cmp x3,#'L'
bne 61f
mov x0,#CONST_I + CONST_L
bl functionFZ
b 100f
61:
cmp x3,#'R'
bne 62f
mov x0,#CONST_E + CONST_I
bl functionFZ
b 100f
62:
cmp x3,#'U'
bne 63f
mov x0,#CONST_E + CONST_L
bl functionFZ
b 100f
63:
mov x0,#CONST_I + CONST_E + CONST_L
bl functionFZ
b 100f
7:
cmp x6,#7
beq 70f
cmp x6,#11
bne 8f
70:
cmp x3,#'R'
bne 71f
mov x0,#CONST_I + CONST_G
bl functionFZ
b 100f
71:
cmp x3,#'U'
bne 72f
mov x0,#CONST_G + CONST_L
bl functionFZ
b 100f
72:
cmp x3,#'D'
bne 73f
mov x0,#CONST_I + CONST_L
bl functionFZ
b 100f
73:
mov x0,#CONST_I + CONST_G + CONST_L
bl functionFZ
b 100f
8:
cmp x6,#4
beq 80f
cmp x6,#8
bne 9f
80:
cmp x3,#'D'
bne 81f
mov x0,#CONST_I + CONST_E
bl functionFZ
b 100f
81:
cmp x3,#'U'
bne 82f
mov x0,#CONST_G + CONST_E
bl functionFZ
b 100f
82:
cmp x3,#'L'
bne 83f
mov x0,#CONST_I + CONST_G
bl functionFZ
b 100f
83:
mov x0,#CONST_G + CONST_E + CONST_I
bl functionFZ
b 100f
9:
cmp x3,#'D'
bne 91f
mov x0,#CONST_I + CONST_E + CONST_L
bl functionFZ
b 100f
91:
cmp x3,#'L'
bne 92f
mov x0,#CONST_I + CONST_G + CONST_L
bl functionFZ
b 100f
92:
cmp x3,#'R'
bne 93f
mov x0,#CONST_I + CONST_G + CONST_E
bl functionFZ
b 100f
93:
cmp x3,#'U'
bne 94f
mov x0,#CONST_G + CONST_E + CONST_L
bl functionFZ
b 100f
94:
mov x0,#CONST_G + CONST_L + CONST_I + CONST_E
bl functionFZ
b 100f
99: // error
ldr x0,qAdrszMessErreur
bl affichageMess
100:
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* function FZ */
/* */
/***************************************************************/
/* x0 contains variable w */
functionFZ: // INFO: functionFZ
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
mov x2,x0
and x1,x2,#CONST_I
cmp x1,#0
ble 1f
bl functionFI
bl functionFY
cmp x0,#TRUE
beq 100f
sub x12,x12,#1 // variable n
1:
ands x1,x2,#CONST_G
ble 2f
bl functionFG
bl functionFY
cmp x0,#TRUE
beq 100f
sub x12,x12,#1 // variable n
2:
ands x1,x2,#CONST_E
ble 3f
bl functionFE
bl functionFY
cmp x0,#TRUE
beq 100f
sub x12,x12,#1 // variable n
3:
ands x1,x2,#CONST_L
ble 4f
bl functionFL
bl functionFY
cmp x0,#TRUE
beq 100f
sub x12,x12,#1 // variable n
4:
mov x0,#FALSE
100:
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* function FY */
/******************************************************************/
functionFY: // INFO: functionFY
stp x1,lr,[sp,-16]! // save registres
ldr x1,qAdrqTabN2
ldr x0,[x1,x12,lsl #3]
bl gameOK // game OK ?
cmp x0,#TRUE
beq 100f
ldr x1,qAdrqTabN4
ldr x0,[x1,x12,lsl #3]
cmp x0,x10
bgt 1f
bl functionFN
b 100f
1:
mov x0,#FALSE
100:
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* the empty box is down */
/******************************************************************/
functionFI: // INFO: functionFI
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
ldr x0,qAdrqTabN0
ldr x1,[x0,x12,lsl #3] // empty box
add x2,x1,#4
ldr x3,[x9,x12,lsl #3] // load game current
ldrb w4,[x3,x2] // load box down empty box
add x5,x12,#1 // n+1
add x8,x1,#4 // new position empty case
str x8,[x0,x5,lsl #3] // store new position empty case
ldr x6,qAdrqTabN3
mov x7,#'D' // down
str x7,[x6,x5,lsl #3] // store move
ldr x6,qAdrqTabN4
ldr x7,[x6,x12,lsl #3]
str x7,[x6,x5,lsl #3] // N4 (n+1) = n4(n)
mov x0,x3
bl createGame // create copy game
ldrb w3,[x0,x1] // and inversion box
ldrb w8,[x0,x2]
strb w8,[x0,x1]
strb w3,[x0,x2]
str x0,[x9,x5,lsl #3] // store new game in table
lsr x1,x1,#2 // line position empty case = N°/ 4
ldr x0,qAdrqTabNr
ldr x2,[x0,x4,lsl #3] // load N° line box moved
cmp x2,x1 // compare ????
ble 1f
add x7,x7,#1 // and increment ????
str x7,[x6,x5,lsl #3]
1:
add x12,x12,#1 // increment N
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
qAdrqTabNr: .quad qTabNr
qAdrqTabNc: .quad qTabNc
/******************************************************************/
/* empty case UP see explain in english in function FI */
/******************************************************************/
functionFG: // INFO: functionFG
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
ldr x0,qAdrqTabN0
ldr x1,[x0,x12,lsl #3] // case vide
sub x2,x1,#4 // position case au dessus
ldr x3,[x9,x12,lsl #3] // extrait jeu courant
ldrb w4,[x3,x2] // extrait le contenu case au dessus
add x5,x12,#1 // N+1 = N
sub x8,x1,#4 // nouvelle position case vide
str x8,[x0,x5,lsl #3] // et on la stocke
ldr x6,qAdrqTabN3
mov x7,#'U' // puis on stocke le code mouvement
str x7,[x6,x5,lsl #3]
ldr x6,qAdrqTabN4
ldr x7,[x6,x12,lsl #3]
str x7,[x6,x5,lsl #3] // N4 (N+1) = N4 (N)
mov x0,x3 // jeu courant
bl createGame // création nouveau jeu
ldrb w3,[x0,x1] // et echange les 2 cases
ldrb w8,[x0,x2]
strb w8,[x0,x1]
strb w3,[x0,x2]
str x0,[x9,x5,lsl #3] // stocke la nouvelle situation
lsr x1,x1,#2 // ligne case vide = position /4
ldr x0,qAdrqTabNr
ldr x2,[x0,x4,lsl #3] // extrait table à la position case
cmp x2,x1 // et comparaison ???
bge 1f
add x7,x7,#1 // puis increment N4 de 1 ???
str x7,[x6,x5,lsl #3]
1:
add x12,x12,#1 // increment de N
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* empty case go right see explain finction FI ou FG en français */
/******************************************************************/
functionFE: // INFO: functionFE
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
ldr x0,qAdrqTabN0
ldr x1,[x0,x12,lsl #3]
add x2,x1,#1
ldr x3,[x9,x12,lsl #3]
ldrb w4,[x3,x2] // extrait le contenu case
add x5,x12,#1
add x8,x1,#1
str x8,[x0,x5,lsl #3] // nouvelle case vide
ldr x6,qAdrqTabN3
mov x7,#'R'
str x7,[x6,x5,lsl #3] // mouvement
ldr x6,qAdrqTabN4
ldr x7,[x6,x12,lsl #3]
str x7,[x6,x5,lsl #3] // N4 ??
mov x0,x3
bl createGame
ldrb w3,[x0,x1] // exchange two boxes
ldrb w8,[x0,x2]
strb w8,[x0,x1]
strb w3,[x0,x2]
str x0,[x9,x5,lsl #3] // stocke la nouvelle situation
lsr x3,x1,#2
sub x1,x1,x3,lsl #2
ldr x0,qAdrqTabNc
ldr x2,[x0,x4,lsl #3] // extrait table à la position case
cmp x2,x1
ble 1f
add x7,x7,#1
str x7,[x6,x5,lsl #3]
1:
add x12,x12,#1
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* empty box go left see explain function FI ou FG en français */
/******************************************************************/
functionFL: // INFO: functionFL
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
ldr x0,qAdrqTabN0
ldr x1,[x0,x12,lsl #3] // case vide
sub x2,x1,#1
ldr x3,[x9,x12,lsl #3] // extrait jeu courant
ldrb w4,[x3,x2] // extrait le contenu case
add x5,x12,#1
sub x8,x1,#1
str x8,[x0,x5,lsl #3] // nouvelle case vide
ldr x6,qAdrqTabN3
mov x7,#'L'
str x7,[x6,x5,lsl #3] // mouvement
ldr x6,qAdrqTabN4
ldr x7,[x6,x12,lsl #3]
str x7,[x6,x5,lsl #3] // N4 ??
mov x0,x3
bl createGame
ldrb w3,[x0,x1] // exchange two boxes
ldrb w8,[x0,x2]
strb w8,[x0,x1]
strb w3,[x0,x2]
str x0,[x9,x5,lsl #3] // stocke la nouvelle situation
lsr x3,x1,#2
sub x1,x1,x3,lsl #2 // compute remainder
ldr x0,qAdrqTabNc
ldr x2,[x0,x4,lsl #3] // extrait table colonne à la position case
cmp x2,x1
bge 1f
add x7,x7,#1
str x7,[x6,x5,lsl #3]
1:
add x12,x12,#1
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* create new Game */
/******************************************************************/
/* x0 contains box address */
/* x0 return address new game */
createGame: // INFO: createGame
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
mov x4,x0 // save value
mov x0,#0 // allocation place heap
mov x8,BRK // call system 'brk'
svc #0
cmp x0,#-1 // allocation error
beq 99f
mov x5,x0 // save address heap for output string
add x0,x0,#SIZE * SIZE // reservation place one element
mov x8,BRK // call system 'brk'
svc #0
cmp x0,#-1 // allocation error
beq 99f
mov x2,#0
1: // loop copy boxes
ldrb w3,[x4,x2]
strb w3,[x5,x2]
add x2,x2,#1
cmp x2,#NBBOX
blt 1b
add x11,x11,#1
mov x0,x5
b 100f
99: // error
ldr x0,qAdrszMessErreur
bl affichageMess
100:
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* read file */
/******************************************************************/
/* x0 contains address stack begin */
traitFic: // INFO: traitFic
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,fp,[sp,-16]! // save registres
mov fp,x0 // fp <- start address
ldr x4,[fp] // number of Command line arguments
cmp x4,#1
ble 99f
add x5,fp,#16 // second parameter address
ldr x5,[x5]
ldr x0,qAdrqAdrFicName
str x5,[x0]
ldr x0,qAdrszMessTitre
bl affichageMess // display string
mov x0,x5
bl affichageMess
ldr x0,qAdrszCarriageReturn
bl affichageMess // display carriage return
mov x0,AT_FDCWD
mov x1,x5 // file name
mov x2,#O_RDWR // flags
mov x3,#0 // mode
mov x8, #OPEN // call system OPEN
svc 0
cmp x0,#0 // error ?
ble 99f
mov x7,x0 // File Descriptor
ldr x1,qAdrsBuffer // buffer address
mov x2,#TAILLEBUFFER // buffer size
mov x8,#READ // read file
svc #0
cmp x0,#0 // error ?
blt 99f
// extraction datas
ldr x1,qAdrsBuffer // buffer address
add x1,x1,x0
mov x0,#0 // store zéro final
strb w0,[x1]
ldr x0,qAdrtbBox // game box address
ldr x1,qAdrsBuffer // buffer address
bl extracDatas
// close file
mov x0,x7
mov x8, #CLOSE
svc 0
mov x0,#0
b 100f
99: // error
ldr x0,qAdrszMessErreur // error message
bl affichageMess
mov x0,#-1
100:
ldp x8,fp,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
qAdrqAdrFicName: .quad qAdrFicName
qAdrszMessTitre: .quad szMessTitre
qAdrsBuffer: .quad sBuffer
/******************************************************************/
/* extrac digit file buffer */
/******************************************************************/
/* x0 contains boxs address */
/* x1 contains buffer address */
extracDatas: // INFO: extracDatas
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
mov x7,x0
mov x6,x1
mov x2,#0 // string buffer indice
mov x4,x1 // start digit ascii
mov x5,#0 // box index
1:
ldrb w3,[x6,x2]
cmp x3,#0 // datas end ?
beq 4f
cmp x3,#0xA // line end ?
beq 2f
cmp x3,#',' // box end ?
beq 3f
add x2,x2,#1
b 1b
2:
mov x3,#0
strb w3,[x6,x2] // zero final
add x3,x2,#1 // next character
ldrb w3,[x6,x3]
cmp x3,#0xD // line return
bne 21f
add x2,x2,#2 // yes
b 4f
21:
add x2,x2,#1
b 4f
3:
mov x3,#0 // zero final
strb w3,[x6,x2]
add x2,x2,#1
4:
mov x0,x4 // conversion character ascii in integer
bl conversionAtoD
strb w0,[x7,x5] // and store value on 1 byte box
cmp x0,#0 // empty box ?
bne 5f
ldr x0,qAdrqTabN0
str x5,[x0] // empty box in item zéro
5:
add x5,x5,#1 // increment counter boxes
cmp x5,#NBBOX // number box = maxi ?
bge 100f
add x4,x6,x2 // new start address digit ascii
b 1b
100:
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* control of the game solution */
/******************************************************************/
/* x0 contains boxs address */
/* x0 returns 0 if not possible */
/* x0 returns 1 if possible */
controlSolution: // INFO: controlSolution
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
stp x6,x7,[sp,-16]! // save registres
stp x8,x9,[sp,-16]! // save registres
mov x5,x0
ldr x8,qAdrqTabN0
ldr x8,[x8] // empty box
//mov x7,#0
cmp x8,#1
cset x7,eq
beq 1f
cmp x8,#3
cset x7,eq
beq 1f
cmp x8,#4
cset x7,eq
beq 1f
cmp x8,#6
cset x7,eq
beq 1f
cmp x8,#9
cset x7,eq
beq 1f
cmp x8,#11
cset x7,eq
beq 1f
cmp x8,#12
cset x7,eq
beq 1f
cmp x8,#14
cset x7,eq
1:
mov x9,NBBOX - 1
sub x6,x9,x8
add x7,x7,x6
// count permutations
mov x1,#-1
mov x6,#0
2:
add x1,x1,#1
cmp x1,#NBBOX
bge 80f
cmp x1,x8
beq 2b
ldrb w3,[x5,x1]
mov x2,x1
3:
add x2,x2,#1
cmp x2,#NBBOX
bge 2b
cmp x2,x8
beq 3b
ldrb w4,[x5,x2]
cmp x4,x3
cinc x6,x6,lt
b 3b
80:
add x6,x6,x7
tst x6,#1
cset x0,eq
100:
ldp x8,x9,[sp],16 // restaur des 2 registres
ldp x6,x7,[sp],16 // restaur des 2 registres
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* game Ok ? */
/******************************************************************/
/* x0 contains boxs address */
gameOK: // INFO: gameOK
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
mov x2,#0
ldrb w3,[x0,x2]
cmp x3,#0
bne 0f
mov x3,#0xF
0:
add x2,x2,#1
1:
ldrb w4,[x0,x2]
cmp x4,#0
bne 11f
mov x3,#0xF
11:
cmp x4,x3
ble 99f
mov x3,x4
add x2,x2,#1
cmp x2,#NBBOX -2
ble 1b
mov x0,#TRUE // game Ok
b 100f
99:
mov x0,#FALSE // game not Ok
100:
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
/******************************************************************/
/* display game */
/******************************************************************/
/* x0 contains boxs address */
displayGame: // INFO: displayGame
stp x1,lr,[sp,-16]! // save registres
stp x2,x3,[sp,-16]! // save registres
stp x4,x5,[sp,-16]! // save registres
mov x4,x0
ldr x0,qAdrszMessTitre
bl affichageMess // display titre
ldr x0,qAdrqAdrFicName
ldr x0,[x0]
bl affichageMess // display string
ldr x0,qAdrszCarriageReturn
bl affichageMess // display line return
mov x2,#0
ldr x1,qAdrsMessValeur
1:
ldrb w0,[x4,x2]
cmp x0,#0
beq 3f
bl conversion10 // call conversion decimal
cmp x0,1
bne 2f
mov x0,#0x002020
str w0,[x1,#1] // zéro final
b 4f
2:
mov x0,#0x20
str w0,[x1,#2] // zéro final
b 4f
3:
ldr x0,iSpaces // store spaces to empty case
str w0,[x1]
4:
ldr x0,qAdrsMessResult
bl affichageMess // display message
add x0,x2,#1
tst x0,#0b11
bne 5f
ldr x0,qAdrszCarriageReturn
bl affichageMess // display message
5:
add x2,x2,#1
cmp x2,#NBBOX - 1
ble 1b
ldr x0,qAdrszCarriageReturn
bl affichageMess // display line return
100:
ldp x4,x5,[sp],16 // restaur des 2 registres
ldp x2,x3,[sp],16 // restaur des 2 registres
ldp x1,lr,[sp],16 // restaur des 2 registres
ret
iSpaces: .quad 0x00202020 // spaces
qAdrszCarriageReturn: .quad szCarriageReturn
qAdrsMessValeur: .quad sMessValeur
qAdrsMessResult: .quad sMessResult
/********************************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"File name : casR1.txt
File name : casR1.txt
15 14 1 6
9 11 4 12
10 7 3
13 8 5 2
File name : casR1.txt
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15
Solution in 52 moves :
RRRULDDLUUULDRURDDDRULLULURRRDDLDLUURDDLULURRULDRDRD
Ada
Decoding actually...
with Ada.Text_IO;
procedure Puzzle_15 is
type Direction is (Up, Down, Left, Right);
type Row_Type is range 0 .. 3;
type Col_Type is range 0 .. 3;
type Tile_Type is range 0 .. 15;
To_Col : constant array (Tile_Type) of Col_Type :=
(3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2);
To_Row : constant array (Tile_Type) of Row_Type :=
(3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3);
type Board_Type is array (Row_Type, Col_Type) of Tile_Type;
Solved_Board : constant Board_Type :=
((1, 2, 3, 4),
(5, 6, 7, 8),
(9, 10, 11, 12),
(13, 14, 15, 0));
type Try_Type is
record
Board : Board_Type;
Move : Direction;
Cost : Integer;
Row : Row_Type;
Col : Col_Type;
end record;
Stack : array (0 .. 100) of Try_Type;
Top : Natural := 0;
Iteration_Count : Natural := 0;
procedure Move_Down is
Board : Board_Type := Stack (Top).Board;
Row : constant Row_Type := Stack (Top).Row;
Col : constant Col_Type := Stack (Top).Col;
Tile : constant Tile_Type := Board (Row + 1, Col);
Penalty : constant Integer :=
(if To_Row (Tile) <= Row then 0 else 1);
begin
Board (Row, Col) := Tile;
Board (Row + 1, Col) := 0;
Stack (Top + 1) := (Board => Board,
Move => Down,
Row => Row + 1,
Col => Col,
Cost => Stack (Top).Cost + Penalty);
end Move_Down;
procedure Move_Up is
Board : Board_Type := Stack (Top).Board;
Row : constant Row_Type := Stack (Top).Row;
Col : constant Col_Type := Stack (Top).Col;
Tile : constant Tile_Type := Board (Row - 1, Col);
Penalty : constant Integer :=
(if To_Row (Tile) >= Row then 0 else 1);
begin
Board (Row, Col) := Tile;
Board (Row - 1, Col) := 0;
Stack (Top + 1) := (Board => Board,
Move => Up,
Row => Row - 1,
Col => Col,
Cost => Stack (Top).Cost + Penalty);
end Move_Up;
procedure Move_Left is
Board : Board_Type := Stack (Top).Board;
Row : constant Row_Type := Stack (Top).Row;
Col : constant Col_Type := Stack (Top).Col;
Tile : constant Tile_Type := Board (Row, Col - 1);
Penalty : constant Integer :=
(if To_Col (Tile) >= Col then 0 else 1);
begin
Board (Row, Col) := Tile;
Board (Row, Col - 1) := 0;
Stack (Top + 1) := (Board => Board,
Move => Left,
Row => Row,
Col => Col - 1,
Cost => Stack (Top).Cost + Penalty);
end Move_Left;
procedure Move_Right is
Board : Board_Type := Stack (Top).Board;
Row : constant Row_Type := Stack (Top).Row;
Col : constant Col_Type := Stack (Top).Col;
Tile : constant Tile_Type := Board (Row, Col + 1);
Penalty : constant Integer :=
(if To_Col (Tile) <= Col then 0 else 1);
begin
Board (Row, Col) := Tile;
Board (Row, Col + 1) := 0;
Stack (Top + 1) := (Board => Board,
Move => Right,
Row => Row,
Col => Col + 1,
Cost => Stack (Top).Cost + Penalty);
end Move_Right;
function Is_Solution return Boolean;
function Test_Moves return Boolean is
begin
if
Stack (Top).Move /= Down and then
Stack (Top).Row /= Row_Type'First
then
Move_Up;
Top := Top + 1;
if Is_Solution then return True; end if;
Top := Top - 1;
end if;
if
Stack (Top).Move /= Up and then
Stack (Top).Row /= Row_Type'Last
then
Move_Down;
Top := Top + 1;
if Is_Solution then return True; end if;
Top := Top - 1;
end if;
if
Stack (Top).Move /= Right and then
Stack (Top).Col /= Col_Type'First
then
Move_Left;
Top := Top + 1;
if Is_Solution then return True; end if;
Top := Top - 1;
end if;
if
Stack (Top).Move /= Left and then
Stack (Top).Col /= Col_Type'Last
then
Move_Right;
Top := Top + 1;
if Is_Solution then return True; end if;
Top := Top - 1;
end if;
return False;
end Test_Moves;
function Is_Solution return Boolean is
use Ada.Text_IO;
begin
if Stack (Top).Board = Solved_Board then
Put ("Solved in " & Top'Image & " moves: ");
for R in 1 .. Top loop
Put (String'(Stack (R).Move'Image) (1));
end loop;
New_Line;
return True;
end if;
if Stack (Top).Cost <= Iteration_Count then
return Test_Moves;
end if;
return False;
end Is_Solution;
procedure Solve (Row : in Row_Type;
Col : in Col_Type;
Board : in Board_Type) is
begin
pragma Assert (Board (Row, Col) = 0);
Top := 0;
Iteration_Count := 0;
Stack (Top) := (Board => Board,
Row => Row,
Col => Col,
Move => Down,
Cost => 0);
while not Is_Solution loop
Iteration_Count := Iteration_Count + 1;
end loop;
end Solve;
begin
Solve (Row => 2,
Col => 0,
Board => ((15, 14, 1, 6),
(9, 11, 4, 12),
(0, 10, 7, 3),
(13, 8, 5, 2)));
end Puzzle_15;
- Output:
Solved in 52 moves: RRRULDDLUUULDRURDDDRULLULURRRDDLDLUURDDLULURRULDRDRD
ARM Assembly
/* ARM assembly Raspberry PI */
/* program puzzle15solver.s */
/* my first other program find à solution in 134 moves !!! */
/* this second program is a adaptation algorithme C++ and go rosetta code */
/* thanck for the creators */
/* 1 byte by box on game board */
/* create a file with nano */
/* 15, 2, 3, 4
5, 6, 7, 1
9, 10, 8, 11
13, 14, 12, 0 */
/* Run this programm : puzzle15solver <file name> */
/* wait several minutes for résult */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes */
/************************************/
.include "../constantes.inc"
.equ STDIN, 0 @ Linux input console
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ READ, 3 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ OPEN, 5 @ Linux syscall
.equ CLOSE, 6 @ Linux syscall
.equ TRUE, 1
.equ FALSE, 0
.equ O_RDWR, 0x0002 @ open for reading and writing
.equ SIZE, 4
.equ NBBOX, SIZE * SIZE
.equ TAILLEBUFFER, 100
.equ NBMAXIELEMENTS, 100
.equ CONST_I, 1
.equ CONST_G, 8
.equ CONST_E, 2
.equ CONST_L, 4
/*********************************/
/* Initialized data */
/*********************************/
.data
szMessTitre: .asciz "Nom du fichier : "
sMessResult: .ascii " "
sMessValeur: .fill 11, 1, ' ' @ size => 11
szCarriageReturn: .asciz "\n"
szMessCounterSolution: .asciz "Solution in @ moves : \n"
//szMessMoveError: .asciz "Huh... Impossible move !!!!\n"
szMessErreur: .asciz "Error detected.\n"
szMessImpossible: .asciz "!!! Impossible solution !!!\n"
szMessErrBuffer: .asciz "buffer size too less !!"
szMessSpaces: .asciz " "
iTabNr: .int 3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3
iTabNc: .int 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
.align 4
sZoneConv: .skip 24
iAdrHeap: .skip 4
ibox: .skip SIZE * SIZE @ game boxes
iAdrFicName: .skip 4
iTabN0: .skip 4 * NBMAXIELEMENTS @ empty box
iTabN3: .skip 4 * NBMAXIELEMENTS @ moves
iTabN4: .skip 4 * NBMAXIELEMENTS @ ????
iTabN2: .skip 4 * NBMAXIELEMENTS @ table game address
sBuffer: .skip TAILLEBUFFER
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ INFO: main
mov r0,sp @ stack address for load parameter
bl traitFic @ read file and store value in array
cmp r0,#-1
beq 100f @ error ?
ldr r0,iAdribox
bl displayGame @ display array game
ldr r0,iAdribox @ control if solution exists
bl controlSolution
cmp r0,#TRUE
beq 1f
ldr r0,iAdrszMessImpossible @ no solution !!!
bl affichageMess
b 100f
1:
ldr r0,iAdribox
ldr r9,iAdriTabN2
str r0,[r9] @ N2 address global
mov r10,#0 @ variable _n global
mov r12,#0 @ variable n global
bl searchSolution
cmp r0,#TRUE
bne 100f @ no solution ?
ldr r3,iAdriTabN2
ldr r0,[r3,r12,lsl #2] @ visual solution control
bl displayGame
mov r0,r12 @ move counter
ldr r1,iAdrsZoneConv
bl conversion10 @ conversion counter
mov r2,#0
strb r2,[r1,r0] @ and display
ldr r0,iAdrszMessCounterSolution
bl strInsertAtCharInc
ldr r1,iAdrsZoneConv
bl affichageMess
ldr r5,iAdriTabN3
ldr r3,iAdrsBuffer
mov r2,#1
mov r4,#0
2: @ loop solution display
ldrb r1,[r5,r2,lsl #2]
cmp r2,#TAILLEBUFFER
bge 99f
strb r1,[r3,r4]
add r4,r4,#1
add r2,r2,#1
cmp r2,r12
ble 2b
mov r1,#0
str r1,[r3,r4] @ zéro final
mov r0,r3
bl affichageMess
ldr r0,iAdrszCarriageReturn
bl affichageMess
b 100f
99:
ldr r0,iAdrszMessErrBuffer
bl affichageMess
100: @ standard end of the program
mov r0, #0 @ return code
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdribox: .int ibox
iAdriTabN0: .int iTabN0
iAdriTabN2: .int iTabN2
iAdriTabN3: .int iTabN3
iAdriTabN4: .int iTabN4
iAdrszMessCounterSolution: .int szMessCounterSolution
iAdrszMessImpossible: .int szMessImpossible
iAdrszMessErrBuffer: .int szMessErrBuffer
iAdrsZoneConv: .int sZoneConv
/******************************************************************/
/* search Solution */
/******************************************************************/
searchSolution: @ INFO: searchSolution
push {r1-r8,lr} @ save registers
@ address allocation place on the heap
mov r0,#0 @ allocation place heap
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
beq 99f
ldr r1,iAdriAdrHeap
str r0,[r1] @ store heap address
bl functionFN
ldr r3,iAdriTabN2
ldr r0,[r3,r12,lsl #2] @ last current game
bl gameOK @ it is Ok ?
