Solve a Rubik's cube: Difference between revisions
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{{draft task}}
;Task:
Create a program that is capable of solving a Rubik's Cube as efficiently as possible.
Other names are:
::* Magic Cube
::* Speed Cube
::* Puzzle Cube
::* Cube
You may use any sort of input you wish.
<br><br>
=={{header|Go}}==
As in the case of the Kotlin entry, this is a translation of the C++ competition code by Stefan Pochmann.
On the same machine, typical timings for the 100 line dataset are just over 200 milliseconds which is significantly slower than both the Kotlin and C++ code but still acceptable.
The relative slowness may be partly due to maps in Go not being able to accept reference types (such as slices) as a key because they don't support the '==' operator which tests for structural equality. I've therefore had to copy each slice returned by the 'id' function into a forty element array (a value type in Go) and use that as a key instead.
For the single line example, typical timings are around 240 milliseconds which is much faster than Kotlin due, no doubt, to JVM warm up time.
<syntaxhighlight lang="go">/**********************************************************************
*
* A cube 'state' is an int array with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************/
package main
import (
"bufio"
"fmt"
"log"
"os"
"strings"
"time"
)
type ai = [40]int
var applicableMoves = [5]int{0, 262143, 259263, 74943, 74898}
var phase = 0
var affectedCubies = [6][8]int{
{0, 1, 2, 3, 0, 1, 2, 3}, // U
{4, 7, 6, 5, 4, 5, 6, 7}, // D
{0, 9, 4, 8, 0, 3, 5, 4}, // F
{2, 10, 6, 11, 2, 1, 7, 6}, // B
{3, 11, 7, 9, 3, 2, 6, 5}, // L
{1, 8, 5, 10, 1, 0, 4, 7}, // R
}
func btoi(b bool) int {
if b {
return 1
}
return 0
}
func sliceToAi(s []int) ai {
var a ai
copy(a[:], s)
for i := len(s); i < 40; i++ {
a[i] = -1
}
return a
}
func applyMove(move int, state ai) ai {
turns := move%3 + 1
face := move / 3
for turns != 0 {
turns--
oldState := state
for i := 0; i < 8; i++ {
isCorner := btoi(i > 3)
target := affectedCubies[face][i] + isCorner*12
temp := i + 1
if (i & 3) == 3 {
temp = i - 3
}
killer := affectedCubies[face][temp] + isCorner*12
var orientationDelta int
switch {
case i < 4:
orientationDelta = btoi(face > 1 && face < 4)
case face < 2:
orientationDelta = 0
default:
orientationDelta = 2 - (i & 1)
}
state[target] = oldState[killer]
state[target+20] = oldState[killer+20] + orientationDelta
if turns == 0 {
state[target+20] %= 2 + isCorner
}
}
}
return state
}
func inverse(move int) int {
return move + 2 - 2*(move%3)
}
func id(state ai) ai {
//--- Phase 1: Edge orientations.
if phase < 2 {
return sliceToAi(state[20:32])
}
//-- Phase 2: Corner orientations, E slice edges.
if phase < 3 {
result := state[31:40]
for e := uint(0); e < 12; e++ {
result[0] |= (state[e] / 8) << e
}
return sliceToAi(result)
}
//--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
if phase < 4 {
result := []int{0, 0, 0}
for e := uint(0); e < 12; e++ {
temp := 2
if state[e] <= 7 {
temp = state[e] & 1
}
result[0] |= temp << (2 * e)
}
for c := uint(0); c < 8; c++ {
result[1] |= ((state[c+12] - 12) & 5) << (3 * c)
}
for i := 12; i < 19; i++ {
for j := i + 1; j < 20; j++ {
result[2] ^= btoi(state[i] > state[j])
}
}
return sliceToAi(result)
}
//--- Phase 4: The rest.
return state
}
func main() {
startTime := time.Now()
aggregateMoves := 0
//--- Define the goal.
goal := [20]string{
"UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR",
}
//--- Load dataset (file name should be passed as a command line argument).