cmp r0,#TRUE
beq 100f @ yes --> end
ldr r1,iAdriAdrHeap @ free up resources
ldr r0,[r1] @ restaur start address heap
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
beq 99f
add r10,r10,#1 @ _n
mov r12,#0 @ n
bl searchSolution @ next recursif call
b 100f
99:
ldr r0,iAdrszMessErreur
bl affichageMess
100:
pop {r1-r8,lr} @ restaur registers
bx lr @return
iAdrszMessErreur: .int szMessErreur
iAdriAdrHeap: .int iAdrHeap
/******************************************************************/
/* Fonction FN */
/******************************************************************/
functionFN: @ INFO: functionFN
push {lr} @ save register
ldr r4,iAdriTabN3
ldr r3,[r4,r12,lsl #2]
ldr r5,iAdriTabN0 @ load position empty box
ldr r6,[r5,r12,lsl #2]
cmp r6,#15 @ last box
bne 2f
cmp r3,#'R'
bne 11f
mov r0,#CONST_G
bl functionFZ
b 100f
11:
cmp r3,#'D'
bne 12f
mov r0,#CONST_L
bl functionFZ
b 100f
12:
mov r0,#CONST_G + CONST_L
bl functionFZ
b 100f
2:
cmp r6,#12
bne 3f
cmp r3,#'L'
bne 21f
mov r0,#CONST_G
bl functionFZ
b 100f
21:
cmp r3,#'D'
bne 22f
mov r0,#CONST_E
bl functionFZ
b 100f
22:
mov r0,#CONST_E + CONST_G
bl functionFZ
b 100f
3:
cmp r6,#13
beq 30f
cmp r6,#14
bne 4f
30:
cmp r3,#'L'
bne 31f
mov r0,#CONST_G + CONST_L
bl functionFZ
b 100f
31:
cmp r3,#'R'
bne 32f
mov r0,#CONST_G + CONST_E
bl functionFZ
b 100f
32:
cmp r3,#'D'
bne 33f
mov r0,#CONST_E + CONST_L
bl functionFZ
b 100f
33:
mov r0,#CONST_L + CONST_E + CONST_G
bl functionFZ
b 100f
4:
cmp r6,#3
bne 5f
cmp r3,#'R'
bne 41f
mov r0,#CONST_I
bl functionFZ
b 100f
41:
cmp r3,#'U'
bne 42f
mov r0,#CONST_L
bl functionFZ
b 100f
42:
mov r0,#CONST_I + CONST_L
bl functionFZ
b 100f
5:
cmp r6,#0
bne 6f
cmp r3,#'L'
bne 51f
mov r0,#CONST_I
bl functionFZ
b 100f
51:
cmp r3,#'U'
bne 52f
mov r0,#CONST_E
bl functionFZ
b 100f
52:
mov r0,#CONST_I + CONST_E
bl functionFZ
b 100f
6:
cmp r6,#1
beq 60f
cmp r6,#2
bne 7f
60:
cmp r3,#'L'
bne 61f
mov r0,#CONST_I + CONST_L
bl functionFZ
b 100f
61:
cmp r3,#'R'
bne 62f
mov r0,#CONST_E + CONST_I
bl functionFZ
b 100f
62:
cmp r3,#'U'
bne 63f
mov r0,#CONST_E + CONST_L
bl functionFZ
b 100f
63:
mov r0,#CONST_I + CONST_E + CONST_L
bl functionFZ
b 100f
7:
cmp r6,#7
beq 70f
cmp r6,#11
bne 8f
70:
cmp r3,#'R'
bne 71f
mov r0,#CONST_I + CONST_G
bl functionFZ
b 100f
71:
cmp r3,#'U'
bne 72f
mov r0,#CONST_G + CONST_L
bl functionFZ
b 100f
72:
cmp r3,#'D'
bne 73f
mov r0,#CONST_I + CONST_L
bl functionFZ
b 100f
73:
mov r0,#CONST_I + CONST_G + CONST_L
bl functionFZ
b 100f
8:
cmp r6,#4
beq 80f
cmp r6,#8
bne 9f
80:
cmp r3,#'D'
bne 81f
mov r0,#CONST_I + CONST_E
bl functionFZ
b 100f
81:
cmp r3,#'U'
bne 82f
mov r0,#CONST_G + CONST_E
bl functionFZ
b 100f
82:
cmp r3,#'L'
bne 83f
mov r0,#CONST_I + CONST_G
bl functionFZ
b 100f
83:
mov r0,#CONST_G + CONST_E + CONST_I
bl functionFZ
b 100f
9:
cmp r3,#'D'
bne 91f
mov r0,#CONST_I + CONST_E + CONST_L
bl functionFZ
b 100f
91:
cmp r3,#'L'
bne 92f
mov r0,#CONST_I + CONST_G + CONST_L
bl functionFZ
b 100f
92:
cmp r3,#'R'
bne 93f
mov r0,#CONST_I + CONST_G + CONST_E
bl functionFZ
b 100f
93:
cmp r3,#'U'
bne 94f
mov r0,#CONST_G + CONST_E + CONST_L
bl functionFZ
b 100f
94:
mov r0,#CONST_G + CONST_L + CONST_I + CONST_E
bl functionFZ
b 100f
99: @ error
ldr r0,iAdrszMessErreur
bl affichageMess
100:
pop {lr} @ restaur registers
bx lr @return
/******************************************************************/
/* function FZ */
/* */
/***************************************************************/
/* r0 contains variable w */
functionFZ: @ INFO: functionFZ
push {r1,r2,lr} @ save registers
mov r2,r0
and r1,r2,#CONST_I
cmp r1,#0
ble 1f
bl functionFI
bl functionFY
cmp r0,#TRUE
beq 100f
sub r12,r12,#1 @ variable n
1:
ands r1,r2,#CONST_G
ble 2f
bl functionFG
bl functionFY
cmp r0,#TRUE
beq 100f
sub r12,r12,#1 @ variable n
2:
ands r1,r2,#CONST_E
ble 3f
bl functionFE
bl functionFY
cmp r0,#TRUE
beq 100f
sub r12,r12,#1 @ variable n
3:
ands r1,r2,#CONST_L
ble 4f
bl functionFL
bl functionFY
cmp r0,#TRUE
beq 100f
sub r12,r12,#1 @ variable n
4:
mov r0,#FALSE
100:
pop {r1,r2,lr} @ restaur registers
bx lr @return
/******************************************************************/
/* function FY */
/******************************************************************/
functionFY: @ INFO: functionFY
push {lr} @ save registers
ldr r1,iAdriTabN2
ldr r0,[r1,r12,lsl #2]
bl gameOK @ game OK ?
cmp r0,#TRUE
beq 100f
ldr r1,iAdriTabN4
ldr r0,[r1,r12,lsl #2]
cmp r0,r10
bgt 1f
bl functionFN
b 100f
1:
mov r0,#FALSE
100:
pop {lr} @ restaur registers
bx lr @return
/******************************************************************/
/* the empty box is down */
/******************************************************************/
functionFI: @ INFO: functionFI
push {r0-r8,lr} @ save registers
ldr r0,iAdriTabN0
ldr r1,[r0,r12,lsl #2] @ empty box
add r2,r1,#4
ldr r3,[r9,r12,lsl #2] @ load game current
ldrb r4,[r3,r2] @ load box down empty box
add r5,r12,#1 @ n+1
add r8,r1,#4 @ new position empty case
str r8,[r0,r5,lsl #2] @ store new position empty case
ldr r6,iAdriTabN3
mov r7,#'D' @ down
str r7,[r6,r5,lsl #2] @ store move
ldr r6,iAdriTabN4
ldr r7,[r6,r12,lsl #2]
str r7,[r6,r5,lsl #2] @ N4 (n+1) = n4(n)
mov r0,r3
bl createGame @ create copy game
ldrb r3,[r0,r1] @ and inversion box
ldrb r8,[r0,r2]
strb r8,[r0,r1]
strb r3,[r0,r2]
str r0,[r9,r5,lsl #2] @ store new game in table
lsr r1,r1,#2 @ line position empty case = N°/ 4
ldr r0,iAdriTabNr
ldr r2,[r0,r4,lsl #2] @ load N° line box moved
cmp r2,r1 @ compare ????
ble 1f
add r7,r7,#1 @ and increment ????
str r7,[r6,r5,lsl #2]
1:
add r12,r12,#1 @ increment N
pop {r0-r8,lr}
bx lr @return
iAdriTabNr: .int iTabNr
iAdriTabNc: .int iTabNc
/******************************************************************/
/* empty case UP see explain in english in function FI */
/******************************************************************/
functionFG: @ INFO: functionFG
push {r0-r8,lr} @ save registers
ldr r0,iAdriTabN0
ldr r1,[r0,r12,lsl #2] @ case vide
sub r2,r1,#4 @ position case au dessus
ldr r3,[r9,r12,lsl #2] @ extrait jeu courant
ldrb r4,[r3,r2] @ extrait le contenu case au dessus
add r5,r12,#1 @ N+1 = N
sub r8,r1,#4 @ nouvelle position case vide
str r8,[r0,r5,lsl #2] @ et on la stocke
ldr r6,iAdriTabN3
mov r7,#'U' @ puis on stocke le code mouvement
str r7,[r6,r5,lsl #2]
ldr r6,iAdriTabN4
ldr r7,[r6,r12,lsl #2]
str r7,[r6,r5,lsl #2] @ N4 (N+1) = N4 (N)
mov r0,r3 @ jeu courant
bl createGame @ création nouveau jeu
ldrb r3,[r0,r1] @ et echange les 2 cases
ldrb r8,[r0,r2]
strb r8,[r0,r1]
strb r3,[r0,r2]
str r0,[r9,r5,lsl #2] @ stocke la nouvelle situation
lsr r1,r1,#2 @ ligne case vide = position /4
ldr r0,iAdriTabNr
ldr r2,[r0,r4,lsl #2] @ extrait table à la position case
cmp r2,r1 @ et comparaison ???
bge 1f
add r7,r7,#1 @ puis increment N4 de 1 ???
str r7,[r6,r5,lsl #2]
1:
add r12,r12,#1 @ increment de N
pop {r0-r8,lr}
bx lr @return
/******************************************************************/
/* empty case go right see explain finction FI ou FG en français */
/******************************************************************/
functionFE: @ INFO: functionFE
push {r0-r8,lr} @ save registers
ldr r0,iAdriTabN0
ldr r1,[r0,r12,lsl #2]
add r2,r1,#1
ldr r3,[r9,r12,lsl #2]
ldrb r4,[r3,r2] @ extrait le contenu case
add r5,r12,#1
add r8,r1,#1
str r8,[r0,r5,lsl #2] @ nouvelle case vide
ldr r6,iAdriTabN3
mov r7,#'R'
str r7,[r6,r5,lsl #2] @ mouvement
ldr r6,iAdriTabN4
ldr r7,[r6,r12,lsl #2]
str r7,[r6,r5,lsl #2] @ N4 ??
mov r0,r3
bl createGame
ldrb r3,[r0,r1] @ exchange two boxes
ldrb r8,[r0,r2]
strb r8,[r0,r1]
strb r3,[r0,r2]
str r0,[r9,r5,lsl #2] @ stocke la nouvelle situation
lsr r3,r1,#2
sub r1,r1,r3,lsl #2
ldr r0,iAdriTabNc
ldr r2,[r0,r4,lsl #2] @ extrait table à la position case
cmp r2,r1
ble 1f
add r7,r7,#1
str r7,[r6,r5,lsl #2]
1:
add r12,r12,#1
pop {r0-r8,lr}
bx lr @return
/******************************************************************/
/* empty box go left see explain function FI ou FG en français */
/******************************************************************/
functionFL: @ INFO: functionFL
push {r0-r8,lr} @ save registers
ldr r0,iAdriTabN0
ldr r1,[r0,r12,lsl #2] @ case vide
sub r2,r1,#1
ldr r3,[r9,r12,lsl #2] @ extrait jeu courant
ldrb r4,[r3,r2] @ extrait le contenu case
add r5,r12,#1
sub r8,r1,#1
str r8,[r0,r5,lsl #2] @ nouvelle case vide
ldr r6,iAdriTabN3
mov r7,#'L'
str r7,[r6,r5,lsl #2] @ mouvement
ldr r6,iAdriTabN4
ldr r7,[r6,r12,lsl #2]
str r7,[r6,r5,lsl #2] @ N4 ??
mov r0,r3
bl createGame
ldrb r3,[r0,r1] @ exchange two boxes
ldrb r8,[r0,r2]
strb r8,[r0,r1]
strb r3,[r0,r2]
str r0,[r9,r5,lsl #2] @ stocke la nouvelle situation
lsr r3,r1,#2
sub r1,r1,r3,lsl #2 @ compute remainder
ldr r0,iAdriTabNc
ldr r2,[r0,r4,lsl #2] @ extrait table colonne à la position case
cmp r2,r1
bge 1f
add r7,r7,#1
str r7,[r6,r5,lsl #2]
1:
add r12,r12,#1
pop {r0-r8,lr}
bx lr @return
/******************************************************************/
/* create new Game */
/******************************************************************/
/* r0 contains box address */
/* r0 return address new game */
createGame: @ INFO: createGame
push {r1-r8,lr} @ save registers
mov r4,r0 @ save value
mov r0,#0 @ allocation place heap
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
beq 99f
mov r5,r0 @ save address heap for output string
add r0,#SIZE * SIZE @ reservation place one element
mov r7,#0x2D @ call system 'brk'
svc #0
cmp r0,#-1 @ allocation error
beq 99f
mov r2,#0
1: @ loop copy boxes
ldrb r3,[r4,r2]
strb r3,[r5,r2]
add r2,r2,#1
cmp r2,#NBBOX
blt 1b
add r11,r11,#1
mov r0,r5
b 100f
99: @ error
ldr r0,iAdrszMessErreur
bl affichageMess
100:
pop {r1-r8,lr} @ restaur registers
bx lr @return
/******************************************************************/
/* read file */
/******************************************************************/
/* r0 contains address stack begin */
traitFic: @ INFO: traitFic
push {r1-r8,fp,lr} @ save registers
mov fp,r0 @ fp <- start address
ldr r4,[fp] @ number of Command line arguments
cmp r4,#1
movle r0,#-1
ble 99f
add r5,fp,#8 @ second parameter address
ldr r5,[r5]
ldr r0,iAdriAdrFicName
str r5,[r0]
ldr r0,iAdrszMessTitre
bl affichageMess @ display string
mov r0,r5
bl affichageMess
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display carriage return
mov r0,r5 @ file name
mov r1,#O_RDWR @ flags
mov r2,#0 @ mode
mov r7, #OPEN @ call system OPEN
svc 0
cmp r0,#0 @ error ?
ble 99f
mov r8,r0 @ File Descriptor
ldr r1,iAdrsBuffer @ buffer address
mov r2,#TAILLEBUFFER @ buffer size
mov r7,#READ @ read file
svc #0
cmp r0,#0 @ error ?
blt 99f
@ extraction datas
ldr r1,iAdrsBuffer @ buffer address
add r1,r0
mov r0,#0 @ store zéro final
strb r0,[r1]
ldr r0,iAdribox @ game box address
ldr r1,iAdrsBuffer @ buffer address
bl extracDatas
@ close file
mov r0,r8
mov r7, #CLOSE
svc 0
mov r0,#0
b 100f
99: @ error
ldr r1,iAdrszMessErreur @ error message
bl displayError
mov r0,#-1
100:
pop {r1-r8,fp,lr} @ restaur registers
bx lr @return
iAdriAdrFicName: .int iAdrFicName
iAdrszMessTitre: .int szMessTitre
iAdrsBuffer: .int sBuffer
/******************************************************************/
/* extrac digit file buffer */
/******************************************************************/
/* r0 contains boxs address */
/* r1 contains buffer address */
extracDatas: @ INFO: extracDatas
push {r1-r8,lr} @ save registers
mov r7,r0
mov r6,r1
mov r2,#0 @ string buffer indice
mov r4,r1 @ start digit ascii
mov r5,#0 @ box index
1:
ldrb r3,[r6,r2]
cmp r3,#0
beq 4f @ end
cmp r3,#0xA
beq 2f
cmp r3,#','
beq 3f
add r2,#1
b 1b
2:
mov r3,#0
strb r3,[r6,r2]
ldrb r3,[r6,r2]
cmp r3,#0xD
addeq r2,#2
addne r2,#1
b 4f
3:
mov r3,#0
strb r3,[r6,r2]
add r2,#1
4:
mov r0,r4
bl conversionAtoD
strb r0,[r7,r5]
cmp r0,#0
ldreq r0,iAdriTabN0
streq r5,[r0] @ empty box in item zéro
add r5,#1
cmp r5,#NBBOX @ number box = maxi ?
bge 100f
add r4,r6,r2 @ new start address digit ascii
b 1b
100:
pop {r1-r8,lr} @ restaur registers
bx lr @return
/******************************************************************/
/* control of the game solution */
/******************************************************************/
/* r0 contains boxs address */
/* r0 returns 0 if not possible */
/* r0 returns 1 if possible */
controlSolution: @ INFO: controlSolution
push {r1-r8,lr} @ save registers
mov r5,r0
ldr r8,iAdriTabN0
ldr r8,[r8] @ empty box
@ empty box
mov r7,#0
cmp r8,#1
moveq r7,#1
beq 1f
cmp r8,#3
moveq r7,#1
beq 1f
cmp r8,#4
moveq r7,#1
beq 1f
cmp r8,#6
moveq r7,#1
beq 1f
cmp r8,#9
moveq r7,#1
beq 1f
cmp r8,#11
moveq r7,#1
beq 1f
cmp r8,#12
moveq r7,#1
beq 1f
cmp r8,#14
moveq r7,#1
1:
rsb r6,r8,#NBBOX - 1
add r7,r6
@ count permutations
mov r1,#-1
mov r6,#0
2:
add r1,#1
cmp r1,#NBBOX
bge 80f
cmp r1,r8
beq 2b
ldrb r3,[r5,r1]
mov r2,r1
3:
add r2,#1
cmp r2,#NBBOX
bge 2b
cmp r2,r8
beq 3b
ldrb r4,[r5,r2]
cmp r4,r3
addlt r6,#1
b 3b
80:
add r6,r7
tst r6,#1
movne r0,#0 @ impossible
moveq r0,#1 @ OK
100:
pop {r1-r8,lr} @ restaur registers
bx lr @return
/******************************************************************/
/* game Ok ? */
/******************************************************************/
/* r0 contains boxs address */
gameOK: @ INFO: gameOK
push {r1-r4,lr} @ save registers
mov r2,#0
ldrb r3,[r0,r2]
cmp r3,#0
moveq r3,#0xF
add r2,#1
1:
ldrb r4,[r0,r2]
cmp r4,#0
moveq r3,#0xF
cmp r4,r3
movle r0,#FALSE @ game not Ok
ble 100f
mov r3,r4
add r2,#1
cmp r2,#NBBOX -2
ble 1b
mov r0,#TRUE @ game Ok
100:
pop {r1-r4,lr} @ restaur registers
bx lr @return
/******************************************************************/
/* display game */
/******************************************************************/
/* r0 contains boxs address */
displayGame: @ INFO: displayGame
push {r0-r5,lr} @ save registers
mov r4,r0
ldr r0,iAdrszMessTitre
bl affichageMess @ display string
ldr r0,iAdriAdrFicName
ldr r0,[r0]
bl affichageMess @ display string
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display line return
mov r2,#0
ldr r1,iAdrsMessValeur
1:
ldrb r0,[r4,r2]
cmp r0,#0
ldreq r0,iSpaces @ store spaces
streq r0,[r1]
beq 2f
bl conversion10 @ call conversion decimal
mov r0,#0
strb r0,[r1,#3] @ zéro final
2:
ldr r0,iAdrsMessResult
bl affichageMess @ display message
add r0,r2,#1
tst r0,#0b11
bne 3f
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display message
3:
add r2,#1
cmp r2,#NBBOX - 1
ble 1b
ldr r0,iAdrszCarriageReturn
bl affichageMess @ display line return
100:
pop {r0-r5,lr} @ restaur registers
bx lr @return
iSpaces: .int 0x00202020 @ spaces
//iAdrszMessMoveError: .int szMessMoveError
iAdrszCarriageReturn: .int szCarriageReturn
iAdrsMessValeur: .int sMessValeur
iAdrsMessResult: .int sMessResult
/***************************************************/
/* ROUTINES INCLUDE */
/***************************************************/
.include "../affichage.inc"Nom du fichier : casR1.txt
Nom du fichier : casR1.txt
15 14 1 6
9 11 4 12
10 7 3
13 8 5 2
Nom du fichier : casR1.txt
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15
Solution in 52 moves :
RRRULDDLUUULDRURDDDRULLULURRRDDLDLUURDDLULURRULDRDRD
C
IDA*
/**@file HybridIDA.c
* @brief solve 4x4 sliding puzzle with IDA* algorithm
* by RMM 2021-feb-22
* The Interative Deepening A* is relatively easy to code in 'C' since
* it does not need Queues and Lists to manage memory. Instead the
* search space state is held on the LIFO stack frame of recursive
* search function calls. Millions of nodes may be created but they
* are automatically deleted during backtracking.
* Run-time is a disadvantage with complex puzzles. Also it struggles
* to solve puzzles with depth g>50. I provided a test puzzle of g=52
* that works with ordinary search but the Rosetta challenge puzzle
* cycles forever. The HybridIDA solves it in 18 seconds.
* The HybridIDA solution has two phases.
* 1. It stops searching when a permutation begins with 1234.
* 2. Phase2 begins a regular search with the output of phase 1.
* (But an regular one time search can be done with phase 2
* only). Phase 1 is optional.)
* Pros: Hybrid IDA* is faster and solves more puzzles.
* Cons: May not find shortest path.
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
typedef unsigned char u8t;
typedef unsigned short u16t;
enum { NR=4, NC=4, NCELLS = NR*NC };
enum { UP, DOWN, LEFT, RIGHT, NDIRS };
enum { OK = 1<<8, XX = 1<<9, FOUND = 1<<10, zz=0x80 };
enum { MAX_INT=0x7E, MAX_NODES=(16*65536)*90};
enum { BIT_HDR=1<<0, BIT_GRID=1<<1, BIT_OTHER=1<<2 };
enum { PHASE1,PHASE2 }; // solution phase
typedef struct { u16t dn; u16t hn; }HSORT_T;
typedef struct {
u8t data[NCELLS]; unsigned id; unsigned src;
u8t h; u8t g; u8t udlr;
}NODE_T; // contains puzzle data and metadata
NODE_T goal44={
{1,2,3,4, 5,6,7,8, 9,10,11,12, 13,14,15,0},0,0,0,0,0};
NODE_T work; // copy of puzzle with run-time changes
NODE_T G34={ //g=34; n=248,055; (1phase)
{13,9,5,4, 15,6,1,8, 0,10,2,11, 14,3,7,12},0,0,0,0,0};
NODE_T G52={ // g=52; n=34,296,567; (1phase)
{15,13,9,5, 14,6,1,4, 10,12,0,8, 3,7,11,2},0,0,0,0,0};
NODE_T G99={ // formidable Rosetta challenge (2phases)
{15,14,1,6, 9,11,4,12, 0,10,7,3, 13,8,5,2},0,0,0,0,0};
struct {
unsigned nodes;
unsigned gfound;
unsigned root_visits;
unsigned verbose;
unsigned locks;
unsigned phase;
}my;
u16t HybridIDA_star(NODE_T *pNode);
u16t make_node(NODE_T *pNode, NODE_T *pNew, u8t udlr );
u16t search(NODE_T *pNode, u16t bound);
u16t taxi_dist( NODE_T *pNode);
u16t tile_home( NODE_T *p44);
void print_node( NODE_T *pN, const char *pMsg, short force );
u16t goal_found(NODE_T *pNode);
char udlr_to_char( char udlr );
void idx_to_rc( u16t idx, u16t *row, u16t *col );
void sort_nodes(HSORT_T *p);
int main( )
{
my.verbose = 0; // minimal print node
// my.verbose |= BIT_HDR; // node header
// my.verbose |= BIT_GRID; // node 4x4 data
memcpy(&work, &G99, sizeof(NODE_T)); // select puzzle here
if(1){ // phase1 can skipped for easy puzzles
printf("Phase1: IDA* search for 1234 permutation..\n");
my.phase = PHASE1;
(void) HybridIDA_star(&work);
}
printf("Phase2: IDA* search phase1 seed..\n");
my.phase = PHASE2;
(void)HybridIDA_star(&work);
return 0;
}
/// \brief driver for Iterative Deepining A*
u16t HybridIDA_star(NODE_T *pN){
my.nodes = 1;
my.gfound = 0;
my.root_visits = 0;
pN->udlr = NDIRS;
pN->g = 0;
pN->h = taxi_dist(pN);
pN->id = my.nodes;
pN->src = 0;
const char *pr = {"Start"}; // for g++
print_node( pN,pr,1 );
u16t depth = pN->h;
while(1){
depth = search(pN,depth);
if( depth & FOUND){
return FOUND; // goodbye
}
if( depth & 0xFF00 ){
printf("..error %x\n",depth);
return XX;
}
my.root_visits++;
printf("[root visits: %u, depth %u]\n",my.root_visits,depth);
}
return 0;
}
/// \brief search is recursive. nodes are instance variables
u16t search(NODE_T *pN, u16t bound){
if(bound & 0xff00){ return bound; }
u16t f = pN->g + pN->h;
if( f > bound){ return f; }
if(goal_found(pN)){
my.gfound = pN->g;
memcpy(&work,pN,sizeof(NODE_T));
printf("total nodes=%d, g=%u \n", my.nodes, my.gfound);
const char *pr = {"Found.."}; // for g++
print_node( &work,pr,1 );
return FOUND;
}
NODE_T news;
// Sort successor nodes so that the lowest heuristic is visited
// before the less promising at the same level. This reduces the
// number of searches and finds more solutions
HSORT_T hlist[NDIRS];
for( short i=0; i<NDIRS; i++ ){
u16t rv = make_node(pN,&news, i );
hlist[i].dn = i;
if( rv & OK ){
hlist[i].hn = news.h;
continue;
}
hlist[i].hn = XX;
}
sort_nodes(&hlist[0]);
u16t temp, min = MAX_INT;
for( short i=0; i<NDIRS; i++ ){
if( hlist[i].hn > 0xff ) continue;
temp = make_node(pN,&news, hlist[i].dn );
if( temp & XX ) return XX;
if( temp & OK ){
news.id = my.nodes++;
print_node(&news," succ",0 );
temp = search(&news, bound);
if(temp & 0xff00){ return temp;}
if(temp < min){ min = temp; }
}
}
return min;
}
/// \brief sort nodes to prioitize heuristic low
void sort_nodes(HSORT_T *p){
for( short s=0; s<NDIRS-1; s++ ){
HSORT_T tmp = p[0];
if( p[1].hn < p[0].hn ){tmp=p[0]; p[0]=p[1]; p[1]=tmp; }
if( p[2].hn < p[1].hn ){tmp=p[1]; p[1]=p[2]; p[2]=tmp; }
if( p[3].hn < p[2].hn ){tmp=p[2]; p[2]=p[3]; p[3]=tmp; }
}
}
/// \brief return index of blank tile
u16t tile_home(NODE_T *pN ){
for( short i=0; i<NCELLS; i++ ){
if( pN->data[i] == 0 ) return i;
}
return XX;
}
/// \brief print node (or not) depending upon flags
void print_node( NODE_T *pN, const char *pMsg, short force ){
const int tp1 = 0;
if( my.verbose & BIT_HDR || force || tp1){
char ch = udlr_to_char(pN->udlr);
printf("id:%u src:%u; h=%d, g=%u, udlr=%c, %s\n",
pN->id, pN->src, pN->h, pN->g, ch, pMsg);
}
if(my.verbose & BIT_GRID || force || tp1){
for(u16t i=0; i<NR; i++ ){
for( u16t j=0; j<NC; j++ ){
printf("%3d",pN->data[i*NR+j]);
}
printf("\n");
}
printf("\n");
}
//putchar('>'); getchar();
}
/// \brief return true if selected tiles are settled
u16t goal_found(NODE_T *pN) {
if(my.phase==PHASE1){
short tags = 0;
for( short i=0; i<(NC); i++ ){
if( pN->data[i] == i+1 ) tags++;
}
if( tags==4 ) return 1; // Permutation starts with 1234
}
for( short i=0; i<(NR*NC); i++ ){
if( pN->data[i] != goal44.data[i] ) return 0;
}
return 1;
}
/// \brief convert UDLR index to printable char
char udlr_to_char( char udlr ){
char ch = '?';
switch(udlr){
case UP: ch = 'U'; break;
case DOWN: ch = 'D'; break;
case LEFT: ch = 'L'; break;
case RIGHT: ch = 'R'; break;
default: break;
}
return ch;
}
/// \brief convert 1-D array index to 2-D row-column
void idx_to_rc( u16t idx, u16t *row, u16t *col ){
*row = idx/NR; *col = abs( idx - (*row * NR));
}
/// \brief make successor node with blank tile moved UDRL
/// \return success or error
u16t make_node(NODE_T *pSrc, NODE_T *pNew, u8t udlr ){
u16t row,col,home_idx,idx2;
if(udlr>=NDIRS||udlr<0 ){ printf("invalid udlr %u\n",udlr); return XX; }
if(my.nodes > MAX_NODES ){ printf("excessive nodes %u\n",my.nodes);
return XX; }
memcpy(pNew,pSrc,sizeof(NODE_T));
home_idx = tile_home(pNew);
idx_to_rc(home_idx, &row, &col );
if( udlr == LEFT) { if( col < 1 ) return 0; col--; }
if( udlr == RIGHT ){ if( col >= (NC-1) ) return 0; col++; }
if( udlr == DOWN ) { if(row >= (NR-1)) return 0; row++; }
if( udlr == UP ){ if(row < 1) return 0; row--; }
idx2 = row * NR + col;
if( idx2 < NCELLS ){
u8t *p = &pNew->data[0];
p[home_idx] = p[idx2];
p[idx2] = 0; // swap
pNew->src = pSrc->id;
pNew->g = pSrc->g + 1;
pNew->h = taxi_dist(pNew);
pNew->udlr = udlr; // latest move;
return OK;
}
return 0;
}
/// \brief sum of 'manhattan taxi' distance between tile locations
u16t taxi_dist( NODE_T *pN){
u16t tile,sum = 0, r1,c1,r2,c2;
u8t *p44 = &pN->data[0];
for( short i=0; i<(NR*NC); i++ ){
tile = p44[i];
if( tile==0 ) continue;
idx_to_rc(i, &r2, &c2 );
idx_to_rc(tile-1, &r1, &c1 );
sum += abs(r1-r2) + abs(c1-c2);
}
}
return sum;
}
- Output:
Phase1: IDA* search for 1234 permutation.. id:1 src:0; h=36, g=0, udlr=?, Start 15 14 1 6 9 11 4 12 0 10 7 3 13 8 5 2 total nodes=838133, g=32 id:838132 src:838131; h=12, g=32, udlr=D, Found.. 1 2 3 4 15 0 7 6 9 10 5 12 13 14 11 8 Phase2: IDA* search phase1 seed.. id:1 src:0; h=12, g=0, udlr=?, Start 1 2 3 4 15 0 7 6 9 10 5 12 13 14 11 8 total nodes=8598744, g=26 id:8598743 src:8598742; h=0, g=26, udlr=D, Found.. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0
Literate Programming
I think I used the same algorithm as Nigel Galloway, but I'm still not sure I understood his C++ code. For anyone who also had trouble understanding, I thoroughly explained how everything works in this literate program.
The program takes about 12 seconds to solve the puzzle on my machine. I sacrificed efficiency for readability and extensibility.
C#
using System;
using System.IO;
using System.IO.Compression;
using System.Runtime.InteropServices;
using System.Text;
public static class Program
{
public static void Main(string[] args)
{
byte[] t = new byte[]
{
15, 14, 1, 6,
9, 11, 4, 12,
0, 10, 7, 3,
13, 8, 5, 2,
};
Ultimate.SolvePuzzle15(t);
}
}
public static class NativeLibraryHelper
{
[DllImport("kernel32.dll")]
public static extern IntPtr LoadLibrary(string DllToLoad);
[DllImport("kernel32.dll")]
public static extern IntPtr GetProcAddress(IntPtr DllHandle, string ProcedureName);
[DllImport("kernel32.dll")]
public static extern bool FreeLibrary(IntPtr DllHandle);
public static T GetMethod<T>(IntPtr DllHandle, string MethodName) where T : class
{
T Method = null;
IntPtr MethodHandle = NativeLibraryHelper.GetProcAddress(DllHandle, MethodName);
if (MethodHandle != IntPtr.Zero)
{
Method = (T)((Object)Marshal.GetDelegateForFunctionPointer(MethodHandle, typeof(T)));
}
return Method;
}
}
public static class Ultimate
{
[UnmanagedFunctionPointer(CallingConvention.StdCall)]
[return: MarshalAs(UnmanagedType.LPWStr)]
private delegate string GetSolverName();
[UnmanagedFunctionPointer(CallingConvention.StdCall)]
[return: MarshalAs(UnmanagedType.LPWStr)]
private delegate string CallSolver([In] [Out] byte[] Array, int Len);
public static void SolvePuzzle15(byte[] t)
{
string LibPath = "Solver.dll";
byte[] ZipedData = Convert.FromBase64String(Data.ToString());
byte[] UnzipedData = DecompressGZipArhive(new MemoryStream(ZipedData));
File.WriteAllBytes(LibPath, UnzipedData);
IntPtr DllHandle = NativeLibraryHelper.LoadLibrary(LibPath);
GetSolverName GetSolverName = NativeLibraryHelper.GetMethod<GetSolverName>(DllHandle, "GetSolverName");
Console.WriteLine("Hi! My name is {0}.", GetSolverName());
Console.WriteLine();
Console.WriteLine("And I try solve puzzle15 with board:");
for (int i = 0; i < t.Length; i += 4) Console.WriteLine("{0} {1} {2} {3}", t[i], t[i + 1], t[i + 2], t[i + 3]);
Console.WriteLine();
CallSolver SolveThis = NativeLibraryHelper.GetMethod<CallSolver>(DllHandle, "SolvePuzzle15");
DateTime StartTime = DateTime.Now;
string Path = SolveThis(t, t.Length);
if (!String.IsNullOrEmpty(Path))
{
Path = Path.Trim();
Console.WriteLine("Ready! Solution path is : {0}", Path);
Console.WriteLine("Moves {0} and Time: {1}", Path.Length, (DateTime.Now - StartTime).ToString());
Console.WriteLine();
Console.WriteLine("Bye bye :)");
}
else
{
Console.WriteLine("Sorry! I do know a solution :(");
}
NativeLibraryHelper.FreeLibrary(DllHandle);
File.Delete(LibPath);
Console.ReadKey();
}
private static byte[] DecompressGZipArhive(Stream FStream)
{
if (FStream == null) return new byte[0];
FStream.Seek(0, SeekOrigin.Begin);
MemoryStream OutStream = new MemoryStream();
using (GZipStream DecompressedStream = new GZipStream(FStream, CompressionMode.Decompress))
{
byte[] Buffer = new byte[1024];
int CountReadingBytes = 0;
while ((CountReadingBytes = DecompressedStream.Read(Buffer, 0, Buffer.Length)) > 0)
{
OutStream.Write(Buffer, 0, CountReadingBytes);
}
}
return OutStream.ToArray();
}
// no way make normal long string literal
private delegate StringBuilder AppendDelegate(string v);
private static StringBuilder Data = new StringBuilder(100000);
static Ultimate()
{
AppendDelegate a = Data.Append;
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a("5RDDof4on26I/OAx79QTDVkmwcOTTboTgxxYQm+yimOcYU8c2eZORLaP/xi253dmdnZmdnZmd3EzgxJhQIguDEL5MRhHbB+qsV");
a("/vmvGb/1t3hxfeHZojfL20X1zfKjzzl3UdnFdRedXTd/YdmC+RdeeFGw7IyzyupCF5ade2GZ77CjyhZedOZZO02f7qnI0jjcLw");
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a("8uC4Uzh9tvCf/8653ynMLvjr/p2CZ10eRIk5WwLdSZObilMmCKfvdOb84HzUoRfIDJy5JLNjCl4tyOxUR4jg6xGhE/QXo0ythV");
a("e708UcD3O05irsgfIdlHa8MxYtQpWvhVDpXLc9EN8Djjya6m76xIBHLD0o7fKda/HdfTrXOQwJZfE68M7KzoOvUZbeHJR2+erO");
a("uuCiBQLWhq8RcFBuuhbePOH/vyl/ma3PuNE5BT7RBh9pgw+2wfNs8F42eBcbvJ0N3tIGz7HBM22wxwY7bPDEDVPh723wiA1ebY");
a("NX2eB+G7zcBidt8Is2+Bkb/KgNvs8G326Db7DBbTZ4sQ2+0gbX2eDzbPAZNvhEG3ykDT7YBs+zwXvZ4F1s8HY2eEsbPMcGz7TB");
a("HhvssMET19vW3waP2ODVNniVDe63wcttcNIGv2iDn7HBj9rg+2zw7Tb4BhvcZoMX2+ArbXCdDT7PBp9hg0+0wUfa4INt8DwbvJ");
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a("wnWjgknCaZz5kNYUX9iQlGM8tbT/n3/68xHeVZKEADYEAA==");
}
}- Output:
Hi! My name is Pascal Slover. And I try solve puzzle15 with board: 15 14 1 6 9 11 4 12 0 10 7 3 13 8 5 2 Ready! Solution path is : rrruldluuldrurdddluulurrrdlddruldluurddlulurruldrrdd Moves 52 and Time: 00:00:00.7509766 Bye bye :)
C++
see for an analysis of 20 randomly generated 15 puzzles solved with this solver.
The Solver
// Solve Random 15 Puzzles : Nigel Galloway - October 18th., 2017
class fifteenSolver{
const int Nr[16]{3,0,0,0,0,1,1,1,1,2,2,2,2,3,3,3}, Nc[16]{3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2};
int n{},_n{}, N0[100]{},N3[100]{},N4[100]{};
unsigned long N2[100]{};
const bool fY(){
if (N4[n]<_n) return fN();
if (N2[n]==0x123456789abcdef0) {std::cout<<"Solution found in "<<n<<" moves :"; for (int g{1};g<=n;++g) std::cout<<(char)N3[g]; std::cout<<std::endl; return true;};
if (N4[n]==_n) return fN(); else return false;
}
const bool fN(){
if (N3[n]!='u' && N0[n]/4<3){fI(); ++n; if (fY()) return true; --n;}
if (N3[n]!='d' && N0[n]/4>0){fG(); ++n; if (fY()) return true; --n;}
if (N3[n]!='l' && N0[n]%4<3){fE(); ++n; if (fY()) return true; --n;}
if (N3[n]!='r' && N0[n]%4>0){fL(); ++n; if (fY()) return true; --n;}
return false;
}
void fI(){
const int g = (11-N0[n])*4;
const unsigned long a = N2[n]&((unsigned long)15<<g);
N0[n+1]=N0[n]+4; N2[n+1]=N2[n]-a+(a<<16); N3[n+1]='d'; N4[n+1]=N4[n]+(Nr[a>>g]<=N0[n]/4?0:1);
}
void fG(){
const int g = (19-N0[n])*4;
const unsigned long a = N2[n]&((unsigned long)15<<g);
N0[n+1]=N0[n]-4; N2[n+1]=N2[n]-a+(a>>16); N3[n+1]='u'; N4[n+1]=N4[n]+(Nr[a>>g]>=N0[n]/4?0:1);
}
void fE(){
const int g = (14-N0[n])*4;
const unsigned long a = N2[n]&((unsigned long)15<<g);
N0[n+1]=N0[n]+1; N2[n+1]=N2[n]-a+(a<<4); N3[n+1]='r'; N4[n+1]=N4[n]+(Nc[a>>g]<=N0[n]%4?0:1);
}
void fL(){
const int g = (16-N0[n])*4;
const unsigned long a = N2[n]&((unsigned long)15<<g);
N0[n+1]=N0[n]-1; N2[n+1]=N2[n]-a+(a>>4); N3[n+1]='l'; N4[n+1]=N4[n]+(Nc[a>>g]>=N0[n]%4?0:1);
}
public:
fifteenSolver(int n, unsigned long g){N0[0]=n; N2[0]=g;}
void Solve(){for(;not fY();++_n);}
};
The Task
int main (){
fifteenSolver start(8,0xfe169b4c0a73d852);
start.Solve();
}
- Output:
Solution found in 52 moves: rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd real 0m0.517s
Extra Credit
int main (){
fifteenSolver start(0,0x0c9dfbae37254861);
start.Solve();
}
- Output:
Solution found in 80 moves :dddrurdruuulllddrulddrrruuullddruulldddrrurulldrruulldlddrurullddrrruullulddrdrr real 249m18.464s
Common Lisp
Using an A* search algorithm which is good enough for the first task. I increased SBCL's dynamic memory to 2GB for the code to run smoothly.
;;; Using a priority queue for the A* search
(eval-when (:load-toplevel :compile-toplevel :execute)
(ql:quickload "pileup"))
;; * The package definition
(defpackage :15-solver
(:use :common-lisp :pileup)
(:export "15-puzzle-solver" "*initial-state*" "*goal-state*"))
(in-package :15-solver)
;; * Data types
(defstruct (posn (:constructor posn))
"A posn is a pair struct containing two integer for the row/col indices."
(row 0 :type fixnum)
(col 0 :type fixnum))
(defstruct (state (:constructor state))
"A state contains a vector and a posn describing the position of the empty slot."
(matrix '#(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0) :type simple-vector)
(empty-slot (posn :row 3 :col 3) :type posn))
(defparameter directions '(up down left right)
"The possible directions shifting the empty slot.")
(defstruct (node (:constructor node))
"A node contains a state, a reference to the previous node, a g value (actual
costs until this node, and a f value (g value + heuristics)."
(state (state) :type state)
(prev nil)
(cost 0 :type fixnum)
(f-value 0 :type fixnum))
;; * Some constants
(defparameter *side-size* 4 "The size of the puzzle.")
(defvar *initial-state*
(state :matrix #(15 14 1 6
9 11 4 12
0 10 7 3
13 8 5 2)
:empty-slot (posn :row 2 :col 0)))
(defvar *initial-state-2*
(state :matrix #( 0 12 9 13
15 11 10 14
3 7 2 5
4 8 6 1)
:empty-slot (posn :row 0 :col 0)))
(defvar *goal-state*
(state :matrix #( 1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 0)
:empty-slot (posn :row 3 :col 3)))
;; * The functions
;; ** Accessing the elements of the puzzle
(defun matrix-ref (matrix row col)
"Matrices are simple vectors, abstracted by following functions."
(svref matrix (+ (* row *side-size*) col)))
(defun (setf matrix-ref) (val matrix row col)
(setf (svref matrix (+ (* row *side-size*) col)) val))
;; ** The final predicate
(defun target-state-p (state goal-state)
"Returns T if STATE is the goal state."
(equalp state goal-state))
(defun valid-movement-p (direction empty-slot)
"Returns T if direction is allowed for the current empty slot position."
(case direction
(up (< (posn-row empty-slot) (1- *side-size*)))
(down (> (posn-row empty-slot) 0))
(left (< (posn-col empty-slot) (1- *side-size*)))
(right (> (posn-col empty-slot) 0))))
;; ** Pretty print the state
(defun print-state (state)
"Helper function to pretty-print a state."
(format t " ====================~%")
(loop
with matrix = (state-matrix state)
for i from 0 below *side-size*
do
(loop
for j from 0 below *side-size*
do (format t "| ~2,D " (matrix-ref matrix i j)))
(format t " |~%"))
(format t " ====================~%"))
;; ** Move the empty slot
(defun move (state direction)
"Returns a new state after moving STATE's empty-slot in DIRECTION assuming a
valid direction."
(let* ((matrix (copy-seq (state-matrix state)))
(empty-slot (state-empty-slot state))
(r (posn-row empty-slot))
(c (posn-col empty-slot))
(new-empty-slot
(ccase direction
(up (setf (matrix-ref matrix r c) (matrix-ref matrix (1+ r) c)
(matrix-ref matrix (1+ r) c) 0)
(posn :row (1+ r) :col c))
(down (setf (matrix-ref matrix r c) (matrix-ref matrix (1- r) c)
(matrix-ref matrix (1- r) c) 0)
(posn :row (1- r) :col c))
(left (setf (matrix-ref matrix r c) (matrix-ref matrix r (1+ c))
(matrix-ref matrix r (1+ c)) 0)
(posn :row r :col (1+ c)))
(right (setf (matrix-ref matrix r c) (matrix-ref matrix r (1- c))
(matrix-ref matrix r (1- c)) 0)
(posn :row r :col (1- c))))))
(state :matrix matrix :empty-slot new-empty-slot)))
;; ** The heuristics
(defun l1-distance (posn0 posn1)
"Returns the L1 distance between two positions."
(+ (abs (- (posn-row posn0) (posn-row posn1)))
(abs (- (posn-col posn0) (posn-col posn1)))))
(defun element-cost (val current-posn)
"Returns the L1 distance between the current position and the goal-position
for VAL."
(if (zerop val)
(l1-distance current-posn (posn :row 3 :col 3))
(multiple-value-bind (target-row target-col)
(floor (1- val) *side-size*)
(l1-distance current-posn (posn :row target-row :col target-col)))))
(defun distance-to-goal (state)
"Returns the L1 distance from STATE to the goal state."
(loop
with matrix = (state-matrix state)
with sum = 0
for i below *side-size*
do (loop
for j below *side-size*
for val = (matrix-ref matrix i j)
for cost = (element-cost val (posn :row i :col j))
unless (zerop val)
do (incf sum cost))
finally (return sum)))
(defun out-of-order-values (list)
"Returns the number of values out of order."
(flet ((count-values (list)
(loop
with a = (first list)
with rest = (rest list)
for b in rest
when (> b a)
count b)))
(loop
for candidates = list then (rest candidates)
while candidates
summing (count-values candidates) into result
finally (return (* 2 result)))))
(defun row-conflicts (row state0 state1)
"Returns the number of conflicts in the given row, i.e. value in the right row
but in the wrong order. For each conflicted pair add 2 to the value, but a
maximum of 6 to avoid over-estimation."
(let* ((goal-row (loop
with matrix1 = (state-matrix state1)
for j below *side-size*
collect (matrix-ref matrix1 row j)))
(in-goal-row (loop
with matrix0 = (state-matrix state0)
for j below *side-size*
for val = (matrix-ref matrix0 row j)
when (member val goal-row)
collect val)))
(min 6 (out-of-order-values
;; 0 does not lead to a linear conflict
(remove 0 (nreverse in-goal-row))))))
(defun col-conflicts (col state0 state1)
"Returns the number of conflicts in the given column, i.e. value in the right
row but in the wrong order. For each conflicted pair add 2 to the value, but a
maximum of 6 to avoid over-estimation."
(let* ((goal-col (loop
with matrix1 = (state-matrix state1)
for i below *side-size*
collect (matrix-ref matrix1 i col)))
(in-goal-col (loop
with matrix0 = (state-matrix state0)
for i below *side-size*
for val = (matrix-ref matrix0 i col)
when (member val goal-col)
collect val)))
(min 6 (out-of-order-values
;; 0 does not lead to a linear conflict
(remove 0 (nreverse in-goal-col))))))
(defun linear-conflicts (state0 state1)
"Returns the linear conflicts for state1 with respect to state0."
(loop
for i below *side-size*
for row-conflicts = (row-conflicts i state0 state1)
for col-conflicts = (col-conflicts i state0 state1)
summing row-conflicts into all-row-conflicts
summing col-conflicts into all-col-conflicts
finally (return (+ all-row-conflicts all-col-conflicts))))
(defun state-heuristics (state)
"Using the L1 distance and the number of linear conflicts as heuristics."
(+ (distance-to-goal state)
(linear-conflicts state *goal-state*)))
;; ** Generate the next possible states.
(defun next-state-dir-pairs (current-node)
"Returns a list of pairs containing the next states and the direction for the
movement of the empty slot."
(let* ((state (node-state current-node))
(empty-slot (state-empty-slot state))
(valid-movements (remove-if-not (lambda (dir) (valid-movement-p dir empty-slot))
directions)))
(map 'list (lambda (dir) (cons (move state dir) dir)) valid-movements)))
;; ** Searching the shortest paths and reconstructing the movements
(defun reconstruct-movements (leaf-node)
"Traverse all nodes until the initial state and return a list of symbols
describing the path."
(labels ((posn-diff (p0 p1)
;; Compute a pair describing the last move
(posn :row (- (posn-row p1) (posn-row p0))
:col (- (posn-col p1) (posn-col p0))))
(find-movement (prev-state state)
;; Describe the last movement of the empty slot with R, L, U or D.
(let* ((prev-empty-slot (state-empty-slot prev-state))
(this-empty-slot (state-empty-slot state))
(delta (posn-diff prev-empty-slot this-empty-slot)))
(cond ((equalp delta (posn :row 1 :col 0)) 'u)
((equalp delta (posn :row -1 :col 0)) 'd)
((equalp delta (posn :row 0 :col 1)) 'l)
((equalp delta (posn :row 0 :col -1)) 'r))))
(iter (node path)
(if (or (not node) (not (node-prev node)))
path
(iter (node-prev node)
(cons (find-movement (node-state node)
(node-state (node-prev node)))
path)))))
(iter leaf-node '())))
(defun A* (initial-state
&key (goal-state *goal-state*) (heuristics #'state-heuristics)
(information 0))
"An A* search for the shortest path to *GOAL-STATE*"
(let ((visited (make-hash-table :test #'equalp))) ; All states visited so far
;; Some internal helper functions
(flet ((pick-next-node (queue)
;; Get the next node from the queue
(heap-pop queue))
(expand-node (node queue)
;; Expand the next possible nodes from node and add them to the
;; queue if not already visited.
(loop
with costs = (node-cost node)
with successors = (next-state-dir-pairs node)
for (state . dir) in successors
for succ-cost = (1+ costs)
for f-value = (+ succ-cost (funcall heuristics state))
;; Check if this state was already looked at
unless (gethash state visited)
do
;; Insert the next node into the queue
(heap-insert
(node :state state :prev node :cost succ-cost
:f-value f-value)
queue))))
;; The actual A* search
(loop
;; The priority queue
with queue = (make-heap #'<= :name "queue" :size 1000 :key #'node-f-value)
with initial-state-cost = (funcall heuristics initial-state)
initially (heap-insert (node :state initial-state :prev nil :cost 0
:f-value initial-state-cost)
queue)
for counter from 1
for current-node = (pick-next-node queue)
for current-state = (node-state current-node)
;; Output some information each counter or nothing if information
;; equals 0.
when (and (not (zerop information))
(zerop (mod counter information)))
do (format t "~Dth State, heap size: ~D, current costs: ~D~%"
counter (heap-count queue)
(node-cost current-node))
;; If the target is not reached continue
until (target-state-p current-state goal-state)
do
;; Add the current state to the hash of visited states
(setf (gethash current-state visited) t)
;; Expand the current node and continue
(expand-node current-node queue)
finally (return (values (reconstruct-movements current-node) counter))))))
;; ** Pretty print the path
(defun print-path (path)
"Prints the directions of PATH and its length."
(format t "~{~A~} ~D moves~%" path (length path)))
;; ** Get some timing information
(defmacro timing (&body forms)
"Return both how much real time was spend in body and its result"
(let ((start (gensym))
(end (gensym))
(result (gensym)))
`(let* ((,start (get-internal-real-time))
(,result (progn ,@forms))
(,end (get-internal-real-time)))
(values ,result (/ (- ,end ,start) internal-time-units-per-second)))))
;; ** The main function
(defun 15-puzzle-solver (initial-state &key (goal-state *goal-state*))
"Solves a given and valid 15 puzzle and returns the shortest path to reach the
goal state."
(print-state initial-state)
(multiple-value-bind (result time)
(timing (multiple-value-bind (path steps)
(a* initial-state :goal-state goal-state)
(print-path path)
steps))
(format t "Found the shortest path in ~D steps and ~3,2F seconds~%" result time))
(print-state goal-state))
- Output:
15-SOLVER> (15-puzzle-solver *initial-state*) ==================== | 15 | 14 | 1 | 6 | | 9 | 11 | 4 | 12 | | 0 | 10 | 7 | 3 | | 13 | 8 | 5 | 2 | ==================== RRRULDDLUUULDRURDDDRULLULURRRDDLDLUURDDLULURRULDRDRD 52 moves Found the shortest path in 1130063 steps and 17.61 seconds ==================== | 1 | 2 | 3 | 4 | | 5 | 6 | 7 | 8 | | 9 | 10 | 11 | 12 | | 13 | 14 | 15 | 0 | ====================
Dart
import 'package:collection/collection.dart';
typedef OffsetFunction = int Function(int a, int b);
Function eq = const ListEquality().equals;
/// Solve Random 15 Puzzles
class FifteenSolver {
static const target = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0];
static const trN = [3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3];
static const tcN = [3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2];
var pos0 = List.filled(100, 0);
var moves = List.filled(100, 0);
var dirs = List.filled(100, '');
int step = 0, best = 0;
var board = List.generate(100, (int i) => List.filled(16, 0));
bool isFinished() {
if (moves[step] < best) return nextMove();
if (eq(board[step], target)) {
print("Solution found in $step moves :${dirs.join('')}");
return true;
}
return (moves[step] == best) ? nextMove() : false;
}
var passNumber = 0;
/// Try all valid moves from here, but don't retrace your steps.
/// Return true if a solution is found.
bool nextMove() {
// if (passNumber++ ~/ 100000 == 0) print("${dirs.join('')}");
return (dirs[step] != 'u' && pos0[step] ~/ 4 < 3 && down()) ||
(dirs[step] != 'd' && pos0[step] ~/ 4 > 0 && up()) ||
(dirs[step] != 'l' && pos0[step] % 4 < 3 && right()) ||
(dirs[step] != 'r' && pos0[step] % 4 > 0 && left()) ||
false;
}
bool move(int offset, String dir, List<int> rcArray, OffsetFunction rcFunc) {
final int ix = pos0[step] + offset;
final n = board[step][ix];
pos0[step + 1] = pos0[step] + offset;
board[step + 1] = board[step].toList()
..[pos0[step]] = n
..[ix] = 0;
dirs[step + 1] = dir;
moves[step + 1] = moves[step] + rcFunc(rcArray[n], pos0[step]);
step++;
if (isFinished()) return true;
step--;
return false;
}
bool right() => move(1, 'r', tcN, (a, b) => (a <= b % 4 ? 0 : 1));
bool left() => move(-1, 'l', tcN, (a, b) => (a >= b % 4 ? 0 : 1));
bool down() => move(4, 'd', trN, (a, b) => (a <= b ~/ 4 ? 0 : 1));
bool up() => move(-4, 'u', trN, (a, b) => (a >= b ~/ 4 ? 0 : 1));
void solve(List<int> initBoard) {
pos0[0] = initBoard.indexOf(0);
board[0] = initBoard;
while (!isFinished()) best++;
}
}
void main(List<String> args) {
print("running");
// test values
// final start = [5, 1, 2, 3, 6, 10, 7, 4, 13, 9, 11, 8, 14, 0, 15, 12];
// final start = [9, 1, 2, 4, 13, 6, 5, 7, 3, 11, 14, 15, 10, 0, 8, 12];
// final start = [10, 3, 1, 4, 13, 5, 8, 7, 9, 6, 0, 11, 14, 15, 12, 2];
// required solution
final start = [15, 14, 1, 6, 9, 11, 4, 12, 0, 10, 7, 3, 13, 8, 5, 2];
// Extra credit
// final start = [0, 12, 9, 13, 15, 11, 10, 14, 3, 7, 2, 5, 4, 8, 6, 1];
print(start);
FifteenSolver().solve(start);
}
- Output:
running Solution found in 52 moves :rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd
F#
The Function
// A Naive 15 puzzle solver using no memory. Nigel Galloway: October 6th., 2017
let Nr,Nc = [|3;0;0;0;0;1;1;1;1;2;2;2;2;3;3;3|],[|3;0;1;2;3;0;1;2;3;0;1;2;3;0;1;2|]
type G= |N |I |G |E |L
type N={i:uint64;g:G list;e:int;l:int}
let fN n=let g=(11-n.e)*4 in let a=n.i&&&(15UL<<<g)
{i=n.i-a+(a<<<16);g=N::n.g;e=n.e+4;l=n.l+(if Nr.[int(a>>>g)]<=n.e/4 then 0 else 1)}
let fI i=let g=(19-i.e)*4 in let a=i.i&&&(15UL<<<g)
{i=i.i-a+(a>>>16);g=I::i.g;e=i.e-4;l=i.l+(if Nr.[int(a>>>g)]>=i.e/4 then 0 else 1)}
let fG g=let l=(14-g.e)*4 in let a=g.i&&&(15UL<<<l)
{i=g.i-a+(a<<<4) ;g=G::g.g;e=g.e+1;l=g.l+(if Nc.[int(a>>>l)]<=g.e%4 then 0 else 1)}
let fE e=let l=(16-e.e)*4 in let a=e.i&&&(15UL<<<l)
{i=e.i-a+(a>>>4) ;g=E::e.g;e=e.e-1;l=e.l+(if Nc.[int(a>>>l)]>=e.e%4 then 0 else 1)}
let fL=let l=[|[I;E];[I;G;E];[I;G;E];[I;G];[N;I;E];[N;I;G;E];[N;I;G;E];[N;I;G];[N;I;E];[N;I;G;E];[N;I;G;E];[N;I;G];[N;E];[N;G;E];[N;G;E];[N;G];|]
(fun n g->List.except [g] l.[n] |> List.map(fun n->match n with N->fI |I->fN |G->fE |E->fG))
let solve n g l=let rec solve n=match n with // n is board, g is pos of 0, l is max depth
|n when n.i =0x123456789abcdef0UL->Some(n.g)
|n when n.l>l ->None
|g->let rec fN=function h::t->match solve h with None->fN t |n->n
|_->None
fN (fL g.e (List.head n.g)|>List.map(fun n->n g))
solve {i=n;g=[L];e=g;l=0}
let n = Seq.collect fN n
The Task
let test n g=match [1..15]|>Seq.tryPick(solve n g) with
Some n->n|>List.rev|>List.iter(fun n->printf "%c" (match n with N->'d'|I->'u'|G->'r'|E->'l'|L->'\u0000'));printfn " (%n moves)" (List.length n)
|_ ->printfn "No solution found"
test 0xfe169b4c0a73d852UL 8
- Output:
rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd (52 moves)
Forth
The idea is taken from C++ or F# version above.
The code was tested with gforth 0.7.3. It required a 64-bit system.
#! /usr/bin/gforth
cell 8 <> [if] s" 64-bit system required" exception throw [then]
\ In the stack comments below,
\ "h" stands for the hole position (0..15),
\ "s" for a 64-bit integer representing a board state,
\ "t" a tile value (0..15, 0 is the hole),
\ "b" for a bit offset of a position within a state,
\ "m" for a masked value (4 bits selected out of a 64-bit state),
\ "w" for a weight of a current path,
\ "d" for a direction constant (0..3)
\ Utility
: 3dup 2 pick 2 pick 2 pick ;
: 4dup 2over 2over ;
: shift dup 0 > if lshift else negate rshift then ;
hex 123456789abcdef0 decimal constant solution
: row 2 rshift ; : col 3 and ;
: up-valid? ( h -- f ) row 0 > ;
: down-valid? ( h -- f ) row 3 < ;
: left-valid? ( h -- f ) col 0 > ;
: right-valid? ( h -- f ) col 3 < ;
: up-cost ( h t -- 0|1 ) 1 - row swap row < 1 and ;
: down-cost ( h t -- 0|1 ) 1 - row swap row > 1 and ;
: left-cost ( h t -- 0|1 ) 1 - col swap col < 1 and ;
: right-cost ( h t -- 0|1 ) 1 - col swap col > 1 and ;
\ To iterate over all possible directions, put direction-related functions into arrays:
: ith ( u addr -- w ) swap cells + @ ;
create valid? ' up-valid? , ' left-valid? , ' right-valid? , ' down-valid? , does> ith execute ;
create cost ' up-cost , ' left-cost , ' right-cost , ' down-cost , does> ith execute ;
create step -4 , -1 , 1 , 4 , does> ith ;
\ Advance from a single state to another:
: bits ( h -- b ) 15 swap - 4 * ;
: tile ( s b -- t ) rshift 15 and ;
: new-state ( s h d -- s' ) step dup >r + bits 2dup tile ( s b t ) swap lshift tuck - swap r> 4 * shift + ;
: new-weight ( w s h d -- w' ) >r tuck r@ step + bits tile r> cost + ;
: advance ( w s h d -- w s h w' s' h' ) 4dup new-weight >r 3dup new-state >r step over + 2r> rot ;
\ Print a solution:
: rollback 2drop drop ;
: .dir ( u -- ) s" d..r.l..u" drop 4 + swap + c@ emit ;
: .dirs ( .. -- ) 0 begin >r 3 pick -1 <> while 3 pick over - .dir rollback r> 1+ repeat r> ;
: win cr ." solved (read right-to-left!): " .dirs ." - " . ." moves" bye ;
\ The main recursive function for depth-first search:
create limit 1 , : deeper 1 limit +! ;
: u-turn ( .. h2 w1 s1 h1 ) 4 pick 2 pick - ;
: search ( .. h2 w1 s1 h1 )
over solution = if win then
2 pick limit @ > if exit then
4 0 do dup i valid? if i step u-turn <> if i advance recurse rollback then then loop ;
\ Iterative-deepening search:
: solve 1 limit ! begin search deeper again ;
\ -1 0 hex 0c9dfbae37254861 decimal 0 solve \ uhm.
-1 0 hex fe169b4c0a73d852 decimal 8 solve \ the 52 moves case
\ -1 0 hex 123456789afbde0c decimal 14 solve \ some trivial case, 3 moves
bye
- Output:
time ./15_puzzle_solver.fs redefined search solved (read right-to-left!): ddrrdlurrululddruuldlurddldrrruluuldddrurdluuldlurrr - 52 moves real 1m14.605s user 1m5.212s sys 0m0.048s
Fortran
The Plan
There is a straightforward method for dealing with problems of this sort, the Red Tide. Imagine a maze and pouring red-dyed water into the "entry" - eventually, red water issues forth from the exit, or, back pressure will indicate that there is no such path. In other words, from the starting position find all possible positions that can be reached in one step, then from those positions, all possible positions that can be reached in one step from them, and so on. Eventually, either the stopping position will be reached, or, there will be no more new (still dry) positions to inspect. What is needed is some way of recording whether a position has been marked red or not, and an arrangement for identifying positions that are on the leading edge of the tide as it spreads. Keeping as well some sort of information identifying the path followed by each droplet, so that when a droplet spreads to the end position, its path from the source can be listed.
One could imagine an array FROM whose value for a given position identifies the position from which a step was taken to reach it. The value could be a number identifying that position or be a (sixteen element) list of the placement of the tiles possibly encoded into one number. An index for FROM would span the values zero to fifteen, and there would be sixteen dimensions... Alternatively, an array MOVE would record the move that led to its element's positiion: four possibilities would require just two bits for each element. But 1616 is about 1020 Avogadro's constant is 6·0221415x1023 Oh well.
Since there are only 16! possible board layouts, only about a millionth of the array would be in use (16!/1616 = 0·0000011342267) which is rather a stiff price to pay for a convenient relationship between a board layout and the corresponding location in the array. Actually, calculating a sixteen-dimensional location in an array is not so trivial and earlier compilers would not allow so many dimensions anyway. An alternative calculation might serve. This is the method of "hash tables", whereby, given a key (here, the values of the tiles in the sixteen places of the board), calculate a number, H, by some expedient and use that to index into a table. Entries are added sequentially to the table of positions but the hash number for a position is arbitrary so an array is used: INDEX(H) for the first position stored is one, and for the second position with its value of H, INDEX(H) is two, and so on, Two different positions may well yield the same hash number in a variant of the "birthday paradox", so the value of INDEX(H) is really a pointer to the start of a linked-list of table entries for different positions that all have the same hash number. The length of such chains is expected to be short because the hash number selects within a large INDEX array. Searching should be swift as for a given position, either INDEX(H) will be zero (meaning that the position is unknown), or, there will be one or two entries to probe to see if their position matches.
Because a board position involves sixteen numbers, each in the range of zero to fifteen, it is irresistible to have the board layout described by INTEGER*1 BOARD(16) since eight-bit integers can be defined, though not four-bit integers, alas. Further, an EQUIVALENCE statement can make this storage area the same place that an array INTEGER*4 BORED(4) occupies: no data transfer operations are needed for four 32-bit integers to hold the contenet of sixteen 8-bit integers. Next, the calculations BRD(1) = BORED(1)*16 + BORED(2) and BRD(2) = BORED(3)*16 + BORED(4) will squeeze two four-bit fields into one eight-bit pair, and moreover, do so four pairs at a time in parallel. Thus, array BRD in two 32-bit integers describes a position. A 64-bit integer could be involved instead of two 32-bit integers, but the hash calculation uses BRD(1)*BRD(2) to encourage a good mix. In The Art of Computer Programming, Prof. Knuth advises that the wild hash number be reduced to the range 0:M - 1 by taking the remainder, modulo M, where M is a (large) prime number. The index array then is a fixed size, INDEX(0:M - 1) The output shows these calculations for two entries; notably the ordering of the bytes is peculiar, this being a "little-endian" cpu.
Accordingly, a table entry is defined by TYPE AREC with a NEXT (to link to the next table entry in a chain) and a BRD array to describe the board layout the entry is for. The payload for this problem consists of a PREV which identifies the entry from which this position was reached, and MOVE which identifies the move that had been made to do so.
The initial idea was to work from the given starting position, ascertaining all positions that could be reached in one step, then from each of those the positions reachable by a second step, and so on, until the "solved" state is reached. This is somewhat like the "all possible paths" of Quantum Electrodynamics when considering photon paths. Necessarily, on first contact the linked-list of PREV entries will be a minimum-length path. Loops are precluded by passing over any candidate new position that has already been reached and so already has an entry in the table: it can be reached by a path of the same or lesser length. In some games, loops are not possible, or are truncated by a special rule as in chess, when on the third attainment of a position a draw is declared. Then reading a remark in the Phix solution prompted the realisation that the flow could start from the "solved" position and stop on attainment of the specified position; the linked list via PREV could be reported in reverse order to go from the specified position back to the solved position. Some games are not symmetrical, as in chess where a pawn can only advance, but in this game, a move from A to B is just as allowable as a move from B to A - indeed, when checking the moves from a position, the reverse of the move that led to that position is skipped - it would just lead to a position that is already in the table and so be passed over. Similarly, the table does not record the possible moves from a position (there being two, three or four of them) but only the one move that led to the position. While there might be two, three, or four such moves possible (from different positions), only one move from one position is recorded, the one that got there first.
Starting a Red Tide from the "solved" or ZERO position has the advantage that if the table is retained, a new run for a different start position would take advantage of the previous effort. A table based around moves from one start position would be of little use when given a different start position.
Alas, the Red Tide ran into too much dry sand. A sixteen-dimensional volume has a lot of space in which it can possess a surface. The revised plan was to spread a Red Tide from the ZERO position and at the same time spread a Blue Tide from the specified start position, hoping that they would meet rather sooner. In Numerical Methods that Work (Usually), F. S. Acton remarks upon "Perverse Formulations", such as "... who insists on solving a boundary-value problem in ordinary differential equations via initial-value techniques may get away with it for a while, but ..." One can easily imagine pouring red paint onto the floor in one place, and blue paint in another place: most of the extension of the puddles is in directions that will not meet. With a single puddle, very little of the expansion is towards the target. Details are shown in the results.
A great deal of computer effort could be avoided if the spread could be given good guidance. For instance, a function that for any given position, gives the minimum number of moves needed to reach the ZERO position from it. Thus, from the start position, evaluate the function for each of the positions that can be reached via the available moves (at most, four), and select that one with the smallest value; repeat until at ZERO. Such a function certainly exists, though our ingenuity may not bring it forth. Perhaps some thought may do so. Perhaps not any time soon. But in any case, there is a definite procedure for generating such a function, and it is simple. Analyse all the board positions (they are finite in number) as in the Red Tide process, for each entry retaining the number of moves needed to reach that position from ZERO. Clearly, this is computable by a Turing Machine and so the function is computable, and so exists.
Such a guide function is rather like a "distance" function, so along these lines, when a minimum-step move sequence is found, the distances of each position from ZERO are calculated by various distance functions and the results shown in the output. Notably, function ZDIST calculates an encodement of the board position by referring to the layout of the ZERO position. It relies on the first square of a position having sixteen possible values, then the second square has fifteen and so on down; the number of possible layouts is 16! rather than 1616. Given the list of values of the squares in the ZERO sequence, values that have been taken are marked off (in array AVAIL) and the count of possibilities remaining as each square is identified reduces. The ZDIST number is like an encodement of an integer from its digits, but with a successively-reducing base.
As an experiment, when the Red Tide was poured to completion for a board of three rows and four columns, every position in the stash was presented to ZDIST and the result written out. The filesystem presented difficulties: reading the stash file as a sequential file failed! So, a slog through reading specified record numbers, one after the other, taking half an hour. By contrast, the B6700 filesystem of the 1970s employed a feature called "diagonal I/O" whereby the style of the previous I/O for a file was retained and compared to the style of the new I/O operation: for matching styles, conclusions could be drawn. The first and last few ZDIST values are 0, 105, 1, 328449, 609, 632, 4, 3271809, 3312009, ... 287247191, 446727869, 287039663. That last is entry 23950800 which is 12!/2: every possible attainable position has been tested and stored in the stash (once each), since a parity condition means that half the layout combinations have one parity and half the other, the possible moves being unable to change the parity. Alas, the ZDIST figures do not show anything so simple as odd/even for this. Every value should be unique, but in the past it has suspiciously often been easy to find a proof of a desired situation, so a test: sort the values and check. UltraEdit ran for a long time, then reported that there was insufficient memory to maintain an "undo" list. Very well. And then it wiped the file! Fortunately, the stash was still intact. On restarting in Linux the "sort" utility was available, and after some impressive running of all six cpus at 100% in cyclic bursts, I was looking at a file in a mad order: 0, 1, 10, 100, 1000, 10000, ... Apparently some sort of "word" order, even though the text file used leading spaces so that the numbers were all aligned right. As usual, the "man"ual information was brief and vague, but option "g" for "general number" looked likely, and so it proved. In sorted order: 0, 1, 4, 8, 9, 11, 12, 13, ... 479001589, 479001590, 479001593, 479001594, 479001597, 479001598. And 12! = 479001600. All values were unique.
The ZDIST function would be a candidate for a hash function, as it looks to give a good spray. But it requires rather more computation. It is always possible to calculate a "perfect" hash function, one that not only gives a distinct integer value for every possible key but also produces no gaps, so if there are N keys, there are N hash values in the range 1:N (or 0:N - 1) and the mapping is one to one. There even exist "hyper perfect" hash functions, that possess useful ordering properties: an example is the conversion of dates to a day number, which is one-to-one, without gaps, and ordered by date. However, the calculation of such perfection may be lengthy, so a fast hash is preferable, except for special cases.
In the event, when running, TaskInfo showed that almost all of the time was spent in the filesystem's I/O procedures, no "user time" was visible. The hash calculation indeed was fast, but the I/O was slow. Probably because the disc file was scattered in blocks across the disc device (actually a solid-state drive) and finding the appropriate block took a lot of messing about. In the past, a large disc file would be in one or very few pieces on the actual disc, with a straightforward direct calculation between a record number and a disc's corresponding cylinder, surface, track and sector. These days, the operating system uses "spare" memory to hold the content of recently-used disc blocks, but alas, each index file is 781MB, and the stash files are over 3,000MB. Some systems have many gigabytes of memory, but this one has 4GB.
The Code
The source code started off as a mainline only, but then facilities were added and service routines became helpful. This prompted the use of F90's MODULE facility so that the PARAMETER statement could be used to describe the shape of the board with this information available to each routine without the need for passing the values as parameters or messing with COMMON storage, or repeating the PARAMETER statement in each routine. Otherwise, literal constants such as 4 would appear in various places. These appearances could now be documented by using the appropriate name such as NR and NC rather than just 4 and similar. However, inside FORMAT statements the use of <NR - 1> (and not <NC - 1>) rather than 3 will succeed only if the compiler accepts this usage, and not all do. More complex calculations involving the board size have not been attempted. The PARAMETER facility is useful only for simple calculations, and the compiler typically does not allow the use of many functions, even library functions, in expressions. Considerations such as a 4x4 board having 16 squares is easy, but the consequences of this count fitting into a four-bit binary field are not, thus the equivalences involving BOARD, BORED and BOAR are not general for different board shapes, nor are the column headings adjustable. Similarly, subroutine UNPACK does not attempt to use a loop but employs explicit code.
This approach is also followed in the calculation of the hash code. Not using a loop (for two items only) but, by writing out the product rather than using the compiler's built-in PRODUCT function. A startling difference results:
59: H = MOD(ABS(PRODUCT(BRD)),APRIME) 004016E3 mov esi,1 004016E8 mov ecx,1 004016ED cmp ecx,2 004016F0 jg MAIN$SLIDESOLVE+490h (0040171e) 004016F2 cmp ecx,1 004016F5 jl MAIN$SLIDESOLVE+46Eh (004016fc) 004016F7 cmp ecx,2 004016FA jle MAIN$SLIDESOLVE+477h (00401705) 004016FC xor eax,eax 004016FE mov dword ptr [ebp-54h],eax 00401701 dec eax 00401702 bound eax,qword ptr [ebp-54h] 00401705 imul edx,ecx,4 00401708 mov edx,dword ptr H (00473714)[edx] 0040170E imul edx,esi 00401711 mov esi,edx 00401713 mov eax,ecx 00401715 add eax,1 0040171A mov ecx,eax 0040171C jmp MAIN$SLIDESOLVE+45Fh (004016ed) 0040171E mov eax,esi 00401720 cmp eax,0 00401725 jge MAIN$SLIDESOLVE+49Bh (00401729) 00401727 neg eax 00401729 mov edx,10549h 0040172E mov dword ptr [ebp-54h],edx 00401731 cdq 00401732 idiv eax,dword ptr [ebp-54h] 00401735 mov eax,edx 00401737 mov dword ptr [H (00473714)],eax 60: write (6,*) H,bored
Whereas by writing out the product,
59: H = MOD(ABS(BRD(1)*BRD(2)),APRIME) 004016E3 mov eax,dword ptr [BRD (00473718)] 004016E9 imul eax,dword ptr [BRD+4 (0047371c)] 004016F0 cmp eax,0 004016F5 jge MAIN$SLIDESOLVE+46Bh (004016f9) 004016F7 neg eax 004016F9 mov esi,10549h 004016FE cdq 004016FF idiv eax,esi 00401701 mov eax,edx 00401703 mov dword ptr [H (00473714)],eax 60: write (6,*) H,bored
(The source below has the ABS outside the MOD: I don't care what sort of mod is used here, just that negative numbers be as scrambled as positive) In both cases the array indexing is checkable by the compiler at compile time so that there need be no run-time checking on that. Such bound checking may be not as strict as might be expected when EQUIVALENCE tricks are involved. In tests with a variant board size of 3x4, the board position array was declared BOARD(N) where N = 12, but was still equivalenced to BORED(4) and so still allowed room for sixteen elements in BOARD. Subroutine UNPACK was not written to deal with anything other than a 4x4 board and so accessed elements 13, 14, 15, and 16 of BOARD that were outside its declared upper bound of 12, but no run-time objection was made. Similarly with a 3x3 board.
Granted a flexible pre-processor scheme (as in pl/i, say) one could imagine a menu of tricks being selected from according to the board shape specified, but without such a facility, the constants are merely named rather than literal. Any change, such as to a 3x4 board, can be made by adjusting the appropriate PARAMETER and many usages will adjust accordingly. Others will require adjustment by the diligent programmer for good results. In the absence of a pre-processor one could present the various possible code sequences surrounded by tests as in
IF (NR.EQ.4) THEN
code specialised for NR = 4
ELSE IF (NR.EQ.3) THEN
code specialised for NR = 3
END IF
and hope that the compiler would carry forward the actual value of NR into the IF-statement's conditional expression, recognise that the result is also constant (for the current compilation with a particular value of NR) and so generate code only for the case that the expression came out as true, without any test to select this being employed in the compiled code. This soon becomes a tangle of combinations, and has not been attempted. And there could be difficulties too. One wonders if, say, with NR = 3, the specialised code for the NR = 4 case could contain a mention of element 4 of an array which is actually of size NR. Would the compiler regard this as an error, given that it will be discarding this code anyway? Even if one used NR rather than a literal such as 4 there could still be problems, such as code calling for a division by (NR - 3).
Implementing the plan had its problems. Since the INDEX array is accessed randomly it should be in memory, but alas if it is large (and now there are two of them) the Compaq Visual Fortran 6.6 F90/95 compiler complains "total image size exceeds max (268435456): image may not run" - but if it is not so large, when many entries are made the hash separation will be heavily overloaded and the chains of entries with equal hash codes will not be short. One could possibly mess about with allocatable arrays as a different storage scheme is used for them, but instead, a disc file for the index array as well as a stash file for the entries. This also would mean that the stash and its index could survive for another run, otherwise if the index data were in memory only, some scheme would be needed to save the index, or to redevelop the index from the stash file on a restart. Both the stash and index files require random access, but the stash file grows sequentially. The index file however has to start full-sized, with all values zero. The obvious ploy of writing zero values to the file as a sequential file works well enough, but on re-opening the index file for random access, there are complaints about accessing a non-existing record. By initialising the file via random access, writing a zero to record one, two, three, etc. sequentially, no such complaint appeared and everything worked. But the initialisation was very slow, taking many minutes. Oddly, writing a zero to the last record without doing anything to intervening records not only worked but did so rapidly. It appeared that the intervening records were not prepared by the I/O subsystem at all, as very little I/O action took place. At a guess, only if a filesystem's allocation block was written to was that block made into a proper file piece with all zero values.
During these developments, a mistype produced an odd result. With F90, many array operations became possible, and accidentally, I typed WRITE (WRK,REC = array) etc but omitted to specify which element of the array was to be used, as in WRITE (WRK,REC = array(1)) etc A positive interpretation of this construction would be to hope that the I/O list (the etc) would be written to multiple records of I/O unit WRK, to array(1), array(2), and so on without re-evaluation of the I/O list. Alas, a file containing 19MB of zeroes resulted. Obviously some mistake. Similarly, one could hope that WRITE (OUT,66) stuff where OUT(1) = 6 (for standard output), and OUT(2) = 10 (a disc file, logging what has been written) would save on repeating WRITE statements, but alas, compatibility with older Fortran requires that such a statement places its output into the storage occupied by array OUT. This might be avoided by a variant form, WRITE (UNIT = OUT,66) stuff to signify that I/O unit numbers are being given, but alas, the compiler doesn't agree.
Source
SUBROUTINE PROUST(T) !Remembrance of time passed.
DOUBLE PRECISION T !The time, in seconds. Positive only, please.
DOUBLE PRECISION S !A copy I can mess with.
TYPE TIMEWARP !Now prepare a whole lot of trickery for expressing the wait time.
INTEGER LIMIT !The upper limit for the usage.
INTEGER STEP !Conversion to the next unit.
CHARACTER*4 NAME !A suitable abbreviated name for the accepted unit.
END TYPE TIMEWARP !Enough of this.
INTEGER CLOCKCRACK !How many different units might I play with?
PARAMETER (CLOCKCRACK = 5) !This should so.
TYPE(TIMEWARP) TIME(CLOCKCRACK) !One set, please.
PARAMETER (TIME = (/ !The mention of times lost has multiple registers.
1 TIMEWARP(99, 60,"secs"), !Beware 99.5+ rounding up to 100.
2 TIMEWARP(99, 60,"mins"), !Likewise with minutes.
3 TIMEWARP(66, 24,"hrs!"), !More than a few days might as well be in days.
4 TIMEWARP(99,365,"days"), !Too many days, and we will speak of years.
5 TIMEWARP(99,100,"yrs!")/)) !And the last gasp converts to centuries.
INTEGER CC !A stepper for these selections.
CHARACTER*4 U !The selected unit.
INTEGER MSG !The mouthpiece.
COMMON/IODEV/ MSG !Used in common.
S = T !A working copy.
DO CC = 1,CLOCKCRACK !Now re-assess DT, with a view to announcing a small number.
IF (S.LE.TIME(CC).LIMIT) THEN !Too big a number?
U = TIME(CC).NAME !No, this unit will suffice.
GO TO 10 !Make off to use it.
END IF !But if the number is too big,
S = S/TIME(CC).STEP !Escalate to the next larger unit.
END DO !And see if that will suffice.
U = "Cys!!" !In case there are too many years, this is the last gasp.
10 WRITE (MSG,11) S,U !Say it.
11 FORMAT (F7.1,A4,$) !But don't finish the line.
END SUBROUTINE PROUST !A sigh.
CHARACTER*15 FUNCTION HMS(T) !Report the time of day.
Careful! Finite precision and binary/decimal/sexagesimal conversion could cause 2:30:00am. to appear as 2:29:60am.
DOUBLE PRECISION S,T !Seconds (completed) into the day.
INTEGER H,M !More traditional units are to be extracted.
INTEGER SECONDSINDAY !A canonical day.
PARAMETER (SECONDSINDAY = 24*60*60) !Of nominal seconds.
CHARACTER*15 TEXT !A scratchpad.
H = T !Truncate into an integer.
S = T - (H - 1)/SECONDSINDAY*SECONDSINDAY !Thus allow for midnight = hour 24.
IF (S.EQ.SECONDSINDAY/2) THEN !This might happen.
TEXT = "High Noon!" !Though the chances are thin.
ELSE IF (S.EQ.SECONDSINDAY) THEN !This is synonymous with the start of the next day.
TEXT = "Midnight!" !So this presumably won't happen.
ELSE !But more likely are miscellaneous values.
H = S/3600 !Convert seconds into whole hours completed.
S = S - H*3600 !The remaining time.
M = S/60 !Seconds into minutes completed.
S = S - M*60 !Remove them.
IF (S .GE. 59.9995D0) THEN !Via format F6.3, will this round up to 60?
S = 0 !Yes. Curse recurring binary sequences for decimal.
M = M + 1 !So, up the minute count.
IF (M.GE.60) THEN !Is there an overflow here too?
M = 0 !Yes.
H = H + 1 !So might appear 24:00:00.000 though it not be Midnight!
END IF !So much for twiddling the minutes.
END IF !And twiddling the hours.
IF (H.LT.12) THEN !A plague on the machine mentality.
WRITE (TEXT,1) H,M,S,"am." !Ante-meridian.
1 FORMAT (I2,":",I2,":",F6.3,A3) !Thus.
ELSE !For the post-meridian, H >= 12.
IF (H.GT.12) H = H - 12 !Adjust to civil usage. NB! 12 appears.
WRITE (TEXT,1) H,M,S,"pm." !Thus. Post-meridian.
END IF !So much for those fiddles.
IF (TEXT(4:4).EQ." ") TEXT(4:4) = "0" !Now help hint that the
IF (TEXT(7:7).EQ." ") TEXT(7:7) = "0" ! character string is one entity.
END IF !So much for preparation.
HMS = TEXT !The result.
END FUNCTION HMS !Possible compiler confusion if HMS is invoked in a WRITE statement.
DOUBLE PRECISION FUNCTION NOWWAS(WOT) !Ascertain the local time for interval assessment.
Compute with whole day numbers, to avoid day rollover annoyances.
Can't use single precision and expect much discrimination within a day.
C I'd prefer a TIMESTAMP(Local) and a TIMESTAMP(GMT) system function.
C Quite likely, the system separates its data to deliver the parameters, which I then re-glue.
INTEGER WOT !What sort of time do I want?
REAL*8 TIME !A real good time.
INTEGER MARK(8) !The computer's clock time will appear here, but fragmented.
IF (WOT.LE.0) THEN !Just the CPU time for this.
CALL CPU_TIME(TIME) !Apparently in seconds since starting.
ELSE !But normally, I want a time-of-day now.
CALL DATE_AND_TIME(VALUES = MARK) !Unpack info that I will repack.
c WRITE (6,1) MARK
c 1 FORMAT ("The computer clock system reports:",
c 1 /"Year",I5,", Month",I3,", Day",I3,
c 2 /" Minutes from GMT",I5,
c 3 /" Hour",I3,", Minute",I3,",Seconds",I3,".",I3)
TIME = (MARK(5)*60 + MARK(6))*60 + MARK(7) + MARK(8)/1000D0 !By the millisecond, to seconds.
IF (WOT.GT.1) TIME = TIME - MARK(4)*60 !Shift back to GMT, which may cross a day boundary.
c TIME = DAYNUM(MARK(1),MARK(2),MARK(3)) + TIME/SECONDSINDAY !The fraction of a day is always less than 1 as MARK(5) is declared < 24.
TIME = MARK(3)*24*60*60 + TIME !Not bothering with DAYNUM, and converting to use seconds rather than days as the unit.
END IF !A simple number, but, multiple trickeries. The GMT shift includes daylight saving's shift...
NOWWAS = TIME !Thus is the finger of time found.
END FUNCTION NOWWAS !But the Hand of Time has already moved on.
MODULE SLIDESOLVE !Collect the details for messing with the game board.
INTEGER NR,NC,N !Give names to some sizes.
PARAMETER (NR = 4, NC = 4, N = NR*NC) !The shape of the board.
INTEGER*1 BOARD(N),TARGET(N),ZERO(N) !Some scratchpads.
INTEGER BORED(4) !A re-interpretation of the storage containing the BOARD.
CHARACTER*(N) BOAR !Another, since the INDEX function only accepts these.
EQUIVALENCE (BORED,BOARD,BOAR) !All together now!
CHARACTER*1 DIGIT(0:35) !This will help to translate numbers to characters.
PARAMETER (DIGIT = (/"0","1","2","3","4","5","6","7","8","9",
1 "A","B","C","D","E","F","G","H","I","J", !I don't anticipate going beyond 15.
2 "K","L","M","N","O","P","Q","R","S","T", !But, for completeness...
3 "U","V","W","X","Y","Z"/)) !Add a few more.
CONTAINS
SUBROUTINE SHOW(NR,NC,BOARD) !The layout won't work for NC > 99...
INTEGER NR,NC !Number of rows and columns.
INTEGER*1 BOARD(NC,NR) !The board is stored transposed, in Furrytran!
INTEGER R,C !Steppers.
INTEGER MSG !Keep the compiler quiet.
COMMON/IODEV/ MSG !I talk to the trees...
WRITE (MSG,1) (C,C = 1,NC) !Prepare a heading.
1 FORMAT ("Row|",9("__",I1,:),90("_",I2,:)) !This should suffice.
DO R = 1,NR !Chug down the rows, for each showing a succession of columns.
WRITE (MSG,2) R,BOARD(1:NC,R) !Thus, successive elements of storage. Storage style is BOARD(column,row).
2 FORMAT (I3,"|",99I3) !Could use parameters, but enough.
END DO !Show columns across and rows down, despite the storage order.
END SUBROUTINE SHOW !Remember to transpose the array an odd number of times.
SUBROUTINE UNCRAM(IT,BOARD) !Recover the board layout..
INTEGER IT(2) !Two 32-bit integers hold 16 four-bit fields in a peculiar order.
INTEGER*1 BOARD(*) !This is just a simple, orderly sequence of integers.
INTEGER I,HIT !Assistants.
DO I = 0,8,8 !Unpack into the work BOARD.
HIT = IT(I/8 + 1) !Grab eight positions, in four bits each..
BOARD(I + 5) = IAND(HIT,15) !The first is position 5.
HIT = ISHFT(HIT,-4); BOARD(I + 1) = IAND(HIT,15) !Hex 48372615
HIT = ISHFT(HIT,-4); BOARD(I + 6) = IAND(HIT,15) !and C0BFAE9D
HIT = ISHFT(HIT,-4); BOARD(I + 2) = IAND(HIT,15) !For BOARD(1) = 1, BOARD(2) = 2,...
HIT = ISHFT(HIT,-4); BOARD(I + 7) = IAND(HIT,15) !This computer is (sigh) little-endian.
HIT = ISHFT(HIT,-4); BOARD(I + 3) = IAND(HIT,15) !Rather than mess with more loops,
HIT = ISHFT(HIT,-4); BOARD(I + 8) = IAND(HIT,15) !Explicit code is less of a brain strain.
HIT = ISHFT(HIT,-4); BOARD(I + 4) = IAND(HIT,15) !And it should run swiftly, too...
END DO !Only two of them.
END SUBROUTINE UNCRAM !A different-sized board would be a problem too.
INTEGER*8 FUNCTION ZDIST(BOARD) !Encode the board's positions against the ZERO sequence.
INTEGER*1 BOARD(N) !The values of the squares.
LOGICAL*1 AVAIL(N) !The numbers will be used one-by-one to produce ZC.
INTEGER BASE !This is not a constant, such as ten.
INTEGER M,IT !Assistants.
AVAIL = .TRUE. !All numbers are available.
BASE = N !The first square has all choices.
ZDIST = 0 !Start the encodement of choices.
DO M = 1,N !Step through the board's squares.
IT = BOARD(M) !Grab the square's number. It is the index into ZERO.
IF (IT.EQ.0) IT = N !But in ZERO, the zero is at the end, damnit.
AVAIL(IT) = .FALSE. !This number is now used.
ZDIST = ZDIST*BASE + COUNT(AVAIL(1:IT - 1)) !The number of available values to skip to reach it.
BASE = BASE - 1 !Option count for the next time around.
END DO !On to the next square.
END FUNCTION ZDIST !ZDIST(ZERO) = 0.
SUBROUTINE REPORT(R,WHICH,MOVE,BRD) !Since this is invoked in two places.
INTEGER R !The record number of the position.
CHARACTER*(*) WHICH !In which stash.
CHARACTER*1 MOVE !The move code.
INTEGER BRD(2) !The crammed board position.
INTEGER*1 BOARD(N) !Uncrammed for nicer presentation.
INTEGER*8 ZC !Encodes the position in a mixed base.
INTEGER ZM,ZS !Alternate forms of distance.
DOUBLE PRECISION ZE !This is Euclidean.
INTEGER MSG !Being polite about usage,
COMMON/IODEV/MSG !Rather than mysterious constants.
CALL UNCRAM(BRD,BOARD) !Isolate the details.
ZM = MAXVAL(ABS(BOARD - ZERO)) !A norm. |(x,y)| = r gives a square shape.
ZS = SUM(ABS(BOARD - ZERO)) !A norm. |(x,y)| = r gives a diamond shape.
ZE = SQRT(DFLOAT(SUM((BOARD - ZERO)**2))) !A norm. |(x,y)| = r gives a circle.
ZC = ZDIST(BOARD) !Encodement against ZERO.
WRITE (MSG,1) R,WHICH,MOVE,DIGIT(BOARD),ZM,ZS,ZE,ZC !After all that,
1 FORMAT (I11,A6,A5,1X,"|",<NR - 1>(<NC>A1,"/"),<NC>A1,"|", !Show the move and the board
1 2I8,F12.3,I18) !Plus four assorted distances.
END SUBROUTINE REPORT !Just one line is produced.
SUBROUTINE PURPLE HAZE(BNAME) !Spreads a red and a blue tide.
CHARACTER*(*) BNAME !Base name for the work files.
CHARACTER*(N) BRAND !Name part based on the board sequence.
CHARACTER*(LEN(BNAME) + 1 + N + 4) FNAME !The full name.
Collect the details for messing with the game board.
CHARACTER*4 TIDE(2) !Two tides will spread forth.
PARAMETER (TIDE = (/" Red","Blue"/)) !With these names.
INTEGER LZ,LOCZ(2),LOCI(2),ZR,ZC !Location via row and column.
EQUIVALENCE(LOCZ(1),ZR),(LOCZ(2),ZC) !Sometimes separate, sometimes together.
INTEGER WAY(4),HENCE,W,M,D,WAYS(2,4) !Direction codes.
PARAMETER (WAY = (/ +1, -NC, -1, +NC/)) !Directions for the zero square, in one dimension.
PARAMETER (WAYS = (/0,+1, -1,0, 0,-1, +1,0/)) !The same, but in (row,column) style.
CHARACTER*1 WNAMEZ(0:4),WNAMEF(0:4) !Names for the directions.
PARAMETER (WNAMEZ = (/" ","R","U","L","D"/)) !The zero square's WAYS.
PARAMETER (WNAMEF = (/" ","L","D","R","U"/)) !The moved square's ways are opposite.
Create two hashed stashes. A stash file and its index file, twice over.
INTEGER APRIME !Determines the size of the index.
PARAMETER (APRIME = 199 999 991) !Prime 11078917. Prime 6666666 = 116 743 349. Perhaps 1999999973?
INTEGER HCOUNT(2),NINDEX(2) !Counts the entries in the stashes and their indices.
INTEGER P,HIT !Fingers to entries in the stash.
INTEGER SLOSH,HNEXT !Advances from one surge to the next.
INTEGER IST(2),LST(2),SURGE(2) !Define the perimeter of a surge.
INTEGER HEAD,LOOK !For chasing along a linked-list of records.
TYPE AREC !Stores the board position, and helpful stuff.
INTEGER NEXT !Links to the next entry that has the same hash value.
INTEGER PREV !The entry from which this position was reached.
INTEGER MOVE !By moving the zero in this WAY.
INTEGER BRD(2) !Squeezed representation of the board position.
END TYPE AREC !Greater compaction (especially of MOVE) would require extra crunching.
INTEGER LREC !Record length, in INTEGER-size units. I do some counting.
PARAMETER (LREC = 5) !For the OPEN statement.
TYPE(AREC) ASTASH,APROBE !I need two scratchpads.
INTEGER NCHECK !Number of new positions considered.
INTEGER NLOOK(2),PROBES(2),NP(2),MAXP(2)!Statistics for the primary and secondary searches resulting.
LOGICAL SURGED(2) !A SLOSH might not result in a SURGE.
Catch the red/blue meetings, if any.
INTEGER MANY,LONG !They may be many, and, long.
PARAMETER (MANY = 666,LONG = 66) !This should do.
INTEGER NMET,MET(2,MANY) !Identify the meeting positions, in their own stash.
INTEGER NTRAIL,TRAIL(LONG) !Needed to follow the moves.
INTEGER NS,LS(MANY) !Count the shove sequences.
CHARACTER*128 SHOVE(MANY) !Record them.
Conglomeration of support stuff.
LOGICAL EXIST !For testing the presence of a disc file.
INTEGER I,IT !Assistants.
DOUBLE PRECISION T1,T2,E1,E2,NOWWAS !Time details.
CHARACTER*15 HMS !A clock.
INTEGER MSG,KBD,WRK(2),NDX(2) !I/O unit numbers.
COMMON/IODEV/ MSG,KBD,WRK,NDX !I talk to the trees...
NS = 0 !No shove sequences have been found.
Concoct some disc files for storage areas, reserving the first record of each as a header.
10 BOARD = ZERO !The red tide spreads from "zero".
DO W = 1,2 !Two work files are required.
WRITE(MSG,11) TIDE(W) !Which one this time?
11 FORMAT (/,"Tide ",A) !Might as well supply a name.
DO I = 1,N !Produce a text sequence for the board layout.
BRAND(I:I) = DIGIT(BOARD(I)) !One by one...
END DO !BRAND = DIGIT(BOARD)
FNAME = BNAME//"."//BRAND//".dat" !It contains binary stuff, so what else but data?
INQUIRE (FILE = FNAME, EXIST = EXIST) !Perhaps it is lying about.
20 IF (EXIST) THEN !Well?
WRITE (MSG,*) "Restarting from file ",FNAME !One hopes its content is good.
OPEN (WRK(W),FILE = FNAME,STATUS = "OLD",ACCESS = "DIRECT", !Random access is intended.
1 FORM = "UNFORMATTED",BUFFERED = "YES",RECL = LREC) !Using record numbers as the key.
FNAME = BNAME//"."//BRAND//".ndx" !Now go for the accomplice.
INQUIRE (FILE = FNAME, EXIST = EXIST) !That contains the index.
IF (.NOT.EXIST) THEN !Well?
WRITE (MSG,*) " ... except, no file ",FNAME !Oh dear.
CLOSE(WRK(W)) !So, no index for the work file. Abandon it.
GO TO 20 !And thus jump into the ELSE clause below.
END IF !Seeing as an explicit GO TO would be regarded as improper...
READ (WRK(W),REC = 1) HCOUNT(W),SURGE(W),IST(W),LST(W)!Get the header information.
WRITE (MSG,22) HCOUNT(W),SURGE(W),IST(W),LST(W) !Reveal.
22 FORMAT (" Stashed ",I0,". At surge ",I0, !Perhaps it will be corrupt.
1 " with the boundary stashed in elements ",I0," to ",I0) !If so, this might help the reader.
OPEN (NDX(W),FILE = FNAME,STATUS = "OLD",ACCESS="DIRECT", !Now for the accomplice.
1 FORM = "UNFORMATTED",BUFFERED = "YES",RECL = 1) !One INTEGER per record.
READ(NDX(W), REC = 1) NINDEX(W) !This count is maintained, to avoid a mass scan.
WRITE (MSG,23) NINDEX(W),APRIME !Exhibit the count.
23 FORMAT (" Its index uses ",I0," of ",I0," entries.") !Simple enough.
ELSE !But, if there is no stash, create a new one.
WRITE (MSG,*) "Preparing a stash in file ",FNAME !Start from scratch.
OPEN (WRK(W),FILE = FNAME,STATUS="REPLACE",ACCESS="DIRECT", !I intend non-sequential access...
1 FORM = "UNFORMATTED",BUFFERED = "YES",RECL = LREC) !And, not text.
HCOUNT(W) = 1 !Just one position is known, the final position.
SURGE(W) = 0 !It has not been clambered away from.
IST(W) = 1 !The first to inspect at the current level.
LST(W) = 1 !The last.
WRITE (WRK(W),REC = 1) HCOUNT(W),SURGE(W),IST(W),LST(W),0 !The header.
FNAME = BNAME//"."//BRAND//".ndx" !Now for the associated index file..
WRITE (MSG,*) "... with an index in file ",FNAME !Announce before attempting access.
OPEN (NDX(W),FILE = FNAME,STATUS = "REPLACE",ACCESS= !Lest there be a mishap.
1 "DIRECT",FORM = "UNFORMATTED",BUFFERED = "YES",RECL = 1) !Yep. Just one value per record.
WRITE (MSG,*) APRIME," zero values for an empty index." !This may cause a pause.
NINDEX(W) = 1 !The index will start off holding one used entry.
WRITE (NDX(W),REC = 1) NINDEX(W) !Save this count in the header record.
WRITE (NDX(W),REC = 1 + APRIME) 0 !Zero values will also appear in the gap!
ASTASH.NEXT = 0 !The first index emtry can never collide with another in an empty index.
ASTASH.PREV = 0 !And it is created sufficient unto itself.
ASTASH.MOVE = 0 !Thus, it is not a descendant, but immaculate.
ASTASH.BRD(1) = BORED(1)*16 + BORED(2) !Only four bits of the eight supplied are used.
ASTASH.BRD(2) = BORED(3)*16 + BORED(4) !So interleave them, pairwise.
SLOSH = ASTASH.BRD(1)*ASTASH.BRD(2) !Mash the bits together.
HIT = ABS(MOD(SLOSH,APRIME)) + 2 !Make a hash. Add one since MOD starts with zero.
WRITE (NDX(W),REC = HIT) HCOUNT(W) !Adding another one to dodge the header as well.
WRITE (MSG,24) BOARD,BORED,ASTASH.BRD, !Reveal the stages.
1 SLOSH,SLOSH,SLOSH,APRIME,HIT !Of the mostly in-place reinterpretations.
24 FORMAT (<N>Z2," is the board layout in INTEGER*1",/, !Across the columns and down the rows.
1 4Z8," is the board layout in INTEGER*4",/, !Reinterpret as four integers.
2 2(8X,Z8)," ..interleaved into two INTEGER*4",/, !Action: Interleaved into two.
3 Z32," multiplied together in INTEGER*4",/, !Action: Their product.
4 I32," as a decimal integer.",/, !Abandoning hexadecimal.
5 "ABS(MOD(",I0,",",I0,")) + 2 = ",I0, !The final step.
6 " is the record number for the first index entry.") !The result.
WRITE (WRK(W),REC = HCOUNT(W) + 1) ASTASH !Record one is reserved as a header...
END IF !Either way, a workfile should be ready now.
IF (W.EQ.1) BOARD = TARGET !Thus go for the other work file.
END DO !Only two iterations, but a lot of blather.
SLOSH = MINVAL(SURGE,DIM = 1) !Find the laggard.
Cast forth a heading for the progress table to follow..
WRITE (MSG,99)
99 FORMAT (/,7X,"|",3X,"Tidewrack Boundary Positions |",
1 6X,"Positions",5X,"|",7X,"Primary Probes",9X,"Index Use",
2 4X,"|",5X,"Secondary Probes",3X,"|"," Memory of Time Passed",/,
3 "Surge",2X,"|",6X,"First",7X,"Last",6X,"Count|",
4 4X,"Checked Deja vu%|",7X,"Made Max.L Avg.L| Used%",
5 5X,"Load%|",7X,"Made Max.L Avg.L|",6X,"CPU",8X,"Clock")
Chase along the boundaries of the red and the blue tides, each taking turns as primary and secondary interests.
100 SLOSH = SLOSH + 1 !Another advance begins.
WW:DO W = 1,2 !The advance is made in two waves, each with its own statistics.
M = 3 - W !Finger the other one.
NMET = 0 !No meetings have happened yet.
IF (SURGE(W).GE.SLOSH) CYCLE WW !Prefer to proceed with matched surges.
WRITE (MSG,101) SLOSH,TIDE(W),IST(W),LST(W),LST(W)-IST(W)+1 !The boundary to be searched.
101 FORMAT (I2,1X,A4,"|",3I11,"|",$) !This line will be continued.
NCHECK = 0 !No new positions have been prepared.
NLOOK = 0 !So the stashes have not been searched for any of them.
PROBES = 0 !And no probes have been made in any such searches.
MAXP = 0 !So the maximum length of all probe chains is zero so far.
HNEXT = LST(W) + 1 !This will be where the first new position will be stashed.
T1 = NOWWAS(0) !Note the accumulated CPU time at the start of the boundary ride..
E1 = NOWWAS(2) !Time of day, in seconds. GMT style (thus not shifted by daylight saving)
PP:DO P = IST(W),LST(W) !These are on the edge of the tide. Spreading proceeds.
READ (WRK(W),REC = P + 1) ASTASH !Obtain a position, remembering to dodge the header record.
HENCE = ASTASH.MOVE !The move (from ASTASH.PREV) that reached this position.
IF (HENCE.NE.0) HENCE = MOD(HENCE + 1,4) + 1 !The reverse of that direction. Only once zero. Sigh.
CALL UNCRAM(ASTASH.BRD,BOARD) !Unpack into the work BOARD.
LZ = INDEX(BOAR,CHAR(0)) !Find the BOARD square with zero.
ZR = (LZ - 1)/NC + 1 !Convert to row and column in LOCZ to facilitate bound checking.
ZC = MOD(LZ - 1,NC) + 1 !Two divisions, sigh. Add a special /\ syntax? (ZR,ZC) = (LZ - 1)/\NC + 1
Consider all possible moves from position P, If a new position is unknown, add it to the stash.
DD:DO D = 1,4 !Step through the possible directions in which the zero square might move.
IF (D.EQ.HENCE) CYCLE DD !Don't try going back whence this came.
LOCI = LOCZ + WAYS(1:2,D) !Finger the destination of the zero square, (row,column) style.
IF (ANY(LOCI.LE.0)) CYCLE DD !No wrapping left/right or top/bottom.
IF (ANY(LOCI.GT.(/NR,NC/))) CYCLE DD !No .OR. to avoid the possibility of non-shortcut full evaluation.
NCHECK = NCHECK + 1 !So, here is another position to inspect.
NP = 0 !No probes of stashes W or M for it have been made.
IT = WAY(D) + LZ !Finger the square that is to move to the adjacent zero.
BOARD(LZ) = BOARD(IT) !Move that square's content to the square holding the zero.
BOARD(IT) = 0 !It having departed.
ASTASH.BRD(1) = BORED(1)*16 + BORED(2) !Pack the position list
ASTASH.BRD(2) = BORED(3)*16 + BORED(4) !Without fussing over adjacency,
HIT = ABS(MOD(ASTASH.BRD(1)*ASTASH.BRD(2),APRIME)) + 2 !Crunch the hash index.
READ (NDX(W),REC = HIT) HEAD !Refer to the index, which fingers the first place to look.
LOOK = HEAD !This may be the start of a linked-list.
IF (LOOK.EQ.0) NINDEX(W) = NINDEX(W) + 1 !Or, a new index entry will be made.
IF (LOOK.NE.0) NLOOK(1) = NLOOK(1) + 1 !Otherwise, we're looking at a linked-list, hopefully short.
DO WHILE (LOOK.NE.0) !Is there a stash entry to look at?
NP(1) = NP(1) + 1 !Yes. Count a probe of the W stash.
READ (WRK(W),REC = LOOK + 1) APROBE !Do it. (Dodging the header record)
IF (ALL(ASTASH.BRD.EQ.APROBE.BRD)) GO TO 109 !Already seen? Ignore all such as previously dealt with.
LOOK = APROBE.NEXT !Perhaps there follows another entry having the same index.
END DO !And eventually, if there was no matching entry,
HCOUNT(W) = HCOUNT(W) + 1 !A new entry is to be added to stash W, linked from its index.
IF (HCOUNT(W).LE.0) STOP "HCOUNT overflows!" !Presuming the usual two's complement style.
WRITE (NDX(W),REC = HIT) HCOUNT(W) !The index now fingers the new entry in ASTASH.
ASTASH.NEXT = HEAD !Its follower is whatever the index had fingered before.
ASTASH.PREV = P !This is the position that led to it.
ASTASH.MOVE = D !Via this move.
WRITE (WRK(W),REC = HCOUNT(W) + 1) ASTASH !Place the new entry, dodging the header.
Check the other stash for this new position. Perhaps there, a meeting will be found!
READ (NDX(M),REC = HIT) LOOK !The other stash uses the same hash function but has its own index.
IF (LOOK.NE.0) NLOOK(2) = NLOOK(2) + 1 !Perhaps stash M has something to look at.
DO WHILE(LOOK.NE.0) !Somewhere along a linked-list.
NP(2) = NP(2) + 1 !A thorough look may involve multiple probes.
READ(WRK(M),REC = LOOK + 1) APROBE !Make one.
IF (ALL(ASTASH.BRD.EQ.APROBE.BRD)) THEN!A match?
IF (NMET.LT.MANY) THEN !Yes! Hopefully, not too many already.
NMET = NMET + 1 !Count another.
MET(W,NMET) = HCOUNT(W) !Save a finger to the new entry.
MET(M,NMET) = LOOK !And to its matching counterparty.
ELSE !But if too numerous for my list,
WRITE (MSG,108) TIDE(W),HCOUNT(W),TIDE(M),LOOK !Announce each.
108 FORMAT ("Can't save ",A,1X,I0," matching ",A,1X,I0)!Also wrecking my tabular layout.
END IF !So much for recording a match.
GO TO 109 !Look no further for the new position; it is found..
END IF !So much for a possible match.
LOOK = APROBE.NEXT !Chase along the linked-list.
END DO !Thus checking all those hashing to the same index.
Completed the probe.
109 MAXP = MAX(MAXP,NP) !Track the maximum number of probes in any search..
PROBES = PROBES + NP !As well as their count.
BOARD(IT) = BOARD(LZ) !Finally, undo the move.
BOARD(LZ) = 0 !To be ready for the next direction.
END DO DD !Consider another direction.
END DO PP !Advance P to the next spreading possibility.
Completed one perimeter sequence. Cast forth some statistics.
110 T2 = NOWWAS(0) !A boundary patrol has been completed.
E2 = NOWWAS(2) !And time has passed.
HIT = HCOUNT(W) - HNEXT + 1 !The number of new positions to work from in the next layer.
WRITE (MSG,111) NCHECK,100.0*(NCHECK - HIT)/NCHECK, !Tested, and %already seen
1 NLOOK(1),MAXP(1),FLOAT(PROBES(1))/MAX(NLOOK(1),1), !Search statistics.
2 100.0*NINDEX(W)/APRIME,100.0*HCOUNT(W)/APRIME, !Index occupancy: used entries, and load.
3 NLOOK(2),MAXP(2),FLOAT(PROBES(2))/MAX(NLOOK(2),1) !Other stash's search statistics.
111 FORMAT (I11,F9.2,"|",I11,I6,F7.3,"|",F8.3,F10.3,"|", !Attempt to produce regular columns.
1 I11,I6,F7.3,"|"$) !To be continued...
T1 = T2 - T1 !Thus, how much CPU time was used perusing the perimeter.
E1 = E2 - E1 !Over the elapsed time.
CALL PROUST(T1) !Muse over the elapsed CPU time, in seconds.
CALL PROUST(E1) !And likewise the elapsed clock time.
E2 = NOWWAS(1) !Civil clock, possibly adjusted for daylight saving.
IF (E1.LE.0) THEN !The offered timing may be too coarse.
WRITE (MSG,112) HMS(E2) !So, just finish the line.
112 FORMAT (8X,A) !With a time of day.
ELSE !But if some (positive) clock time was measured as elapsing,
WRITE (MSG,113) T1/E1*100,HMS(E2) !Offer a ratio as well.
113 FORMAT (F6.2,"%",1X,A) !Percentages are usual.
END IF !Enough annotation.
Could there be new positions to check? HCOUNT will have been increased if so.
SURGED(W) = HCOUNT(W).GE.HNEXT !The boundary has been extended to new positions.
IF (SURGED(W)) THEN !But, are there any new positions?
IST(W) = HNEXT !Yes. The first new position would have been placed here.
LST(W) = HCOUNT(W) !This is where the last position was placed.
SURGE(W) = SLOSH !The new surge is ready.
WRITE (WRK(W),REC = 1) HCOUNT(W),SURGE(W),IST(W),LST(W) !Update the headers correspondingly..
WRITE (NDX(W), REC = 1) NINDEX(W) !Otherwise, a rescan would be needed on a restart.
ELSE IF (SURGE(W) + 1 .EQ. SLOSH) THEN !No new positions. First encounter?
LOOK = LST(W) - IST(W) + 1 !Yes. How many dead ends are there?
WRITE (MSG,114) LOOK !Announce.
114 FORMAT (/,"The boundary has not surged to new positions!",/
1 "The now-static boundary has ",I0)
LOOK = LOOK/666 + 1 !If there are many, don't pour forth every one.
IF (LOOK.GT.1) WRITE (MSG,115) LOOK!Some restraint.
115 FORMAT (6X,"... Listing step: ",I0)!Rather than rolling forth a horde.
WRITE (MSG,121) !Re-use the heading for the REPORT.
DO P = IST(W),LST(W),LOOK !Step through the dead ends, possibly sampling every one.
READ (WRK(W),REC = P + 1) ASTASH !Grab a position.
CALL REPORT(P,TIDE(W),WNAMEF(ASTASH.MOVE),ASTASH.BRD) !Describe it.
END DO !On to the next dead end.
END IF !Perhaps the universe has been filled.
Could the clouds have touched? If so, two trails have met.
120 ML:DO P = 1,NMET !Step through the meeting list.
IF (NS.LT.MANY) NS = NS + 1!Note another shove sequence.
LS(NS) = 0 !Details to be determined.
WRITE (MSG,121) !Announce, via a heading.
121 FORMAT (/,5X,"Record Stash Move |Board layout by row|", !Various details
1 2X,"Max|d| Sum|d| Euclidean Encoded vs Zero") !Will be attached.
NTRAIL = 1 !Every trail starts with its first step.
TRAIL(1) = MET(2,P) !This is the blue trail's position that met the red tide..
122 READ(WRK(2),REC = TRAIL(NTRAIL) + 1) ASTASH !Obtain details
IF (ASTASH.PREV.NE.0) THEN !Had this step arrived from somewhere?
IF (NTRAIL.GE.LONG) STOP "The trail is too long!" !Yes.
NTRAIL = NTRAIL + 1 !Count another step.
TRAIL(NTRAIL) = ASTASH.PREV !Finger the preceding step.
GO TO 122 !And investigate it in turn.
END IF !Thus follow the blue trail back to its origin.
130 DO LOOK = NTRAIL,1,-1 !The end of the blue trail is the position in TARGET, the start position.
READ(WRK(2),REC = TRAIL(LOOK) + 1) ASTASH !Grab a position, dodging the header.
CALL REPORT(TRAIL(LOOK),"Blue",WNAMEF(ASTASH.MOVE), !Backwards*backwards = forwards.
1 ASTASH.BRD) !The board layout is always straightforward...
IF (LOOK.NE.NTRAIL) THEN !The start position has no move leading to it.
IF (LS(NS).LT.LEN(SHOVE(1))) LS(NS) = LS(NS) + 1 !But count all subsequent ssociated moves.
SHOVE(NS)(LS(NS):LS(NS)) = WNAMEF(ASTASH.MOVE) !Place it.
END IF !So much for that move.
END DO !On to the next move away from the start position.
140 HEAD = 0 !Syncopation. Prevent the first position of the red trail from being listed.
LOOK = MET(1,P) !It is the same position as the first in the TRAIL, but in the primary stash.
DO WHILE(LOOK.NE.0) !The red chain runs back to its starting position, which is the "solution" state..
READ(WRK(1),REC = LOOK + 1) ASTASH !Which is in the direction I want to list.
IF (HEAD.NE.0) THEN !Except that the moves are one step behind for this list.
CALL REPORT(LOOK,"Red",WNAMEZ(HEAD),ASTASH.BRD) !As this sequence is not being reversed.
IF (LS(NS).LT.LEN(SHOVE(1))) LS(NS) = LS(NS) + 1 !This lists the moves in forwards order.
SHOVE(NS)(LS(NS):LS(NS)) = WNAMEZ(HEAD) !But the directions are reversed....
END IF !This test avoids listing the "Red" position that is the same as the last "Blue" position.
HEAD = ASTASH.MOVE !This is the move that led to this position.
LOOK = ASTASH.PREV !From the next position, which will be listed next.
END DO !Thus, the listed position was led to by the previous position's move.
150 DO I = 1,NS - 1 !Perhaps the move sequence has been found already.
IF (SHOVE(I)(1:LS(I)).EQ.SHOVE(NS)(1:LS(NS))) THEN !So, compare agains previous shoves.
WRITE (MSG,151) I !It has been seen.
151 FORMAT (6X,"... same as for sequence ",I0) !Humm.
NS = NS - 1 !Eject the arriviste.
GO TO 159 !And carry on.
END IF !This shouldn't happen...
END DO !On to the next comparison.
WRITE (MSG,152) LS(NS),SHOVE(NS)(1:LS(NS)) !Show the moves along a line.
152 FORMAT (I4," moves: ",A) !Surely plural? One-steps wouldn't be tried?
159 END DO ML !Perhaps another pair of snakes have met.
END DO WW !Advance W to the other one. M will be swapped correspondingly.
Could there be an end to it all?
IF (.NOT.ANY(SURGED)) STOP "No progress!" !Oh dear.
IF (NMET.LE.0) GO TO 100 !Keep right on to the end of the road...
END SUBROUTINE PURPLE HAZE !That was fun!
END MODULE SLIDESOLVE
PROGRAM POKE
USE SLIDESOLVE
CHARACTER*(19) FNAME !A base name for some files.
INTEGER I,R,C !Some steppers.
INTEGER MSG,KBD,WRK(2),NDX(2) !I/O unit numbers.
COMMON/IODEV/ MSG,KBD,WRK,NDX !I talk to the trees..
KBD = 5 !Standard input. (Keyboard)
MSG = 6 !Standard output.(Display screen)
WRK = (/10,12/) !I need two work files,
NDX = WRK + 1 !Each with its associated index.
WRITE (FNAME,1) NR,NC !Now prepare the file name.
1 FORMAT ("SlideSolveR",I1,"C",I1,".txt") !Allowing for variation, somewhat.
WRITE (MSG,2) NR,NC,FNAME !Announce.
2 FORMAT ("To play 'slide-square' with ",I0," rows and ",
1 I0," columns.",/,"An initial layout will be read from file ",
2 A,/,"The objective is to attain the nice orderly layout"
3 " as follows:",/)
FORALL(I = 1:N - 1) ZERO(I) = I !Regard the final or "solution" state as ZERO.
ZERO(N) = 0 !The zero sqiuare is at the end, damnit!
CALL SHOW(NR,NC,ZERO) !Show the squares in their "solved" arrangement: the "Red" stash.
OPEN(WRK(1),FILE=FNAME,STATUS="OLD",ACTION="READ") !For formatted input.
DO R = 1,NR !Chug down the rows, reading successive columns across a row..
READ (WRK(1),*) (TARGET((R - 1)*NC + C), C = 1,NC) !Into successive storage locations.
END DO !Furrytran's storage order is (column,row) for that, alas.
CLOSE (WRK(1)) !A small input, but much effort follows.
WRITE (MSG,3) !Now show the supplied layout.
3 FORMAT (/,"The starting position:") !The target, working backwards.
CALL SHOW(NR,NC,TARGET) !This will be the starting point for the "Blue" stash.
IF (ALL(TARGET.EQ.BOARD)) STOP "Huh? They're the same!" !Surely not.
WRITE (MSG,4)
4 FORMAT (/'The plan is to spread a red tide from the "solved" ',
1 "layout and a blue tide from the specified starting position.",/
2 "The hope is that these floods will meet at some position,",
3 " and the blue moves plus the red moves in reverse order,",/
4 "will be the shortest sequence from the given starting",
5 " position to the solution.")
CALL PURPLE HAZE(FNAME(1:14))
END
The Results
An important feature of the stash file is that its sequential growth makes it easy to keep track of which entries are on the current boundary. Its positions are stored in entry First (IST) to Last (LST) inclusive, and as the new boundary is identified and checked, its accepted positions are placed in the stash following the last entry to become the First:Last span for the next surge. When a candidate new position is checked, it may be that it is already in the stash so it is declared "Already seen" and ignored. This check can be swift, as if the value of INDEX(H) is zero then that hash code has not been seen before and so the position can't be in the stash. As more and more INDEX entries are used, the proportion of zero INDEX values falls, as tracked by the column headed Used%, and different positions may fall upon the same index entry because their hash numbers are the same. Thus the column headed Load% shows the total number of positions stashed divided by the number of index entries available, the value of APRIME. Some index entries will doubtless remain unused even as others are overloaded. It is important that the hash calculation sprays evenly, avoiding clumps.
If an index value is non-zero, then the candidate position's layout must be compared to the layout of each of the positions that have been linked together as having that hash number. Each comparison is a probe of the stash (the disc record must be read) and hopefully, the average number of probes remains a small number, such as one. Perhaps a match will be found early in the chain, but hopefully, most chains are short. Thus the columns headed Max.L and Avg.L report on this. Only after the last linked entry is checked will it be known that the candidate position's layout is not in the stash, and if so, a new entry to hold it is made.
If a position is declared new and added to the primary stash (be it Red or Blue) as a new border element, a secondary search is made of the other stash (respectively, Blue or Red) to seek a match, and the same statistics are presented. No entries are added to the alternate stash: instead a match means that the two tides have met at this position, and so a step sequence is discovered!
The step sequence is shown along with a board layout, followed by various methods of calculating a position's distance from ZERO, the solved state. All are such that Dist(ZERO) = 0, but, they do not show an obvious direction to follow. Some steps along the path to ZERO raise the distance to ZERO.
Specified Problem
To play 'slide-square' with 4 rows and 4 columns.
An initial layout will be read from file SlideSolveR4C4.txt
The objective is to attain the nice orderly layout as follows:
Row|__1__2__3__4
1| 1 2 3 4
2| 5 6 7 8
3| 9 10 11 12
4| 13 14 15 0
The starting position:
Row|__1__2__3__4
1| 15 14 1 6
2| 9 11 4 12
3| 0 10 7 3
4| 13 8 5 2
The plan is to spread a red tide from the "solved" layout and a blue tide from the specified starting position.
The hope is that these floods will meet at some position, and the blue moves plus the red moves in reverse order,
will be the shortest sequence from the given starting position to the solution.
Tide Red
Preparing a stash in file SlideSolveR4C4.123456789ABCDEF0.dat
... with an index in file SlideSolveR4C4.123456789ABCDEF0.ndx
199999991 zero values for an empty index.
1 2 3 4 5 6 7 8 9 A B C D E F 0 is the board layout in INTEGER*1
4030201 8070605 C0B0A09 F0E0D is the board layout in INTEGER*4
48372615 C0BFAE9D ..interleaved into two INTEGER*4
EF5FA0E1 multiplied together in INTEGER*4
-278945567 as a decimal integer.
ABS(MOD(-278945567,199999991)) + 2 = 78945578 is the record number for the first index entry.
Tide Blue
Preparing a stash in file SlideSolveR4C4.FE169B4C0A73D852.dat
... with an index in file SlideSolveR4C4.FE169B4C0A73D852.ndx
199999991 zero values for an empty index.
F E 1 6 9 B 4 C 0 A 7 3 D 8 5 2 is the board layout in INTEGER*1
6010E0F C040B09 3070A00 205080D is the board layout in INTEGER*4
6C14EBF9 3275A80D ..interleaved into two INTEGER*4
B2B863A5 multiplied together in INTEGER*4
-1296538715 as a decimal integer.
ABS(MOD(-1296538715,199999991)) + 2 = 96538771 is the record number for the first index entry.
| Tidewrack Boundary Positions | Positions | Primary Probes Index Use | Secondary Probes | Memory of Time Passed
Surge | First Last Count| Checked Deja vu%| Made Max.L Avg.L| Used% Load%| Made Max.L Avg.L| CPU Clock
1 Red| 1 1 1| 2 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.5secs 2.94% 1:07:03.093am.
1 Blue| 1 1 1| 3 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.5secs 3.22% 1:07:03.578am.
2 Red| 2 3 2| 4 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.0secs 0.00% 1:07:03.593am.
2 Blue| 2 4 3| 6 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.1secs 0.5secs 11.75% 1:07:04.125am.
3 Red| 4 7 4| 10 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.1secs 0.7secs 11.63% 1:07:04.812am.
3 Blue| 5 10 6| 14 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.0secs 1:07:04.812am.
4 Red| 8 17 10| 24 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.0secs 0.00% 1:07:04.875am.
4 Blue| 11 24 14| 32 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.1secs 0.00% 1:07:04.953am.
5 Red| 18 41 24| 54 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.0secs 0.00% 1:07:05.015am.
5 Blue| 25 56 32| 66 0.00| 0 0 0.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.0secs 50.40% 1:07:05.046am.
6 Red| 42 95 54| 108 0.93| 1 1 1.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.0secs 33.24% 1:07:05.093am.
6 Blue| 57 122 66| 136 1.47| 2 1 1.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.1secs 0.00% 1:07:05.171am.
7 Red| 96 202 107| 215 1.40| 3 1 1.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.1secs 0.00% 1:07:05.265am.
7 Blue| 123 256 134| 285 1.75| 5 1 1.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.1secs 0.00% 1:07:05.375am.
8 Red| 203 414 212| 456 2.19| 10 1 1.000| 0.000 0.000| 0 0 0.000| 0.0secs 0.2secs 8.36% 1:07:05.578am.
8 Blue| 257 536 280| 601 2.66| 16 1 1.000| 0.001 0.001| 0 0 0.000| 0.0secs 0.2secs 20.03% 1:07:05.812am.
9 Red| 415 860 446| 974 2.87| 28 1 1.000| 0.001 0.001| 0 0 0.000| 0.2secs 0.5secs 37.50% 1:07:06.312am.
9 Blue| 537 1121 585| 1254 3.19| 41 1 1.000| 0.001 0.001| 0 0 0.000| 0.2secs 0.5secs 34.38% 1:07:06.812am.
10 Red| 861 1806 946| 2032 4.13| 88 1 1.000| 0.002 0.002| 0 0 0.000| 0.3secs 0.9secs 37.28% 1:07:07.734am.
10 Blue| 1122 2335 1214| 2578 4.50| 117 1 1.000| 0.002 0.002| 0 0 0.000| 0.3secs 1.1secs 25.00% 1:07:08.859am.
11 Red| 1807 3754 1948| 4124 4.51| 189 1 1.000| 0.004 0.004| 0 0 0.000| 0.5secs 1.8secs 29.66% 1:07:10.703am.
11 Blue| 2336 4797 2462| 5188 4.66| 249 1 1.000| 0.005 0.005| 0 0 0.000| 0.6secs 2.2secs 27.54% 1:07:12.859am.
12 Red| 3755 7692 3938| 8244 5.29| 440 1 1.000| 0.008 0.008| 0 0 0.000| 1.0secs 3.6secs 28.51% 1:07:16.421am.
12 Blue| 4798 9743 4946| 10442 5.56| 588 1 1.000| 0.010 0.010| 1 1 1.000| 1.6secs 4.2secs 38.20% 1:07:20.593am.
13 Red| 7693 15500 7808| 16470 5.62| 943 1 1.000| 0.016 0.016| 0 0 0.000| 2.2secs 6.5secs 33.65% 1:07:27.093am.
13 Blue| 9744 19604 9861| 20858 6.03| 1285 2 1.001| 0.020 0.020| 4 1 1.000| 2.8secs 7.5secs 37.00% 1:07:34.625am.
14 Red| 15501 31044 15544| 32950 6.46| 2175 2 1.000| 0.031 0.031| 5 1 1.000| 3.8secs 11.2secs 34.12% 1:07:45.843am.
14 Blue| 19605 39204 19600| 41448 6.66| 2813 2 1.001| 0.039 0.039| 14 1 1.000| 4.6secs 12.7secs 36.19% 1:07:58.578am.
15 Red| 31045 61865 30821| 65311 6.84| 4611 2 1.001| 0.061 0.061| 23 1 1.000| 6.8secs 17.2secs 39.62% 1:08:15.734am.
15 Blue| 39205 77892 38688| 81703 6.87| 5803 2 1.000| 0.077 0.077| 47 1 1.000| 7.2secs 18.2secs 39.64% 1:08:33.906am.
16 Red| 61866 122707 60842| 128412 7.33| 9742 2 1.002| 0.121 0.121| 77 2 1.013| 11.9secs 23.2secs 51.21% 1:08:57.093am.
16 Blue| 77893 153978 76086| 160446 7.49| 12421 2 1.001| 0.151 0.151| 172 1 1.000| 13.6secs 23.2secs 58.57% 1:09:20.250am.
17 Red| 122708 241707 119000| 250818 7.56| 20063 3 1.002| 0.236 0.237| 303 1 1.000| 20.5secs 30.5secs 67.33% 1:09:50.765am.
17 Blue| 153979 302413 148435| 312766 7.89| 26220 2 1.002| 0.294 0.295| 678 2 1.001| 24.3secs 32.3secs 75.17% 1:10:23.109am.
18 Red| 241708 473551 231844| 487982 8.33| 43582 3 1.003| 0.458 0.460| 1229 2 1.002| 38.0secs 46.2secs 82.36% 1:11:09.265am.
18 Blue| 302414 590511 288098| 606919 8.56| 56018 3 1.003| 0.570 0.573| 2440 2 1.004| 47.5secs 59.4secs 80.02% 1:12:08.687am.
19 Red| 473552 920893 447342| 942552 8.79| 93152 3 1.005| 0.883 0.890| 4672 2 1.005| 73.1secs 91.3secs 80.07% 1:13:40.046am.
19 Blue| 590512 1145481 554970| 1168265 9.04| 120435 3 1.006| 1.093 1.104| 8999 3 1.009| 90.6secs 1.9mins 81.12% 1:15:31.765am.
20 Red| 920894 1780637 859744| 1809752 9.52| 202081 3 1.007| 1.687 1.709| 17194 2 1.008| 2.4mins 3.0mins 79.31% 1:18:30.265am.
20 Blue| 1145482 2208109 1062628| 2235235 9.77| 262047 3 1.008| 2.080 2.112| 33025 3 1.014| 3.0mins 3.7mins 79.82% 1:22:14.375am.
21 Red| 1780638 3418020 1637383| 3444691 10.06| 451483 4 1.014| 3.183 3.258| 62538 3 1.015| 4.5mins 5.7mins 79.80% 1:27:56.468am.
21 Blue| 2208110 4224923 2016814| 4238343 10.33| 588823 4 1.017| 3.905 4.013| 118609 5 1.024| 5.7mins 7.1mins 80.08% 1:35:03.140am.
22 Red| 3418021 6516290 3098270| 6506982 10.83| 1022051 4 1.023| 5.926 6.159| 219923 4 1.025| 8.7mins 10.7mins 81.12% 1:45:44.328am.
22 Blue| 4224924 8025605 3800682| 7979315 11.11| 1353159 5 1.029| 7.218 7.559| 414055 4 1.039| 10.9mins 13.8mins 79.04% 1:59:31.875am.
23 Red| 6516291 12318701 5802411| 12178635 11.45| 2470087 6 1.048| 10.780 11.551| 765853 5 1.046| 17.3mins 24.1mins 71.78% 2:23:35.828am.
23 Blue| 8025606 15118814 7093209| 14877107 11.76| 3307729 5 1.058| 13.003 14.123| 1401940 6 1.071| 22.4mins 35.3mins 63.46% 2:58:53.375am.
24 Red| 12318702 23102481 10783780| 22603192 12.29| 6014769 6 1.083| 19.074 21.464| 2526552 6 1.084| 36.7mins 65.6mins 55.95% 4:04:29.375am.
24 Blue| 15118815 28246178 13127364| 27507742 12.56| 8148893 7 1.105| 22.682 26.150| 4539588 7 1.124| 49.4mins 96.5mins 51.22% 5:40:59.265am.
25 Red| 23102482 42928799 19826318| 41532426 12.98| 15508438 9 1.166| 32.086 39.535| 8144188 7 1.151| 84.5mins 3.0hrs! 47.06% 8:40:25.296am.
25 Blue| 28246179 52299632 24053454| 50352435 13.30| 21007872 9 1.207| 37.354 47.979| 13961187 8 1.232| 2.0hrs! 4.4hrs! 44.40% 1:07:12.546pm.
26 Red| 42928800 79070945 36142146| 75611538 13.85| 38688179 10 1.300| 50.548 72.103| 24060624 9 1.278| 3.5hrs! 8.3hrs! 42.77% 9:23:03.250pm.
26 Blue| 52299633 95957208 43657576| 91305518 14.15| 51817830 14 1.379| 57.098 87.170| 39429635 10 1.424| 5.3hrs! 12.5hrs! 42.37% 9:53:57.890am.
Record Stash Move |Board layout by row| Max|d| Sum|d| Euclidean Encoded vs Zero
1 Blue |FE16/9B4C/0A73/D852| 14 86 27.055 19442940853367
2 Blue L |FE16/9B4C/A073/D852| 14 88 27.423 19442940844007
5 Blue L |FE16/9B4C/A703/D852| 14 88 27.677 19442940842087
11 Blue L |FE16/9B4C/A730/D852| 14 88 27.785 19442940841679
25 Blue D |FE16/9B40/A73C/D852| 14 80 26.000 19442940922295
58 Blue R |FE16/9B04/A73C/D852| 14 80 25.846 19442943220535
126 Blue U |FE16/9B34/A70C/D852| 14 80 26.306 19442940271895
265 Blue R |FE16/9B34/A07C/D852| 14 80 26.038 19442940274415
554 Blue D |FE16/9034/AB7C/D852| 14 72 24.290 19442951159375
1156 Blue D |F016/9E34/AB7C/D852| 14 64 21.863 19530129450575
2409 Blue R |0F16/9E34/AB7C/D852| 13 62 21.166 20837803818575
4949 Blue U |9F16/0E34/AB7C/D852| 13 70 22.804 11597104535375
10052 Blue L |9F16/E034/AB7C/D852| 13 72 23.409 11597064618575
20229 Blue D |9016/EF34/AB7C/D852| 10 64 20.688 11684242909775
40459 Blue L |9106/EF34/AB7C/D852| 10 64 20.736 10544698103375
80368 Blue U |9136/EF04/AB7C/D852| 10 64 21.307 10469454209615
158888 Blue U |9136/EF74/AB0C/D852| 11 64 22.583 10469452026935
312029 Blue U |9136/EF74/AB5C/D802| 15 64 23.452 10469452026423
609335 Blue R |9136/EF74/AB5C/D082| 14 64 23.108 10469452026425
1182001 Blue D |9136/EF74/A05C/DB82| 10 62 21.119 10469452028615
2278389 Blue D |9136/E074/AF5C/DB82| 9 54 18.055 10469455657415
4359103 Blue R |9136/0E74/AF5C/DB82| 8 52 17.263 10469531862215
8279825 Blue D |0136/9E74/AF5C/DB82| 8 44 15.033 19623012937415
15596324 Blue L |1036/9E74/AF5C/DB82| 8 44 15.100 1228393494215
29135380 Blue L |1306/9E74/AF5C/DB82| 8 46 15.297 169799958215
53940860 Blue L |1360/9E74/AF5C/DB82| 8 48 15.684 111840764615
98956855 Blue U |1364/9E70/AF5C/DB82| 8 48 16.673 106528120775
47181586 Red R |1364/9E07/AF5C/DB82| 8 48 16.248 106530419015
25400927 Red U |1364/9E57/AF0C/DB82| 11 48 17.436 106527470375
13548279 Red U |1364/9E57/AF8C/DB02| 15 48 19.183 106527469863
7168799 Red L |1364/9E57/AF8C/DB20| 13 44 17.550 106527469862
3761169 Red D |1364/9E57/AF80/DB2C| 13 68 24.413 106527469916
1959965 Red R |1364/9E57/AF08/DB2C| 13 68 24.083 106527470324
1013648 Red U |1364/9E57/AF28/DB0C| 15 68 24.413 106527469693
521247 Red R |1364/9E57/AF28/D0BC| 14 68 23.958 106527469696
266034 Red D |1364/9E57/A028/DFBC| 12 60 21.307 106527470416
135063 Red D |1364/9057/AE28/DFBC| 12 52 18.493 106534727296
68120 Red L |1364/9507/AE28/DFBC| 12 52 18.762 106504971136
34188 Red U |1364/9527/AE08/DFBC| 12 52 19.183 106501659736
17049 Red U |1364/9527/AEB8/DF0C| 15 52 21.354 106501659249
8443 Red R |1364/9527/AEB8/D0FC| 14 50 20.640 106501659251
4119 Red D |1364/9527/A0B8/DEFC| 12 42 17.720 106501660689
1986 Red R |1364/9527/0AB8/DEFC| 12 40 17.146 106501687329
950 Red D |1364/0527/9AB8/DEFC| 12 32 14.900 106781074689
458 Red L |1364/5027/9AB8/DEFC| 12 32 15.232 106414565889
222 Red L |1364/5207/9AB8/DEFC| 12 32 15.362 106381543809
104 Red D |1304/5267/9AB8/DEFC| 12 26 13.711 168648485889
46 Red R |1034/5267/9AB8/DEFC| 12 24 13.491 1227242021889
20 Red U |1234/5067/9AB8/DEFC| 12 24 14.071 36293889
9 Red L |1234/5607/9AB8/DEFC| 12 24 14.491 3271809
4 Red L |1234/5670/9AB8/DEFC| 12 24 14.967 328449
2 Red U |1234/5678/9AB0/DEFC| 12 24 16.971 105
1 Red U |1234/5678/9ABC/DEF0| 0 0 0.000 0
52 moves: LLLDRURDDRULDLUUURDDRDLLLURUULDRURDDLUURDRDLLDRULLUU
Record Stash Move |Board layout by row| Max|d| Sum|d| Euclidean Encoded vs Zero
1 Blue |FE16/9B4C/0A73/D852| 14 86 27.055 19442940853367
2 Blue L |FE16/9B4C/A073/D852| 14 88 27.423 19442940844007
5 Blue L |FE16/9B4C/A703/D852| 14 88 27.677 19442940842087
11 Blue L |FE16/9B4C/A730/D852| 14 88 27.785 19442940841679
25 Blue D |FE16/9B40/A73C/D852| 14 80 26.000 19442940922295
58 Blue R |FE16/9B04/A73C/D852| 14 80 25.846 19442943220535
126 Blue U |FE16/9B34/A70C/D852| 14 80 26.306 19442940271895
266 Blue U |FE16/9B34/A75C/D802| 15 80 27.055 19442940271383
558 Blue R |FE16/9B34/A75C/D082| 14 80 26.758 19442940271385
1163 Blue D |FE16/9B34/A05C/D782| 14 80 25.690 19442940274293
2420 Blue D |FE16/9034/AB5C/D782| 14 72 23.917 19442951159253
4967 Blue D |F016/9E34/AB5C/D782| 14 64 21.448 19530129450453
10090 Blue R |0F16/9E34/AB5C/D782| 13 62 20.736 20837803818453
20306 Blue U |9F16/0E34/AB5C/D782| 13 70 22.405 11597104535253
40605 Blue L |9F16/E034/AB5C/D782| 13 72 23.022 11597064618453
80644 Blue D |9016/EF34/AB5C/D782| 9 64 20.248 11684242909653
159412 Blue L |9106/EF34/AB5C/D782| 9 64 20.298 10544698103253
313039 Blue U |9136/EF04/AB5C/D782| 9 64 20.881 10469454209493
611272 Blue U |9136/EF54/AB0C/D782| 11 64 21.817 10469451664053
1185720 Blue U |9136/EF54/AB8C/D702| 15 64 23.238 10469451663663
2285440 Blue L |9136/EF54/AB8C/D720| 13 60 21.909 10469451663662
4372401 Blue D |9136/EF54/AB80/D72C| 13 84 27.713 10469451663716
8304687 Blue R |9136/EF54/AB08/D72C| 13 84 27.423 10469451664028
15642421 Blue R |9136/EF54/A0B8/D72C| 13 82 27.019 10469451665948
29220003 Blue D |9136/E054/AFB8/D72C| 13 74 24.698 10469455294748
54094941 Blue R |9136/0E54/AFB8/D72C| 13 72 24.125 10469531499548
99233939 Blue D |0136/9E54/AFB8/D72C| 13 64 22.583 19623012574748
53847416 Red L |1036/9E54/AFB8/D72C| 13 64 22.627 1228393131548
29052034 Red L |1306/9E54/AFB8/D72C| 13 66 22.760 169799595548
15525093 Red L |1360/9E54/AFB8/D72C| 13 68 23.022 111840401948
8231956 Red U |1364/9E50/AFB8/D72C| 13 68 23.707 106527758108
4326107 Red U |1364/9E58/AFB0/D72C| 13 68 25.020 106527510356
2258614 Red R |1364/9E58/AF0B/D72C| 13 68 24.576 106527510668
1169712 Red U |1364/9E58/AF2B/D70C| 15 68 24.900 106527510037
602597 Red R |1364/9E58/AF2B/D07C| 14 68 24.617 106527510040
308014 Red D |1364/9E58/A02B/DF7C| 12 60 22.045 106527510760
156652 Red D |1364/9058/AE2B/DF7C| 12 52 19.339 106534767640
79080 Red L |1364/9508/AE2B/DF7C| 12 52 19.596 106505011480
39747 Red U |1364/9528/AE0B/DF7C| 12 52 20.000 106501700080
19843 Red U |1364/9528/AE7B/DF0C| 15 52 21.354 106501699449
9866 Red R |1364/9528/AE7B/D0FC| 14 50 20.640 106501699451
4832 Red D |1364/9528/A07B/DEFC| 12 42 17.720 106501700889
2335 Red R |1364/9528/0A7B/DEFC| 12 40 17.146 106501727529
1114 Red D |1364/0528/9A7B/DEFC| 12 32 14.900 106781114889
534 Red L |1364/5028/9A7B/DEFC| 12 32 15.232 106414606089
259 Red L |1364/5208/9A7B/DEFC| 12 32 15.362 106381584009
124 Red D |1304/5268/9A7B/DEFC| 12 26 13.711 168648526089
56 Red R |1034/5268/9A7B/DEFC| 12 24 13.491 1227242062089
24 Red U |1234/5068/9A7B/DEFC| 12 24 14.071 36334089
10 Red L |1234/5608/9A7B/DEFC| 12 24 14.491 3312009
5 Red U |1234/5678/9A0B/DEFC| 12 24 16.310 609
2 Red L |1234/5678/9AB0/DEFC| 12 24 16.971 105
1 Red U |1234/5678/9ABC/DEF0| 0 0 0.000 0
52 moves: LLLDRUURDDDRULDLUUULDRRDRDLLLUURURDDLUURDRDLLDRULULU
The two paths deviate on the seventh move, from entry 126 Blue either R to 265 Blue or U to 266 Blue. The Euclidean and Encoded distances to ZERO conflict: down and up for the first choice, up and down for the second.
Another Example
Taking the first example from 15_puzzle_solver/20_Random shows that with the red tide expansion in hand, only the new blue tide is poured into the maze:
To play 'slide-square' with 4 rows and 4 columns.
An initial layout will be read from file SlideSolveR4C4.txt
The objective is to attain the nice orderly layout as follows:
Row|__1__2__3__4
1| 1 2 3 4
2| 5 6 7 8
3| 9 10 11 12
4| 13 14 15 0
The starting position:
Row|__1__2__3__4
1| 13 10 11 6
2| 5 3 1 4
3| 8 0 12 2
4| 14 7 9 15
The plan is to spread a red tide from the "solved" layout and a blue tide from the specified starting position.
The hope is that these floods will meet at some position, and the blue moves plus the red moves in reverse order,
will be the shortest sequence from the given starting position to the solution.
Tide Red
Restarting from file SlideSolveR4C4.123456789ABCDEF0.dat
Stashed 144206568. At surge 26 with the boundary stashed in elements 79070946 to 144206568
Its index uses 101095844 of 199999991 entries.
Tide Blue
Preparing a stash in file SlideSolveR4C4.DAB6531480C2E79F.dat
... with an index in file SlideSolveR4C4.DAB6531480C2E79F.ndx
199999991 zero values for an empty index.
D A B 6 5 3 1 4 8 0 C 2 E 7 9 F is the board layout in INTEGER*1
60B0A0D 4010305 20C0008 F09070E is the board layout in INTEGER*4
64B1A3D5 2FC9078E ..interleaved into two INTEGER*4
7340B326 multiplied together in INTEGER*4
1933620006 as a decimal integer.
ABS(MOD(1933620006,199999991)) + 2 = 133620089 is the record number for the first index entry.
| Tidewrack Boundary Positions | Positions | Primary Probes Index Use | Secondary Probes | Memory of Time Passed
Surge | First Last Count| Checked Deja vu%| Made Max.L Avg.L| Used% Load%| Made Max.L Avg.L| CPU Clock
1 Blue| 1 1 1| 4 0.00| 0 0 0.000| 0.000 0.000| 2 1 1.000| 0.0secs 0.0secs 0.00% 9:27:19.468am.
2 Blue| 2 5 4| 10 0.00| 0 0 0.000| 0.000 0.000| 4 2 1.500| 0.0secs 0.5secs 3.33% 9:27:19.937am.
3 Blue| 6 15 10| 20 0.00| 0 0 0.000| 0.000 0.000| 5 2 1.400| 0.0secs 0.4secs 0.00% 9:27:20.296am.
4 Blue| 16 35 20| 38 0.00| 0 0 0.000| 0.000 0.000| 16 3 1.250| 0.0secs 0.3secs 11.75% 9:27:20.562am.
5 Blue| 36 73 38| 80 0.00| 0 0 0.000| 0.000 0.000| 39 4 1.385| 0.0secs 0.1secs 0.00% 9:27:20.625am.
6 Blue| 74 153 80| 178 2.25| 4 1 1.000| 0.000 0.000| 87 4 1.379| 0.0secs 0.1secs 0.00% 9:27:20.750am.
7 Blue| 154 327 174| 380 2.11| 8 1 1.000| 0.000 0.000| 186 5 1.500| 0.2secs 0.3secs 52.79% 9:27:21.046am.
8 Blue| 328 699 372| 790 3.54| 28 1 1.000| 0.001 0.001| 386 5 1.448| 0.2secs 0.4secs 53.51% 9:27:21.484am.
9 Blue| 700 1461 762| 1590 3.14| 50 1 1.000| 0.002 0.002| 738 6 1.407| 0.3secs 0.9secs 37.50% 9:27:22.375am.
10 Blue| 1462 3001 1540| 3234 5.01| 168 1 1.000| 0.003 0.003| 1542 6 1.396| 0.6secs 2.0secs 29.60% 9:27:24.328am.
11 Blue| 3002 6073 3072| 6512 4.85| 318 1 1.000| 0.006 0.006| 3032 5 1.398| 1.2secs 3.9secs 30.77% 9:27:28.187am.
12 Blue| 6074 12269 6196| 13182 6.27| 841 2 1.001| 0.012 0.012| 6007 6 1.406| 2.5secs 7.5secs 33.96% 9:27:35.687am.
13 Blue| 12270 24625 12356| 26134 6.19| 1648 2 1.001| 0.025 0.025| 12261 6 1.410| 5.0secs 15.6secs 32.23% 9:27:51.296am.
14 Blue| 24626 49141 24516| 51646 6.71| 3581 2 1.000| 0.049 0.049| 23554 6 1.395| 9.2secs 24.8secs 37.14% 9:28:16.078am.
15 Blue| 49142 97320 48179| 101393 6.94| 7301 2 1.000| 0.096 0.096| 46888 7 1.411| 15.8secs 41.9secs 37.71% 9:28:58.031am.
16 Blue| 97321 191676 94356| 198950 7.80| 16489 2 1.002| 0.187 0.188| 89521 7 1.399| 27.3secs 62.8secs 43.45% 9:30:00.781am.
17 Blue| 191677 375108 183432| 386686 8.11| 33604 2 1.003| 0.363 0.365| 177033 8 1.418| 52.7secs 1.9mins 45.48% 9:31:56.734am.
18 Blue| 375109 730438 355330| 748406 8.84| 74407 3 1.005| 0.700 0.706| 333730 7 1.405| 96.8secs 3.7mins 43.38% 9:35:39.812am.
19 Blue| 730439 1412688 682250| 1434890 9.27| 154921 4 1.007| 1.340 1.357| 649155 8 1.416| 3.2mins 7.1mins 44.60% 9:42:44.031am.
Record Stash Move |Board layout by row| Max|d| Sum|d| Euclidean Encoded vs Zero
1 Blue |DAB6/5314/80C2/E79F| 15 94 29.155 16535302211892
4 Blue R |DAB6/5314/08C2/E79F| 15 94 28.879 16535302234212
12 Blue D |DAB6/0314/58C2/E79F| 15 94 28.178 16535581621572
30 Blue L |DAB6/3014/58C2/E79F| 15 94 28.284 16535251400772
62 Blue L |DAB6/3104/58C2/E79F| 15 94 28.320 16535218378692
125 Blue D |DA06/31B4/58C2/E79F| 15 86 26.721 16560125373252
266 Blue R |D0A6/31B4/58C2/E79F| 15 84 26.344 16971108746052
568 Blue R |0DA6/31B4/58C2/E79F| 15 82 25.846 20719775267652
1203 Blue U |3DA6/01B4/58C2/E79F| 15 86 26.306 3626483421252
2480 Blue L |3DA6/10B4/58C2/E79F| 15 86 26.344 3626080624452
5044 Blue D |30A6/1DB4/58C2/E79F| 15 78 24.290 3887608240452
10136 Blue L |3A06/1DB4/58C2/E79F| 15 80 24.698 3395673597252
20466 Blue L |3A60/1DB4/58C2/E79F| 15 82 24.940 3343462422852
40817 Blue U |3A64/1DB0/58C2/E79F| 15 82 25.573 3338668697412
81229 Blue U |3A64/1DB2/58C0/E79F| 15 82 25.884 3338668369068
160022 Blue R |3A64/1DB2/580C/E79F| 15 80 25.417 3338668369380
314204 Blue R |3A64/1DB2/508C/E79F| 15 80 25.100 3338668372500
612120 Blue D |3A64/10B2/5D8C/E79F| 15 72 22.935 3338679257460
1187839 Blue D |3064/1AB2/5D8C/E79F| 15 64 21.119 3861730860660
2285373 Blue R |0364/1AB2/5D8C/E79F| 15 62 20.976 19815358150260
53888966 Red U |1364/0AB2/5D8C/E79F| 15 62 21.166 106797401460
29074972 Red U |1364/5AB2/0D8C/E79F| 15 62 22.091 106394277060
15537643 Red L |1364/5AB2/D08C/E79F| 15 64 22.672 106394263380
8238754 Red U |1364/5AB2/D78C/E09F| 15 64 23.875 106394258914
4329748 Red L |1364/5AB2/D78C/E90F| 15 64 24.249 106394258911
2260520 Red L |1364/5AB2/D78C/E9F0| 6 34 11.747 106394258910
1170710 Red D |1364/5AB2/D780/E9FC| 12 58 20.640 106394258989
603117 Red R |1364/5AB2/D708/E9FC| 12 58 20.248 106394259493
308288 Red D |1364/5A02/D7B8/E9FC| 12 50 17.944 106396078573
156795 Red L |1364/5A20/D7B8/E9FC| 12 50 18.055 106393135213
79148 Red U |1364/5A28/D7B0/E9FC| 12 50 19.748 106392847909
39781 Red R |1364/5A28/D70B/E9FC| 12 50 19.183 106392848317
19862 Red R |1364/5A28/D07B/E9FC| 12 50 18.815 106392852037
9877 Red U |1364/5A28/D97B/E0FC| 14 50 20.640 106392848411
4838 Red R |1364/5A28/D97B/0EFC| 13 48 19.950 106392848421
2337 Red D |1364/5A28/097B/DEFC| 12 40 17.146 106392863529
1115 Red L |1364/5A28/907B/DEFC| 12 40 17.664 106392836889
534 Red D |1364/5028/9A7B/DEFC| 12 32 15.232 106414606089
259 Red L |1364/5208/9A7B/DEFC| 12 32 15.362 106381584009
124 Red D |1304/5268/9A7B/DEFC| 12 26 13.711 168648526089
56 Red R |1034/5268/9A7B/DEFC| 12 24 13.491 1227242062089
24 Red U |1234/5068/9A7B/DEFC| 12 24 14.071 36334089
10 Red L |1234/5608/9A7B/DEFC| 12 24 14.491 3312009
5 Red U |1234/5678/9A0B/DEFC| 12 24 16.310 609
2 Red L |1234/5678/9AB0/DEFC| 12 24 16.971 105
1 Red U |1234/5678/9ABC/DEF0| 0 0 0.000 0
45 moves: RDLLDRRULDLLUURRDDRUULULLDRDLURRURDLDLDRULULU
Record Stash Move |Board layout by row| Max|d| Sum|d| Euclidean Encoded vs Zero
1 Blue |DAB6/5314/80C2/E79F| 15 94 29.155 16535302211892
4 Blue R |DAB6/5314/08C2/E79F| 15 94 28.879 16535302234212
12 Blue D |DAB6/0314/58C2/E79F| 15 94 28.178 16535581621572
30 Blue L |DAB6/3014/58C2/E79F| 15 94 28.284 16535251400772
62 Blue L |DAB6/3104/58C2/E79F| 15 94 28.320 16535218378692
125 Blue D |DA06/31B4/58C2/E79F| 15 86 26.721 16560125373252
266 Blue R |D0A6/31B4/58C2/E79F| 15 84 26.344 16971108746052
568 Blue R |0DA6/31B4/58C2/E79F| 15 82 25.846 20719775267652
1203 Blue U |3DA6/01B4/58C2/E79F| 15 86 26.306 3626483421252
2480 Blue L |3DA6/10B4/58C2/E79F| 15 86 26.344 3626080624452
5044 Blue D |30A6/1DB4/58C2/E79F| 15 78 24.290 3887608240452
10136 Blue L |3A06/1DB4/58C2/E79F| 15 80 24.698 3395673597252
20466 Blue L |3A60/1DB4/58C2/E79F| 15 82 24.940 3343462422852
40817 Blue U |3A64/1DB0/58C2/E79F| 15 82 25.573 3338668697412
81229 Blue U |3A64/1DB2/58C0/E79F| 15 82 25.884 3338668369068
160022 Blue R |3A64/1DB2/580C/E79F| 15 80 25.417 3338668369380
314204 Blue R |3A64/1DB2/508C/E79F| 15 80 25.100 3338668372500
612122 Blue U |3A64/1DB2/578C/E09F| 15 80 26.192 3338668368034
1187843 Blue L |3A64/1DB2/578C/E90F| 15 80 26.533 3338668368031
2285379 Blue L |3A64/1DB2/578C/E9F0| 8 50 15.937 3338668368030
53890406 Red D |3A64/1DB2/5780/E9FC| 12 74 23.281 3338668368109
29075781 Red R |3A64/1DB2/5708/E9FC| 12 74 22.935 3338668368613
15538085 Red D |3A64/1D02/57B8/E9FC| 12 66 20.928 3338669819773
8239002 Red L |3A64/1D20/57B8/E9FC| 12 66 21.024 3338666876413
4329887 Red U |3A64/1D28/57B0/E9FC| 12 66 22.494 3338666634469
2260599 Red R |3A64/1D28/570B/E9FC| 12 66 22.000 3338666634877
1170753 Red R |3A64/1D28/507B/E9FC| 12 66 21.679 3338666638597
603141 Red D |3A64/1028/5D7B/E9FC| 12 58 19.131 3338677523557
308302 Red D |3064/1A28/5D7B/E9FC| 12 50 16.912 3861729126757
156805 Red R |0364/1A28/5D7B/E9FC| 12 48 16.733 19815356416357
79152 Red U |1364/0A28/5D7B/E9FC| 12 48 16.971 106795667557
39783 Red U |1364/5A28/0D7B/E9FC| 12 48 18.111 106392865717
19862 Red L |1364/5A28/D07B/E9FC| 12 50 18.815 106392852037
9877 Red U |1364/5A28/D97B/E0FC| 14 50 20.640 106392848411
4838 Red R |1364/5A28/D97B/0EFC| 13 48 19.950 106392848421
2337 Red D |1364/5A28/097B/DEFC| 12 40 17.146 106392863529
1115 Red L |1364/5A28/907B/DEFC| 12 40 17.664 106392836889
534 Red D |1364/5028/9A7B/DEFC| 12 32 15.232 106414606089
259 Red L |1364/5208/9A7B/DEFC| 12 32 15.362 106381584009
124 Red D |1304/5268/9A7B/DEFC| 12 26 13.711 168648526089
56 Red R |1034/5268/9A7B/DEFC| 12 24 13.491 1227242062089
24 Red U |1234/5068/9A7B/DEFC| 12 24 14.071 36334089
10 Red L |1234/5608/9A7B/DEFC| 12 24 14.491 3312009
5 Red U |1234/5678/9A0B/DEFC| 12 24 16.310 609
2 Red L |1234/5678/9AB0/DEFC| 12 24 16.971 105
1 Red U |1234/5678/9ABC/DEF0| 0 0 0.000 0
45 moves: RDLLDRRULDLLUURRULLDRDLURRDDRUULURDLDLDRULULU
Record Stash Move |Board layout by row| Max|d| Sum|d| Euclidean Encoded vs Zero
1 Blue |DAB6/5314/80C2/E79F| 15 94 29.155 16535302211892
4 Blue R |DAB6/5314/08C2/E79F| 15 94 28.879 16535302234212
12 Blue D |DAB6/0314/58C2/E79F| 15 94 28.178 16535581621572
31 Blue D |0AB6/D314/58C2/E79F| 15 86 26.268 20458524891972
65 Blue L |A0B6/D314/58C2/E79F| 15 88 26.646 13048370139972
133 Blue U |A3B6/D014/58C2/E79F| 15 90 27.092 11995513736772
281 Blue L |A3B6/D104/58C2/E79F| 15 90 27.129 11995480714692
599 Blue D |A306/D1B4/58C2/E79F| 15 82 25.456 12026654646852
1266 Blue R |A036/D1B4/58C2/E79F| 15 80 25.338 13004296912452
2610 Blue U |A136/D0B4/58C2/E79F| 15 80 25.495 11777091184452
5305 Blue R |A136/0DB4/58C2/E79F| 15 78 24.980 11777203677252
10671 Blue D |0136/ADB4/58C2/E79F| 15 70 23.324 19623050301252
21525 Blue L |1036/ADB4/58C2/E79F| 15 70 23.367 1228430858052
42928 Blue L |1306/ADB4/58C2/E79F| 15 72 23.495 169837322052
85377 Blue L |1360/ADB4/58C2/E79F| 15 74 23.749 111878128452
168152 Blue U |1364/ADB0/58C2/E79F| 15 74 24.413 106565484612
329996 Blue U |1364/ADB2/58C0/E79F| 15 74 24.739 106565156268
642726 Blue R |1364/ADB2/580C/E79F| 15 72 24.249 106565156580
1246294 Blue R |1364/ADB2/508C/E79F| 15 72 23.917 106565159700
2396768 Blue D |1364/A0B2/5D8C/E79F| 15 64 21.633 106576044660
53888966 Red R |1364/0AB2/5D8C/E79F| 15 62 21.166 106797401460
29074972 Red U |1364/5AB2/0D8C/E79F| 15 62 22.091 106394277060
15537643 Red L |1364/5AB2/D08C/E79F| 15 64 22.672 106394263380
8238754 Red U |1364/5AB2/D78C/E09F| 15 64 23.875 106394258914
4329748 Red L |1364/5AB2/D78C/E90F| 15 64 24.249 106394258911
2260520 Red L |1364/5AB2/D78C/E9F0| 6 34 11.747 106394258910
1170710 Red D |1364/5AB2/D780/E9FC| 12 58 20.640 106394258989
603117 Red R |1364/5AB2/D708/E9FC| 12 58 20.248 106394259493
308288 Red D |1364/5A02/D7B8/E9FC| 12 50 17.944 106396078573
156795 Red L |1364/5A20/D7B8/E9FC| 12 50 18.055 106393135213
79148 Red U |1364/5A28/D7B0/E9FC| 12 50 19.748 106392847909
39781 Red R |1364/5A28/D70B/E9FC| 12 50 19.183 106392848317
19862 Red R |1364/5A28/D07B/E9FC| 12 50 18.815 106392852037
9877 Red U |1364/5A28/D97B/E0FC| 14 50 20.640 106392848411
4838 Red R |1364/5A28/D97B/0EFC| 13 48 19.950 106392848421
2337 Red D |1364/5A28/097B/DEFC| 12 40 17.146 106392863529
1115 Red L |1364/5A28/907B/DEFC| 12 40 17.664 106392836889
534 Red D |1364/5028/9A7B/DEFC| 12 32 15.232 106414606089
259 Red L |1364/5208/9A7B/DEFC| 12 32 15.362 106381584009
124 Red D |1304/5268/9A7B/DEFC| 12 26 13.711 168648526089
56 Red R |1034/5268/9A7B/DEFC| 12 24 13.491 1227242062089
24 Red U |1234/5068/9A7B/DEFC| 12 24 14.071 36334089
10 Red L |1234/5608/9A7B/DEFC| 12 24 14.491 3312009
5 Red U |1234/5678/9A0B/DEFC| 12 24 16.310 609
2 Red L |1234/5678/9AB0/DEFC| 12 24 16.971 105
1 Red U |1234/5678/9ABC/DEF0| 0 0 0.000 0
45 moves: RDDLULDRURDLLLUURRDRULULLDRDLURRURDLDLDRULULU
Record Stash Move |Board layout by row| Max|d| Sum|d| Euclidean Encoded vs Zero
1 Blue |DAB6/5314/80C2/E79F| 15 94 29.155 16535302211892
4 Blue R |DAB6/5314/08C2/E79F| 15 94 28.879 16535302234212
12 Blue D |DAB6/0314/58C2/E79F| 15 94 28.178 16535581621572
31 Blue D |0AB6/D314/58C2/E79F| 15 86 26.268 20458524891972
65 Blue L |A0B6/D314/58C2/E79F| 15 88 26.646 13048370139972
133 Blue U |A3B6/D014/58C2/E79F| 15 90 27.092 11995513736772
281 Blue L |A3B6/D104/58C2/E79F| 15 90 27.129 11995480714692
599 Blue D |A306/D1B4/58C2/E79F| 15 82 25.456 12026654646852
1266 Blue R |A036/D1B4/58C2/E79F| 15 80 25.338 13004296912452
2610 Blue U |A136/D0B4/58C2/E79F| 15 80 25.495 11777091184452
5305 Blue R |A136/0DB4/58C2/E79F| 15 78 24.980 11777203677252
10671 Blue D |0136/ADB4/58C2/E79F| 15 70 23.324 19623050301252
21525 Blue L |1036/ADB4/58C2/E79F| 15 70 23.367 1228430858052
42928 Blue L |1306/ADB4/58C2/E79F| 15 72 23.495 169837322052
85377 Blue L |1360/ADB4/58C2/E79F| 15 74 23.749 111878128452
168152 Blue U |1364/ADB0/58C2/E79F| 15 74 24.413 106565484612
329996 Blue U |1364/ADB2/58C0/E79F| 15 74 24.739 106565156268
642726 Blue R |1364/ADB2/580C/E79F| 15 72 24.249 106565156580
1246294 Blue R |1364/ADB2/508C/E79F| 15 72 23.917 106565159700
2396770 Blue U |1364/ADB2/578C/E09F| 15 72 25.060 106565155234
53890081 Red L |1364/ADB2/578C/E90F| 15 72 25.417 106565155231
29075603 Red L |1364/ADB2/578C/E9F0| 7 42 14.000 106565155230
15537991 Red D |1364/ADB2/5780/E9FC| 12 66 22.000 106565155309
8238950 Red R |1364/ADB2/5708/E9FC| 12 66 21.633 106565155813
4329857 Red D |1364/AD02/57B8/E9FC| 12 58 19.494 106566606973
2260581 Red L |1364/AD20/57B8/E9FC| 12 58 19.596 106563663613
1170743 Red U |1364/AD28/57B0/E9FC| 12 58 21.166 106563421669
603137 Red R |1364/AD28/570B/E9FC| 12 58 20.640 106563422077
308301 Red R |1364/AD28/507B/E9FC| 12 58 20.298 106563425797
156804 Red D |1364/A028/5D7B/E9FC| 12 50 17.550 106574310757
79152 Red R |1364/0A28/5D7B/E9FC| 12 48 16.971 106795667557
39783 Red U |1364/5A28/0D7B/E9FC| 12 48 18.111 106392865717
19862 Red L |1364/5A28/D07B/E9FC| 12 50 18.815 106392852037
9877 Red U |1364/5A28/D97B/E0FC| 14 50 20.640 106392848411
4838 Red R |1364/5A28/D97B/0EFC| 13 48 19.950 106392848421
2337 Red D |1364/5A28/097B/DEFC| 12 40 17.146 106392863529
1115 Red L |1364/5A28/907B/DEFC| 12 40 17.664 106392836889
534 Red D |1364/5028/9A7B/DEFC| 12 32 15.232 106414606089
259 Red L |1364/5208/9A7B/DEFC| 12 32 15.362 106381584009
124 Red D |1304/5268/9A7B/DEFC| 12 26 13.711 168648526089
56 Red R |1034/5268/9A7B/DEFC| 12 24 13.491 1227242062089
24 Red U |1234/5068/9A7B/DEFC| 12 24 14.071 36334089
10 Red L |1234/5608/9A7B/DEFC| 12 24 14.491 3312009
5 Red U |1234/5678/9A0B/DEFC| 12 24 16.310 609
2 Red L |1234/5678/9AB0/DEFC| 12 24 16.971 105
1 Red U |1234/5678/9ABC/DEF0| 0 0 0.000 0
45 moves: RDDLULDRURDLLLUURRULLDRDLURRDRULURDLDLDRULULU
The first and second move sequences start the same, until position 314204 (the sixteenth move) and then advance D to 612120 or U to 612122. In the first case the Euclidean distance falls while the encoded distance rises but in the second case the Euclidean distance rises while the encoded distance falls. If there might be any guidance to be found in these figures, it is not immediately obvious. But, after an increase, the next step achieves a large reduction, beyond the previous distance. Humm.
Maximum Separation
Just how far away can a position be from ZERO? Alas, 16! is rather large, but lesser board sizes can be perused to completion in a reasonable time. Changing the values in NR and NC is easy, though some other changes are helpful. The hash calculation that is nicely balanced for the 4x4 board doesn't give good spray for a lesser board, but an ad-hoc change to BRD(1)*9 + BRD(2) works well enough. The blue tide is plugged by suppressing its code, and the red tide flows until it can flow no more. For these runs, the output is slightly edited to omit redundant information such as that referring to the blue tide which isn't flowing.
To play 'slide-square' with 3 rows and 4 columns.
Tide Red
Preparing a stash in file SlideSolveR3C4.123456789AB0.dat
... with an index in file SlideSolveR3C4.123456789AB0.ndx
199999991 zero values for an empty index.
1 2 3 4 5 6 7 8 9 A B 0 is the board layout in INTEGER*1
4030201 8070605 B0A09 0 is the board layout in INTEGER*4
48372615 B0A090 ..interleaved into two INTEGER*4
8AA0F74D combined.
-1969162419 as a decimal integer.
ABS(MOD(-1969162419,199999991)) + 2 = 169162502 is the record number for the first index entry.
| Tidewrack Boundary Positions| Positions | Primary Probes Index Use |Memory of Time Passed
Surge| First Last Count| Checked Deja vu%| Made Max.L Avg.L| Used% Load%| CPU Clock
1| 1 1 1| 2 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 0.00% 7:57:19.187am.
2| 2 3 2| 4 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.1secs 16.62% 7:57:19.281am.
3| 4 7 4| 9 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 0.00% 7:57:19.296am.
4| 8 16 9| 20 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 7:57:19.312am.
5| 17 36 20| 37 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 7:57:19.312am.
6| 37 73 37| 64 1.56| 1 1 1.000| 0.000 0.000| 0.0secs 0.2secs 0.00% 7:57:19.468am.
7| 74 136 63| 125 2.40| 3 1 1.000| 0.000 0.000| 0.0secs 0.0secs 0.00% 7:57:19.515am.
8| 137 258 122| 241 3.73| 9 1 1.000| 0.000 0.000| 0.0secs 0.1secs 0.00% 7:57:19.609am.
9| 259 490 232| 451 4.43| 20 1 1.000| 0.000 0.000| 0.0secs 0.1secs 0.00% 7:57:19.671am.
10| 491 921 431| 827 5.56| 46 1 1.000| 0.001 0.001| 0.0secs 0.1secs 0.00% 7:57:19.796am.
11| 922 1702 781| 1481 6.01| 89 1 1.000| 0.002 0.002| 0.0secs 0.2secs 15.32% 7:57:20.000am.
12| 1703 3094 1392| 2671 6.63| 177 1 1.000| 0.003 0.003| 0.0secs 0.4secs 8.33% 7:57:20.375am.
13| 3095 5588 2494| 4770 6.88| 328 1 1.000| 0.005 0.005| 0.1secs 1.0secs 11.12% 7:57:21.359am.
14| 5589 10030 4442| 8502 7.62| 652 1 1.000| 0.009 0.009| 0.4secs 1.8secs 21.06% 7:57:23.140am.
15| 10031 17884 7854| 15135 8.17| 1237 2 1.001| 0.016 0.016| 0.6secs 2.8secs 22.90% 7:57:25.937am.
16| 17885 31783 13899| 26554 8.81| 2351 1 1.000| 0.028 0.028| 0.9secs 5.0secs 17.65% 7:57:30.984am.
17| 31784 55998 24215| 46180 9.48| 4409 2 1.000| 0.049 0.049| 1.9secs 7.4secs 26.21% 7:57:38.375am.
18| 55999 97800 41802| 79668 10.67| 8584 2 1.000| 0.084 0.084| 3.1secs 11.7secs 26.87% 7:57:50.062am.
19| 97801 168967 71167| 135867 11.76| 16270 3 1.001| 0.144 0.144| 5.1secs 15.7secs 32.40% 7:58:05.734am.
20| 168968 288855 119888| 228379 13.14| 30689 2 1.001| 0.243 0.244| 9.4secs 21.4secs 43.75% 7:58:27.125am.
21| 288856 487218 198363| 377240 14.32| 55757 2 1.002| 0.404 0.405| 15.0secs 26.5secs 56.39% 7:58:53.671am.
22| 487219 810424 323206| 612123 15.74| 100162 2 1.002| 0.660 0.663| 21.7secs 42.4secs 51.16% 7:59:36.093am.
23| 810425 1326202 515778| 977833 17.06| 176608 3 1.003| 1.060 1.069| 32.7secs 59.2secs 55.29% 8:00:35.296am.
24| 1326203 2137202 811000| 1533678 18.63| 306896 3 1.005| 1.674 1.693| 56.0secs 91.9secs 60.91% 8:02:07.203am.
25| 2137203 3385213 1248011| 2358532 20.07| 522581 4 1.008| 2.592 2.635| 85.7secs 2.1mins 67.00% 8:04:15.062am.
26| 3385214 5270492 1885279| 3554164 21.71| 877235 4 1.012| 3.930 4.026| 2.1mins 3.4mins 60.44% 8:07:40.187am.
27| 5270493 8052888 2782396| 5239108 23.47| 1452058 5 1.017| 5.824 6.031| 3.1mins 4.4mins 70.93% 8:12:05.062am.
28| 8052889 12062610 4009722| 7534021 25.39| 2357673 5 1.025| 8.412 8.842| 4.4mins 6.8mins 64.81% 8:18:50.843am.
29| 12062611 17683964 5621354| 10540894 27.45| 3736777 5 1.037| 11.814 12.666| 5.9mins 8.7mins 67.49% 8:27:35.375am.
30| 17683965 25331836 7647872| 14308274 29.65| 5757092 5 1.052| 16.090 17.699| 8.1mins 12.1mins 66.43% 8:39:42.640am.
31| 25331837 35397636 10065800| 18773730 32.03| 8547647 6 1.072| 21.203 24.079| 10.4mins 14.8mins 70.68% 8:54:28.562am.
32| 35397637 48158049 12760413| 23759506 34.47| 12146155 7 1.097| 27.009 31.864| 13.2mins 19.0mins 69.20% 9:13:31.234am.
33| 48158050 63728835 15570786| 28870409 37.06| 16437759 8 1.126| 33.226 40.950| 15.7mins 21.8mins 72.16% 9:35:16.421am.
34| 63728836 81900441 18171606| 33626342 39.63| 20990966 9 1.157| 39.543 51.100| 18.8mins 31.2mins 60.26% 10:06:28.671am.
35| 81900442 102200317 20299876| 37402396 42.28| 25357818 9 1.193| 45.566 61.894| 21.7mins 43.3mins 50.19% 10:49:46.296am.
36| 102200318 123787565 21587248| 39666978 44.94| 28674025 11 1.222| 51.062 72.814| 24.1mins 55.6mins 43.32% 11:45:22.359am.
37| 123787566 145628724 21841159| 39956652 47.68| 30596301 10 1.253| 55.742 83.268| 24.9mins 62.8mins 39.61% 12:48:08.968pm.
38| 145628725 166535629 20906905| 38122360 50.42| 30382490 10 1.269| 59.612 92.717| 24.8mins 65.3mins 37.94% 1:53:27.953pm.
39| 166535630 185434986 18899357| 34311262 53.20| 28383116 11 1.286| 62.576 100.747| 22.4mins 61.1mins 36.70% 2:54:31.156pm.
40| 185434987 201493321 16058335| 29019233 55.99| 24579603 12 1.283| 64.796 107.133| 19.0mins 52.2mins 36.48% 3:46:40.171pm.
41| 201493322 214265924 12772603| 23016150 58.66| 19948189 10 1.281| 66.330 111.891| 14.8mins 40.7mins 36.41% 4:27:20.140pm.
42| 214265925 223781141 9515217| 17041788 61.37| 14979073 11 1.262| 67.361 115.182| 10.9mins 29.0mins 37.55% 4:56:23.062pm.
43| 223781142 230364322 6583181| 11772739 63.96| 10506946 10 1.249| 67.994 117.304| 7.0mins 19.0mins 37.17% 5:15:21.000pm.
44| 230364323 234607075 4242753| 7532690 66.76| 6789748 11 1.222| 68.366 118.555| 4.3mins 11.3mins 37.93% 5:26:38.500pm.
45| 234607076 237110948 2503873| 4439978 69.59| 4054719 10 1.206| 68.558 119.231| 2.3mins 6.1mins 37.47% 5:32:47.218pm.
46| 237110949 238461216 1350268| 2371273 72.87| 2185279 10 1.176| 68.651 119.552| 70.6secs 2.9mins 39.92% 5:35:44.015pm.
47| 238461217 239104461 643245| 1130010 76.08| 1055623 10 1.160| 68.689 119.687| 29.4secs 74.9secs 39.21% 5:36:58.890pm.
48| 239104462 239374764 270303| 466424 80.21| 440280 10 1.125| 68.702 119.734| 10.8secs 26.0secs 41.36% 5:37:24.921pm.
49| 239374765 239467075 92311| 161691 83.23| 154374 8 1.111| 68.705 119.747| 3.4secs 7.6secs 45.08% 5:37:32.546pm.
50| 239467076 239494191 27116| 44973 88.02| 43422 11 1.071| 68.706 119.750| 0.8secs 1.5secs 56.82% 5:37:34.031pm.
51| 239494192 239499581 5390| 9553 88.33| 9259 6 1.074| 68.706 119.750| 0.1secs 0.4secs 33.32% 5:37:34.453pm.
52| 239499582 239500696 1115| 1625 94.71| 1593 5 1.028| 68.706 119.750| 0.0secs 0.0secs104.17% 5:37:34.468pm.
53| 239500697 239500782 86| 167 89.22| 162 3 1.049| 68.706 119.750| 0.0secs 0.0secs 97.66% 5:37:34.484pm.
54| 239500783 239500800 18| 18 100.00| 18 1 1.000| 68.706 119.750| 0.0secs 0.0secs 5:37:34.484pm.
The boundary has not surged to new positions!
The now-static boundary has 18
Record Stash Move | Board layout | Max|d| Sum|d| Euclidean Encoded vs Zero
239500783 Red D |0869/B725/43A1| 7 44 14.765 466581807
239500784 Red D |0869/B7A1/4325| 9 58 18.601 466582214
239500785 Red R |8759/43A2/0B61| 9 48 16.310 302860487
239500786 Red R |4325/8761/0BA9| 9 38 15.362 127427903
239500787 Red R |0821/B3A5/4769| 9 48 15.811 464885186
239500788 Red D |0B21/3765/48A9| 9 38 14.765 475738105
239500789 Red R |4321/8B65/07A9| 9 42 15.362 127389739
239500790 Red D |0861/B325/47A9| 9 48 15.811 466336825
239500791 Red D |0829/B365/47A1| 6 36 12.410 465127617
239500792 Red R |0829/B7A5/4361| 7 44 14.765 465130767
239500793 Red R |4321/8769/0BA5| 9 30 11.832 127387607
239500794 Red R |B821/37A5/0469| 10 58 19.799 424935162
239500795 Red R |4361/8725/0BA9| 9 42 15.362 128113223
239500796 Red R |4321/B765/08A9| 9 40 15.297 127402699
239500797 Red U |8369/4725/0BA1| 9 38 14.283 288340727
239500798 Red U |8329/476A/0B51| 9 36 14.213 287247191
239500799 Red R |0321/8765/4BA9| 9 30 11.832 446727869
239500800 Red R |8321/4765/0BA9| 9 38 15.362 287039663
No progress!
Whereas for four rows and three columns,
To play 'slide-square' with 4 rows and 3 columns.
Tide Red
Preparing a stash in file SlideSolveR4C3.123456789AB0.dat
... with an index in file SlideSolveR4C3.123456789AB0.ndx
199999991 zero values for an empty index.
1 2 3 4 5 6 7 8 9 A B 0 is the board layout in INTEGER*1
4030201 8070605 B0A09 0 is the board layout in INTEGER*4
48372615 B0A090 ..interleaved into two INTEGER*4
8AA0F74D combined.
-1969162419 as a decimal integer.
ABS(MOD(-1969162419,199999991)) + 2 = 169162502 is the record number for the first index entry.
| Tidewrack Boundary Positions | Positions | Primary Probes Index Use |Memory of Time Passed
Surge| First Last Count| Checked Deja vu%| Made Max.L Avg.L| Used% Load%| CPU Clock
1| 1 1 1| 2 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 0.00% 7:50:20.203pm.
2| 2 3 2| 4 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.1secs 12.50% 7:50:20.328pm.
3| 4 7 4| 9 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 7:50:20.328pm.
4| 8 16 9| 20 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.0secs 0.00% 7:50:20.343pm.
5| 17 36 20| 37 0.00| 0 0 0.000| 0.000 0.000| 0.0secs 0.1secs 0.00% 7:50:20.421pm.
6| 37 73 37| 64 1.56| 1 1 1.000| 0.000 0.000| 0.0secs 0.0secs 0.00% 7:50:20.437pm.
7| 74 136 63| 125 2.40| 3 1 1.000| 0.000 0.000| 0.0secs 0.2secs 8.31% 7:50:20.625pm.
8| 137 258 122| 241 3.73| 9 1 1.000| 0.000 0.000| 0.0secs 0.1secs 50.40% 7:50:20.687pm.
9| 259 490 232| 451 4.43| 20 1 1.000| 0.000 0.000| 0.0secs 0.1secs 49.87% 7:50:20.781pm.
10| 491 921 431| 827 5.56| 46 1 1.000| 0.001 0.001| 0.1secs 0.2secs 63.59% 7:50:20.953pm.
11| 922 1702 781| 1481 6.01| 89 1 1.000| 0.002 0.002| 0.1secs 0.3secs 35.06% 7:50:21.265pm.
12| 1703 3094 1392| 2671 6.63| 177 1 1.000| 0.003 0.003| 0.2secs 0.6secs 41.63% 7:50:21.828pm.
13| 3095 5588 2494| 4770 6.88| 328 1 1.000| 0.005 0.005| 0.5secs 1.5secs 36.19% 7:50:23.296pm.
14| 5589 10030 4442| 8502 7.62| 648 1 1.000| 0.009 0.009| 0.8secs 2.2secs 34.50% 7:50:25.515pm.
15| 10031 17884 7854| 15135 8.17| 1237 1 1.000| 0.016 0.016| 1.3secs 3.9secs 33.60% 7:50:29.421pm.
16| 17885 31783 13899| 26554 8.81| 2344 1 1.000| 0.028 0.028| 2.2secs 5.9secs 36.77% 7:50:35.328pm.
17| 31784 55998 24215| 46180 9.48| 4397 1 1.000| 0.049 0.049| 3.1secs 9.5secs 32.73% 7:50:44.781pm.
18| 55999 97800 41802| 79668 10.67| 8574 2 1.000| 0.084 0.084| 6.0secs 14.5secs 41.25% 7:50:59.328pm.
19| 97801 168967 71167| 135867 11.76| 16154 2 1.000| 0.144 0.144| 9.3secs 20.5secs 45.46% 7:51:19.812pm.
20| 168968 288855 119888| 228379 13.14| 30520 2 1.000| 0.243 0.244| 14.7secs 27.9secs 52.72% 7:51:47.671pm.
21| 288856 487218 198363| 377240 14.32| 55395 2 1.001| 0.404 0.405| 18.5secs 33.0secs 56.18% 7:52:20.656pm.
22| 487219 810424 323206| 612123 15.74| 99611 2 1.002| 0.660 0.663| 22.4secs 41.7secs 53.62% 7:53:02.359pm.
23| 810425 1326202 515778| 977833 17.06| 175049 2 1.003| 1.062 1.069| 35.9secs 61.9secs 57.96% 7:54:04.250pm.
24| 1326203 2137202 811000| 1533678 18.63| 305322 3 1.004| 1.676 1.693| 55.4secs 94.5secs 58.68% 7:55:38.718pm.
25| 2137203 3385213 1248011| 2358532 20.07| 519257 4 1.007| 2.596 2.635| 87.8secs 2.3mins 63.69% 7:57:56.562pm.
26| 3385214 5270492 1885279| 3554164 21.71| 872963 3 1.010| 3.936 4.026| 2.2mins 3.4mins 63.19% 8:01:21.109pm.
27| 5270493 8052888 2782396| 5239108 23.47| 1445680 4 1.016| 5.833 6.031| 3.2mins 4.8mins 66.44% 8:06:08.906pm.
28| 8052889 12062610 4009722| 7534021 25.39| 2348797 4 1.024| 8.426 8.842| 4.5mins 6.9mins 65.49% 8:13:00.218pm.
29| 12062611 17683964 5621354| 10540894 27.45| 3734408 5 1.036| 11.829 12.666| 6.4mins 9.1mins 70.67% 8:22:04.328pm.
30| 17683965 25331836 7647872| 14308274 29.65| 5746564 5 1.051| 16.110 17.699| 8.3mins 12.3mins 67.88% 8:34:21.375pm.
31| 25331837 35397636 10065800| 18773730 32.03| 8552447 6 1.071| 21.220 24.079| 10.9mins 15.7mins 69.40% 8:50:02.062pm.
32| 35397637 48158049 12760413| 23759506 34.47| 12145305 7 1.096| 27.027 31.864| 13.8mins 19.5mins 70.96% 9:09:32.671pm.
33| 48158050 63728835 15570786| 28870409 37.06| 16448462 7 1.125| 33.238 40.950| 16.7mins 23.2mins 71.94% 9:32:46.109pm.
34| 63728836 81900441 18171606| 33626342 39.63| 21022994 9 1.158| 39.540 51.100| 20.1mins 32.4mins 62.17% 10:05:09.859pm.
35| 81900442 102200317 20299876| 37402396 42.28| 25358874 8 1.192| 45.562 61.894| 21.9mins 44.7mins 49.02% 10:49:50.296pm.
36| 102200318 123787565 21587248| 39666978 44.94| 28734429 10 1.224| 51.028 72.814| 25.6mins 56.6mins 45.33% 11:46:25.156pm.
37| 123787566 145628724 21841159| 39956652 47.68| 30572287 11 1.252| 55.720 83.268| 27.1mins 64.5mins 41.99% 0:50:52.171am.
38| 145628725 166535629 20906905| 38122360 50.42| 30446707 10 1.273| 59.558 92.717| 26.6mins 66.4mins 40.12% 1:57:16.468am.
39| 166535630 185434986 18899357| 34311262 53.20| 28341786 10 1.283| 62.543 100.747| 23.7mins 62.2mins 38.16% 2:59:28.250am.
40| 185434987 201493321 16058335| 29019233 55.99| 24605484 10 1.285| 64.750 107.133| 20.0mins 53.8mins 37.26% 3:53:15.640am.
41| 201493322 214265924 12772603| 23016150 58.66| 19903099 11 1.276| 66.306 111.891| 15.5mins 41.1mins 37.86% 4:34:19.671am.
42| 214265925 223781141 9515217| 17041788 61.37| 14979317 10 1.262| 67.337 115.182| 11.3mins 29.2mins 38.48% 5:03:33.937am.
43| 223781142 230364322 6583181| 11772739 63.96| 10478430 12 1.241| 67.985 117.304| 7.4mins 19.1mins 38.79% 5:22:39.250am.
44| 230364323 234607075 4242753| 7532690 66.76| 6785656 11 1.220| 68.358 118.555| 4.4mins 11.4mins 38.96% 5:34:04.359am.
45| 234607076 237110948 2503873| 4439978 69.59| 4041159 10 1.197| 68.558 119.231| 2.4mins 6.2mins 38.76% 5:40:15.031am.
46| 237110949 238461216 1350268| 2371273 72.87| 2182892 11 1.172| 68.652 119.552| 70.1secs 3.0mins 39.48% 5:43:12.625am.
47| 238461217 239104461 643245| 1130010 76.08| 1051526 10 1.149| 68.691 119.687| 30.2secs 76.2secs 39.66% 5:44:28.812am.
48| 239104462 239374764 270303| 466424 80.21| 439307 10 1.118| 68.705 119.734| 11.2secs 26.3secs 42.40% 5:44:55.125am.
49| 239374765 239467075 92311| 161691 83.23| 153927 9 1.102| 68.708 119.747| 3.6secs 7.9secs 45.63% 5:45:03.000am.
50| 239467076 239494191 27116| 44973 88.02| 43358 9 1.067| 68.709 119.750| 0.8secs 1.7secs 44.15% 5:45:04.734am.
51| 239494192 239499581 5390| 9553 88.33| 9231 6 1.062| 68.709 119.750| 0.1secs 0.3secs 52.87% 5:45:05.000am.
52| 239499582 239500696 1115| 1625 94.71| 1598 4 1.029| 68.709 119.750| 0.0secs 0.0secs100.81% 5:45:05.031am.
53| 239500697 239500782 86| 167 89.22| 161 3 1.043| 68.709 119.750| 0.0secs 0.0secs 5:45:05.031am.
54| 239500783 239500800 18| 18 100.00| 18 1 1.000| 68.709 119.750| 0.0secs 0.0secs 5:45:05.031am.
The boundary has not surged to new positions!
The now-static boundary has 18
Record Stash Move | Board layout | Max|d| Sum|d| Euclidean Encoded vs Zero
239500783 Red D |09A/B78/456/321| 9 52 17.720 471375815
239500784 Red L |A90/78B/456/123| 9 60 19.494 391824450
239500785 Red L |BA0/789/546/321| 10 56 18.974 435370175
239500786 Red D |BA0/789/452/361| 10 56 18.493 435370041
239500787 Red R |07A/98B/456/123| 9 56 18.221 464077890
239500788 Red R |09A/B87/465/321| 9 52 17.833 471380879
239500789 Red R |09A/B87/546/321| 9 52 17.833 471380975
239500790 Red R |09A/B87/564/312| 10 54 18.547 471380998
239500791 Red L |970/B8A/465/123| 9 60 19.287 344730714
239500792 Red L |AB0/789/546/123| 9 60 19.950 395453370
239500793 Red L |BA0/879/265/341| 10 56 18.601 435410157
239500794 Red R |09A/B78/546/123| 9 56 18.868 471375930
239500795 Red L |AB0/789/456/132| 9 58 19.339 395453251
239500796 Red R |09A/B78/465/123| 9 56 18.868 471375834
239500797 Red D |AB0/798/456/123| 9 60 19.950 395458290
239500798 Red L |AB0/789/456/213| 10 60 19.950 395453252
239500799 Red L |BA0/789/456/123| 10 60 19.950 435370050
239500800 Red R |0BA/789/456/123| 9 56 18.868 478915650
No progress!
Reducing to a 3x3 board encouraged a reduction in the size of the index. The run took about ten seconds.
To play 'slide-square' with 3 rows and 3 columns.
Tide Red
Preparing a stash in file SlideSolveR3C3.123456780.dat
... with an index in file SlideSolveR3C3.123456780.ndx
199991 zero values for an empty index.
1 2 3 4 5 6 7 8 0 is the board layout in INTEGER*1
4030201 8070605 0 0 is the board layout in INTEGER*4
48372615 0 ..interleaved into two INTEGER*4
89F056BD multiplied together in INTEGER*4
-1980737859 as a decimal integer.
ABS(MOD(-1980737859,199991)) + 2 = 26997 is the record number for the first index entry.
|Tidewrack Boundary Positions| Positions | Primary Probes Index Use
Surge| First Last Count|Checked Deja vu%| Made Max.L Avg.L| Used% Load%
1| 1 1 1| 2 0.00| 0 0 0.000| 0.002 0.002
2| 2 3 2| 4 0.00| 0 0 0.000| 0.004 0.004
3| 4 7 4| 8 0.00| 0 0 0.000| 0.008 0.008
4| 8 15 8| 16 0.00| 0 0 0.000| 0.016 0.016
5| 16 31 16| 20 0.00| 0 0 0.000| 0.026 0.026
6| 32 51 20| 40 2.50| 1 1 1.000| 0.045 0.045
7| 52 90 39| 65 4.62| 3 1 1.000| 0.076 0.076
8| 91 152 62| 124 6.45| 8 1 1.000| 0.134 0.134
9| 153 268 116| 164 7.32| 12 1 1.000| 0.210 0.210
10| 269 420 152| 304 5.92| 18 1 1.000| 0.353 0.353
11| 421 706 286| 430 7.91| 38 1 1.000| 0.549 0.551
12| 707 1102 396| 792 5.56| 53 1 1.000| 0.919 0.925
13| 1103 1850 748| 1114 8.08| 97 2 1.010| 1.427 1.437
14| 1851 2874 1024| 2048 7.57| 189 1 1.000| 2.357 2.384
15| 2875 4767 1893| 2799 10.25| 356 2 1.006| 3.578 3.640
16| 4768 7279 2512| 5024 10.73| 738 2 1.019| 5.721 5.882
17| 7280 11764 4485| 6599 14.56| 1365 2 1.023| 8.338 8.701
18| 11765 17402 5638| 11276 15.49| 2734 3 1.042| 12.610 13.466
19| 17403 26931 9529| 13867 21.55| 4630 3 1.054| 17.228 18.905
20| 26932 37809 10878| 21756 21.89| 8302 4 1.087| 23.956 27.402
21| 37810 54802 16993| 24289 29.56| 11793 4 1.102| 30.204 35.958
22| 54803 71912 17110| 34220 30.01| 18451 4 1.151| 38.089 47.934
23| 71913 95864 23952| 33912 40.36| 21895 6 1.165| 44.097 58.047
24| 95865 116088 20224| 40448 40.55| 27617 6 1.205| 50.513 70.071
25| 116089 140135 24047| 33131 52.98| 25580 7 1.200| 54.289 77.860
26| 140136 155713 15578| 31156 53.27| 24657 5 1.208| 57.539 85.140
27| 155714 170273 14560| 19530 67.88| 16842 6 1.157| 58.883 88.277
28| 170274 176547 6274| 12548 68.84| 10945 5 1.137| 59.684 90.233
29| 176548 180457 3910| 4926 84.57| 4615 6 1.068| 59.840 90.613
30| 180458 181217 760| 1520 85.46| 1424 4 1.064| 59.888 90.723
31| 181218 181438 221| 265 99.25| 264 1 1.000| 59.888 90.724
32| 181439 181440 2| 4 100.00| 4 1 1.000| 59.888 90.724
The boundary has not surged to new positions!
The now-static boundary has 2
Record Stash Move |Board plan| Max|d| Sum|d| Euclidean Encoded vs Zero
181439 Red D |647/850/321| 6 32 12.247 220175
181440 Red U |867/254/301| 8 32 13.038 311247
No progress!
Thus, for a 3x3 board the greatest separation is thirty-two steps to two positions, while the 3x4 and 4x3 boards both have eighteen positions fifty-two steps away from ZERO.
Go
package main
import "fmt"
var (
Nr = [16]int{3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3}
Nc = [16]int{3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2}
)
var (
n, _n int
N0, N3, N4 [85]int
N2 [85]uint64
)
const (
i = 1
g = 8
e = 2
l = 4
)
func fY() bool {
if N2[n] == 0x123456789abcdef0 {
return true
}
if N4[n] <= _n {
return fN()
}
return false
}
func fZ(w int) bool {
if w&i > 0 {
fI()
if fY() {
return true
}
n--
}
if w&g > 0 {
fG()
if fY() {
return true
}
n--
}
if w&e > 0 {
fE()
if fY() {
return true
}
n--
}
if w&l > 0 {
fL()
if fY() {
return true
}
n--
}
return false
}
func fN() bool {
switch N0[n] {
case 0:
switch N3[n] {
case 'l':
return fZ(i)
case 'u':
return fZ(e)
default:
return fZ(i + e)
}
case 3:
switch N3[n] {
case 'r':
return fZ(i)
case 'u':
return fZ(l)
default:
return fZ(i + l)
}
case 1, 2:
switch N3[n] {
case 'l':
return fZ(i + l)
case 'r':
return fZ(i + e)
case 'u':
return fZ(e + l)
default:
return fZ(l + e + i)
}
case 12:
switch N3[n] {
case 'l':
return fZ(g)
case 'd':
return fZ(e)
default:
return fZ(e + g)
}
case 15:
switch N3[n] {
case 'r':
return fZ(g)
case 'd':
return fZ(l)
default:
return fZ(g + l)
}
case 13, 14:
switch N3[n] {
case 'l':
return fZ(g + l)
case 'r':
return fZ(e + g)
case 'd':
return fZ(e + l)
default:
return fZ(g + e + l)
}
case 4, 8:
switch N3[n] {
case 'l':
return fZ(i + g)
case 'u':
return fZ(g + e)
case 'd':
return fZ(i + e)
default:
return fZ(i + g + e)
}
case 7, 11:
switch N3[n] {
case 'd':
return fZ(i + l)
case 'u':
return fZ(g + l)
case 'r':
return fZ(i + g)
default:
return fZ(i + g + l)
}
default:
switch N3[n] {
case 'd':
return fZ(i + e + l)
case 'l':
return fZ(i + g + l)
case 'r':
return fZ(i + g + e)
case 'u':
return fZ(g + e + l)
default:
return fZ(i + g + e + l)
}
}
}
func fI() {
g := (11 - N0[n]) * 4
a := N2[n] & uint64(15<<uint(g))
N0[n+1] = N0[n] + 4
N2[n+1] = N2[n] - a + (a << 16)
N3[n+1] = 'd'
N4[n+1] = N4[n]
cond := Nr[a>>uint(g)] <= N0[n]/4
if !cond {
N4[n+1]++
}
n++
}
func fG() {
g := (19 - N0[n]) * 4
a := N2[n] & uint64(15<<uint(g))
N0[n+1] = N0[n] - 4
N2[n+1] = N2[n] - a + (a >> 16)
N3[n+1] = 'u'
N4[n+1] = N4[n]
cond := Nr[a>>uint(g)] >= N0[n]/4
if !cond {
N4[n+1]++
}
n++
}
func fE() {
g := (14 - N0[n]) * 4
a := N2[n] & uint64(15<<uint(g))
N0[n+1] = N0[n] + 1
N2[n+1] = N2[n] - a + (a << 4)
N3[n+1] = 'r'
N4[n+1] = N4[n]
cond := Nc[a>>uint(g)] <= N0[n]%4
if !cond {
N4[n+1]++
}
n++
}
func fL() {
g := (16 - N0[n]) * 4
a := N2[n] & uint64(15<<uint(g))
N0[n+1] = N0[n] - 1
N2[n+1] = N2[n] - a + (a >> 4)
N3[n+1] = 'l'
N4[n+1] = N4[n]
cond := Nc[a>>uint(g)] >= N0[n]%4
if !cond {
N4[n+1]++
}
n++
}
func fifteenSolver(n int, g uint64) {
N0[0] = n
N2[0] = g
N4[0] = 0
}
func solve() {
if fN() {
fmt.Print("Solution found in ", n, " moves: ")
for g := 1; g <= n; g++ {
fmt.Printf("%c", N3[g])
}
fmt.Println()
} else {
n = 0
_n++
solve()
}
}
func main() {
fifteenSolver(8, 0xfe169b4c0a73d852)
solve()
}
- Output:
Solution found in 52 moves: rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd
Java
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.stream.Collectors;
public final class Puzzle15Solver {
public static void main(String[] aArgs) {
List<Integer> start = List.of( 15, 14, 1, 6, 9, 11, 4, 12, 0, 10, 7, 3, 13, 8, 5, 2 );
final int zeroIndex = 8;
Puzzle initial = new Puzzle(start, new ArrayList<String>(), zeroIndex, 0);
openSet.add(initial);
System.out.println("Solving the 15 puzzle:");
initial.display();
while ( solution == null ) {
search();
}
System.out.println(solution.moves.stream().collect(Collectors.joining("")));
System.out.println("Number of steps: " + solution.moves.size());
System.out.println("Number of puzzle states checked: " + closedSet.size());
}
private static void search() {
Puzzle current = openSet.poll();
closedSet.add(current);
final int zeroIndex = current.zeroIndex;
final int row = zeroIndex / 4;
final int column = zeroIndex % 4;
if ( column > 0 ) {
Puzzle nextPuzzle = current.clone();
nextPuzzle.makeMove(Move.LEFT);
}
if ( column < 3 ) {
Puzzle nextPuzzle = current.clone();
nextPuzzle.makeMove(Move.RIGHT);
}
if ( row > 0 ) {
Puzzle nextPuzzle = current.clone();
nextPuzzle.makeMove(Move.UP);
}
if ( row < 3 ) {
Puzzle nextPuzzle = current.clone();
nextPuzzle.makeMove(Move.DOWN);
}
}
private enum Move {
LEFT("L", -1), RIGHT("R", +1), UP("U", -4), DOWN("D", +4);
private Move(String aSymbol, int aStep) {
symbol = aSymbol;
step = aStep;
}
private String symbol;
private Integer step;
}
private static class Puzzle {
public Puzzle(List<Integer> aTiles, List<String> aMoves, int aZeroIndex, int aSearchDepth) {
tiles = aTiles;
moves = aMoves;
zeroIndex = aZeroIndex;
searchDepth = aSearchDepth;
}
public void makeMove(Move aMove) {
Integer temp = tiles.get(zeroIndex + aMove.step);
tiles.set(zeroIndex + aMove.step, 0);
tiles.set(zeroIndex, temp);
zeroIndex += aMove.step;
moves.add(aMove.symbol);
if ( ! closedSet.contains(this) ) {
openSet.add(this);
if ( tiles.equals(Puzzle.GOAL) ) {
solution = this;
}
}
}
public long heuristic() {
int distance = 0;
for ( int i = 0; i < tiles.size(); i++ ) {
final int tile = tiles.get(i);
if ( tile > 0 ) {
distance += Math.abs( ( i / 4 ) - ( tile - 1 ) / 4 ) + Math.abs( ( i % 4 ) - ( tile - 1 ) % 4 );
}
}
return distance + searchDepth;
}
public Puzzle clone() {
return new Puzzle(new ArrayList<Integer>(tiles), new ArrayList<String>(moves), zeroIndex, searchDepth + 1);
}
public void display() {
for ( int i = 0; i < tiles.size(); i++ ) {
System.out.print(String.format("%s%2d%s",
( i % 4 == 0 ) ? "[" : "", tiles.get(i), ( i % 4 == 3 ) ? "]\n" : " "));
}
System.out.println();
}
@Override
public boolean equals(Object aObject) {
return switch(aObject) {
case Puzzle puzzle -> tiles.equals(puzzle.tiles);
case Object object -> false;
};
}
@Override
public int hashCode() {
int hash = 3;
hash = 23 * hash + tiles.hashCode();
hash = 23 * hash + zeroIndex;
return hash;
}
private List<Integer> tiles;
private List<String> moves;
private int zeroIndex;
private int searchDepth;
private static final List<Integer> GOAL = List.of( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0 );
}
private static Queue<Puzzle> openSet =
new PriorityQueue<Puzzle>( (one, two) -> Long.compare(one.heuristic(), two.heuristic()) );
private static Set<Puzzle> closedSet = new HashSet<Puzzle>();
private static Puzzle solution;
}
- Output:
Solving the 15 puzzle: [15 14 1 6] [ 9 11 4 12] [ 0 10 7 3] [13 8 5 2] RRRULDLUULDRURDDDLUULURRRDLDDRULDLUURDDLULURRULDRRDD Number of steps: 52 Number of puzzle states checked: 2276369
jq
Works with jq, the C implementation of jq
Works with jaq, the Rust implementation of jq
The following program showcases jq's support for backtracking and how little memory is required when a memory-efficient implementation of jq is used. For the "fe169b4c0a73d852" task, (that is, to find a shortest sequence of moves, requiring a search depth of 52), the C implementation of jq requires less than 1MB, and the Rust implementation requires less that 4MB.
The algorithm is very simply: it relies on the fact that at each move, the Manhattan distance between the tile being moved and its target location either increases or decreases by 1. This quantity will be called the delta of the move. The algorithm uses these deltas to guide the selection of moves at each turn.
Some "debug" statements have been included to illustrate how progress of the computation can be tracked.
# The following may be omitted if using the C implementation
# or if the debug messages are deleted.
def debug(msg): (msg | tostring | debug | empty), .;
### Generic functions
def array_swap($i; $j):
if $j < $i then array_swap($j;$i)
elif $i == $j then .
else .[:$i] + [.[$j]] + .[$i+1:$j] + [.[$i]] + .[$j+1:]
end ;
def sum(s): reduce s as $x (0; . + $x);
### The 15-Puzzle
# manhattan distance between points $ix and $iy where these are indices in the flat array
def distance($ix; $jx):
def row: ./4 | floor;
def col: . % 4;
[$ix, $jx]
| map(row) as $mr # [$ri, $rj]
| map(col) as $mc # [$ci, $cj]
| [$mr[0] - $mr[1], $mc[0] - $mc[1]]
| map(length) # i.e. abs
| add;
# What is the Manhattan distance between the position of $tile in the goal
# and the location corresponding to index $ix, where $ix is in range(0;16)
def manhattan($tile; $ix):
.position[$tile|tostring] as $jx
| distance($ix; $jx);
# The total of the discrepancies
def total_manhattan_distance:
sum( range(0;16) as $p | .board[$p] as $tile | select($tile != 0) | manhattan($tile; $p) )
| debug;
# Input:
# .goal is the desired board (flat array)
# .position is the JSON object mapping tiles to the goal index
# .zero is the location of 0
# .board is the current state of the board (flat array)
# .distance is incremented by $delta after each move
# .seen is our memory
# If allowed, move the zero tile to $p where $p has been properly specified in relation to .zero;
# otherwise emit empty
def move($p):
if $p >= 0 and $p < 16
then .board[$p] as $tile
# Are we making things worse off?
| (manhattan($tile; .zero) - manhattan($tile; $p)) as $delta
| if $delta > 0 and .distance > (.N - .n)
then if .n >= .N then debug({n, N, distance,sequence: (.sequence|length)}) end | empty
else # make the move
.zero as $zero
| (.board | array_swap($zero; $p)) as $candidate
| ($candidate|tostring) as $s
| if .seen[$s]
then empty
else .board = $candidate
| .zero = $p
| .n += 1
| .seen[$s] = true
end
end
# We should only reach here if the move has been made
| if $delta != 0
then .distance += $delta
end
else empty
end
;
def row: . / 4 | floor;
def col: . % 4;
def up:
if (.zero | row) == 0 then empty
else move(.zero - 4)
| .sequence += ["u"]
end;
def down:
if (.zero | row) == 3 then empty
else move(.zero + 4)
| .sequence += ["d"]
end;
def left:
if (.zero|col) == 0 then empty
else move(.zero - 1)
| .sequence += ["l"]
end;
def right:
if (.zero|col) == 3 then empty
else move(.zero + 1)
| .sequence += ["r"]
end;
# $array is a permutation of range(0;16), e.g. the goal
# Output: a JSON object such that .[$tile] is the position of $tile in the goal
def positions($array):
reduce range(0; $array|length) as $i ({}; . + {($array[$i]|tostring): $i});
# map a string of lowercase hex digits to an array of decimals
def symbols2array: explode | map(if . > 96 then .-87 else .-48 end);
# $start should be a string of length 16 representing the starting state;
# the goal is: "123456789abcdef0"
def init($start):
if $start|length == 16 then . else error end
| [range(1;16), 0] as $init
| {goal: $init,
position: positions($init),
distance: 0,
n: 0, # number of moves so far
sequence: [], # the sequence of moves so far
seen: {}
}
| .board = ($start | symbols2array)
| .zero = (.board|index(0))
| (.board|tostring) as $s
| .seen[$s] = true
;
# Output: If the move of the zero tile to $p is legal in one step,
# then emit manhattan($tile; .zero) - manhattan($tile; $p)
# where $tile is the tile at $p;
# otherwise: null
def delta_move($p):
if $p >= 0 and $p < 16
then distance($p; .zero) as $base
| if ($base|length) == 1 # abs
then .board[$p] as $tile
| manhattan($tile; .zero) - manhattan($tile; $p)
else null
end
else null
end ;
# For comparing the possible moves:
def moves:
{"u": delta_move( .zero - 4),
"d": delta_move( .zero + 4),
"l": delta_move( .zero - 1),
"r": delta_move( .zero + 1) }
| to_entries
| map(select( .value ) )
| sort_by(.value)
;
# input: the output of moves
def execute($moves):
($moves[] |.key) as $key
| if $key == "l" then left
elif $key == "r" then right
elif $key == "u" then up
elif $key == "d" then down
else empty
end;
# $N is the maximum number of moves allowed
# Input: as per `input`; .n is the number of moves so far
def possible_moves($N):
def possible_moves:
if .board == .goal then . # a solution
elif (.sequence|length) >= $N then empty
else .sequence[-1] as $lastmove
| if $lastmove == "l" then execute(moves | map(select(.key != "r")))
elif $lastmove == "r" then execute(moves | map(select(.key != "l")))
elif $lastmove == "u" then execute(moves | map(select(.key != "d")))
elif $lastmove == "d" then execute(moves | map(select(.key != "u")))
else execute(moves)
end
| possible_moves
end ;
possible_moves;
def solve($goal):
init($goal)
| total_manhattan_distance as $d
| first( range($d; 100) as $n
| .N = $n
| .distance = $d
| debug("before: n=\($n) distance = \($d))")
| possible_moves($n)
| .sequence | join("") ) ;
solve("fe169b4c0a73d852")- Output:
["DEBUG:",36] ["DEBUG:","before: n=36 distance = 36)"] ["DEBUG:","before: n=37 distance = 36)"] ["DEBUG:","before: n=38 distance = 36)"] ... ["DEBUG:","before: n=52 distance = 36)"] "rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd"
Julia
const Nr = [3, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3]
const Nc = [3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]
const N0 = zeros(Int, 85)
const N2 = zeros(UInt64, 85)
const N3 = zeros(UInt8, 85)
const N4 = zeros(Int, 85)
const i = 1
const g = 8
const ee = 2
const l = 4
const _n = Vector{Int32}([0])
function fY(n::Int)
if N2[n + 1] == UInt64(0x123456789abcdef0)
return true, n
end
if N4[n + 1] <= _n[1]
return fN(n)
end
false, n
end
function fZ(w, n)
if w & i > 0
n = fI(n)
(y, n) = fY(n)
if y return (true, n) end
n -= 1
end
if w & g > 0
n = fG(n)
(y, n) = fY(n)
if y return (true, n) end
n -= 1
end
if w & ee > 0
n = fE(n)
(y, n) = fY(n)
if y return (true, n) end
n -= 1
end
if w & l > 0
n = fL(n)
(y, n) = fY(n)
if y return (true, n) end
n -= 1
end
false, n
end
function fN(n::Int)
x = N0[n + 1]
y = UInt8(N3[n + 1])
if x == 0
if y == UInt8('l')
return fZ(i, n)
elseif y == UInt8('u')
return fZ(ee, n)
else
return fZ(i + ee, n)
end
elseif x == 3
if y == UInt8('r')
return fZ(i, n)
elseif y == UInt8('u')
return fZ(l, n)
else
return fZ(i + l, n)
end
elseif x == 1 || x == 2
if y == UInt8('l')
return fZ(i + l, n)
elseif y == UInt8('r')
return fZ(i + ee, n)
elseif y == UInt8('u')
return fZ(ee + l, n)
else
return fZ(l + ee + i, n)
end
elseif x == 12
if y == UInt8('l')
return fZ(g, n)
elseif y == UInt8('d')
return fZ(ee, n)
else
return fZ(ee + g, n)
end
elseif x == 15
if y == UInt8('r')
return fZ(g, n)
elseif y == UInt8('d')
return fZ(l, n)
else
return fZ(g + l, n)
end
elseif x == 13 || x == 14
if y == UInt8('l')
return fZ(g + l, n)
elseif y == UInt8('r')
return fZ(ee + g, n)
elseif y == UInt8('d')
return fZ(ee + l, n)
else
return fZ(g + ee + l, n)
end
elseif x == 4 || x == 8
if y == UInt8('l')
return fZ(i + g, n)
elseif y == UInt8('u')
return fZ(g + ee, n)
elseif y == UInt8('d')
return fZ(i + ee, n)
else
return fZ(i + g + ee, n)
end
elseif x == 7 || x == 11
if y == UInt8('d')
return fZ(i + l, n)
elseif y == UInt8('u')
return fZ(g + l, n)
elseif y == UInt8('r')
return fZ(i + g, n)
else
return fZ(i + g + l, n)
end
else
if y == UInt8('d')
return fZ(i + ee + l, n)
elseif y == UInt8('l')
return fZ(i + g + l, n)
elseif y == UInt8('r')
return fZ(i + g + ee, n)
elseif y == UInt8('u')
return fZ(g + ee + l, n)
else
return fZ(i + g + ee + l, n)
end
end
end
function fI(n)
gg = (11 - N0[n + 1]) * 4
a = N2[n + 1] & (UInt64(0xf) << UInt(gg))
N0[n + 2] = N0[n + 1] + 4
N2[n + 2] = N2[n + 1] - a + (a << 16)
N3[n + 2] = UInt8('d')
N4[n + 2] = N4[n + 1]
cond = Nr[(a >> gg) + 1] <= div(N0[n + 1], 4)
if !cond
N4[n + 2] += 1
end
n += 1
n
end
function fG(n)
gg = (19 - N0[n + 1]) * 4
a = N2[n + 1] & (UInt64(0xf) << UInt(gg))
N0[n + 2] = N0[n + 1] - 4
N2[n + 2] = N2[n + 1] - a + (a >> 16)
N3[n + 2] = UInt8('u')
N4[n + 2] = N4[n + 1]
cond = Nr[(a >> gg) + 1] >= div(N0[n + 1], 4)
if !cond
N4[n + 2] += 1
end
n += 1
n
end
function fE(n)
gg = (14 - N0[n + 1]) * 4
a = N2[n + 1] & (UInt64(0xf) << UInt(gg))
N0[n + 2] = N0[n + 1] + 1
N2[n + 2] = N2[n + 1] - a + (a << 4)
N3[n + 2] = UInt8('r')
N4[n + 2] = N4[n + 1]
cond = Nc[(a >> gg) + 1] <= N0[n + 1] % 4
if !cond
N4[n + 2] += 1
end
n += 1
n
end
function fL(n)
gg = (16 - N0[n + 1]) * 4
a = N2[n + 1] & (UInt64(0xf) << UInt(gg))
N0[n + 2] = N0[n + 1] - 1
N2[n + 2] = N2[n + 1] - a + (a >> 4)
N3[n + 2] = UInt8('l')
N4[n + 2] = N4[n + 1]
cond = Nc[(a >> gg) + 1] >= N0[n + 1] % 4
if !cond
N4[n + 2] += 1
end
n += 1
n
end
function solve(n)
ans, n = fN(n)
if ans
println("Solution found in $n moves: ")
for ch in N3[2:n+1] print(Char(ch)) end; println()
else
println("next iteration, _n[1] will be $(_n[1] + 1)...")
n = 0; _n[1] += 1; solve(n)
end
end
run() = (N0[1] = 8; _n[1] = 1; N2[1] = 0xfe169b4c0a73d852; solve(0))
run()
- Output:
next iteration, _n[1] will be 2... next iteration, _n[1] will be 3... next iteration, _n[1] will be 4... next iteration, _n[1] will be 5... next iteration, _n[1] will be 6... next iteration, _n[1] will be 7... next iteration, _n[1] will be 8... Solution found in 52 moves: rrrulddluuuldrurdddrullulurrrddldluurddlulurruldrdrd
Lua
Original
#!/usr/bin/lua
--[[
Solve 3X3 sliding tile puzzle using Astar on Lua. Requires 3mb and
millions of recursions.
by RMM 2020-may-1
]]--
local SOLUTION_LIMIT, MAX_F_VALUE = 100,100
local NR, NC, RCSIZE = 4,4,4*4
local Up, Down, Right, Left = 'u','d','r','l'
local G_cols = {} -- goal columns
local G_rows = {} -- goal rows
local C_cols = {} -- current cols
local C_rows = {} -- current rows
local Goal = {}
local Tiles = {} -- the puzzle
local Solution = {} -- final path is instance of desc
local desc = {} -- descending path
desc[0] = 0 -- override Lua default "1" index
-- @brief create C compatible array for Lua
local function Amake( list )
array = {}
for i=0, #list do
array[i] = list[i+1] -- simulate "C" array in Lua
end
return array
end
G_cols= Amake({0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, } )
G_rows= Amake({0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, } )
C_cols= Amake({0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, } )
C_rows= Amake({0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, } )
Tiles = Amake({ 15,14,1,6, 9,11,4,12, 0,10,7,3, 13,8,5,2,} )
Goal = Amake({1,2,3,4, 5,6,7,8, 9,10,11,12, 13,14,15,0,} )
local m1 = {recursions=0, found=0, threshold=0, times=0, steps=0,}
-- ---------------------------------------------------------------
-- return 1D array index given 2D row,column
local function rcidx( row, col )
return (row * NR + col)
end
-- @brief recursive search
-- @return f_score
local function search( depth, x_row, x_col, h_score)
local move, go_back_move, last_move_by_current
local f_score, ix, min, temp, hscore2, idx1
local N_minus_one = NR - 1;
local rc1 = {row=0,col=0}
local rc2 = {row=0,col=0}
local gtmp = {row=0,col=0}
f_score = depth + h_score;
if f_score > m1.threshold then return f_score end
if h_score == 0 then do
m1.found = 1
Solution = table.concat(desc)
return f_score end end
m1.recursions = m1.recursions+1
m1.times = m1.times + 1
if m1.times > 200000 then do
print("Recursions ",m1.recursions)
m1.times = 0
end end
min = 999999
last_move_by_current = desc[depth];
rc1.row = x_row;
rc1.col = x_col;
for ix = 0,3 do
if ix==0 then do
move = Up;
go_back_move = Down;
rc2.row = x_row - 1;
rc2.col = x_col;
end
elseif ix==1 then do
move = Down;
go_back_move = Up;
rc2.row = x_row + 1;
rc2.col = x_col;
end
elseif ix==2 then do
move = Left;
go_back_move = Right;
rc2.row = x_row;
rc2.col = x_col - 1;
end
elseif ix==3 then do
move = Right;
go_back_move = Left;
rc2.row = x_row;
rc2.col = x_col + 1;
end end
if move==Up and x_row==0 then goto next end
if move==Down and x_row==N_minus_one then goto next end
if move==Left and x_col==0 then goto next end
if move==Right and x_col==N_minus_one then goto next end
if last_move_by_current==go_back_move then goto next end
hscore2 = h_score
idx1 = Tiles[rcidx(rc2.row,rc2.col)]
gtmp.row = G_rows[idx1]
gtmp.col = G_cols[idx1]
local h_adj=0
if go_back_move==Up then do
if gtmp.row < C_rows[idx1] then
h_adj = -1 else h_adj = 1 end end
end
if go_back_move==Down then do
if gtmp.row > C_rows[idx1] then
h_adj = -1 else h_adj = 1 end end
end
if go_back_move==Left then do
if gtmp.col < C_cols[idx1] then
h_adj = -1 else h_adj = 1 end end
end
if go_back_move==Right then do
if gtmp.col > C_cols[idx1] then
h_adj = -1 else h_adj = 1 end end
end
hscore2 = hscore2 + h_adj
C_rows[0] = rc2.row;
C_cols[0] = rc2.col;
C_rows[idx1] = rc1.row;
C_cols[idx1] = rc1.col;
Tiles[rcidx(rc1.row,rc1.col)] = idx1;
Tiles[rcidx(rc2.row,rc2.col)] = 0;
desc[depth+1] = move
desc[depth+2] = '\0'
temp = search(depth+1, rc2.row, rc2.col, hscore2); -- descend
-- regress
Tiles[rcidx(rc1.row,rc1.col)] = 0
Tiles[rcidx(rc2.row,rc2.col)] = idx1
desc[depth+1] = '\0'
C_rows[0] = rc1.row;
C_cols[0] = rc1.col;
C_rows[idx1] = rc2.row;
C_cols[idx1] = rc2.col;
if m1.found == 1 then return temp end
if temp < min then min = temp end
::next:: -- Lua does not have "continue;" so uses goto
end -- end for
m1.found = 0;
-- return the minimum f_score greater than m1.threshold
return min;
end
-- @brief Run solver using A-star algorithm
-- @param Tiles .. 3X3 sliding tile puzzle
local function solve(Tiles)
local temp, i,j
local x_row, x_col, h_score = 0,0,0
m1.found = 0;
for i=0,(NR