if len(os.Args) != 2 {
log.Fatal("the file name should be passed as a command line argument")
}
file, err := os.Open(os.Args[1])
if err != nil {
log.Fatal(err)
}
defer file.Close()
var lineCount = 0
scanner := bufio.NewScanner(file)
for scanner.Scan() {
line := scanner.Text()
inputs := strings.Fields(line)
lineCount++
phase = 0
totalMoves := 0
//--- Prepare current (start) and goal state.
var currentState ai
var goalState ai
for i := 0; i < 20; i++ {
//--- Goal state.
goalState[i] = i
//--- Current (start) state.
cubie := inputs[i]
for {
idx := -1
for c := 0; c < len(goal); c++ {
if goal[c] == cubie {
idx = c
break
}
}
if idx >= 0 {
currentState[i] = idx
} else {
currentState[i] = 20
}
if currentState[i] != 20 {
break
}
cubie = cubie[1:] + cubie[:1]
currentState[i+20]++
}
}
//--- Dance the funky Thistlethwaite..
nextPhase:
for phase++; phase < 5; phase++ {
//--- Compute ids for current and goal state, skip phase if equal.
currentId := id(currentState)
goalId := id(goalState)
if currentId == goalId {
continue
}
//--- Initialize the BFS queue.
q := []ai{currentState, goalState}
//--- Initialize the BFS tables.
predecessor := make(map[ai]ai)
direction := make(map[ai]int)
lastMove := make(map[ai]int)
direction[currentId] = 1
direction[goalId] = 2
//--- Dance the funky bidirectional BFS...
for {
//--- Get state from queue, compute its ID and get its direction.
oldState := q[0]
q = q[1:]
oldId := id(oldState)
oldDir := direction[oldId]
//--- Apply all applicable moves to it and handle the new state.
for move := 0; move < 18; move++ {
if (applicableMoves[phase] & (1 << uint(move))) != 0 {
//--- Apply the move.
newState := applyMove(move, oldState)
newId := id(newState)
newDir := direction[newId]
//--- Have we seen this state (id) from the other direction already?
//--- I.e. have we found a connection?
if (newDir != 0) && (newDir != oldDir) {
//--- Make oldId represent the forwards
//--- and newId the backwards search state.
if oldDir > 1 {
newId, oldId = oldId, newId
move = inverse(move)
}
//--- Reconstruct the connecting algorithm.
algorithm := []int{move}
for oldId != currentId {
algorithm = append(algorithm, 0)
copy(algorithm[1:], algorithm[0:])
algorithm[0] = lastMove[oldId]
oldId = predecessor[oldId]
}
for newId != goalId {
algorithm = append(algorithm, inverse(lastMove[newId]))
newId = predecessor[newId]
}
//--- Print and apply the algorithm.
for i := 0; i < len(algorithm); i++ {
fmt.Printf("%c", "UDFBLR"[algorithm[i]/3])
fmt.Print(algorithm[i]%3 + 1)
fmt.Print(" ")
totalMoves++
currentState = applyMove(algorithm[i], currentState)
}
//--- Jump to the next phase.
continue nextPhase
}
//--- If we've never seen this state (id) before, visit it.
if newDir == 0 {
q = append(q, newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
}
}
}
}
}
fmt.Printf(" (moves %d)\n", totalMoves)
aggregateMoves += totalMoves
}
if err := scanner.Err(); err != nil {
log.Fatal(err)
}
endTime := time.Now()
elapsedTime := endTime.Sub(startTime).Nanoseconds() / 1000000
fmt.Println("\nAverage number of moves =", float64(aggregateMoves)/float64(lineCount))
fmt.Println("\nAverage time =", elapsedTime/int64(lineCount), "milliseconds")
}</syntaxhighlight>
{{out}}
<pre>
Same as Kotlin entry apart, of course, from the timings.
</pre>
=={{header|Julia}}==
{{trans|Kotlin}}
<syntaxhighlight lang="julia">#=**********************************************************************
*
* A cube 'state' is a vector<int> with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
*********************************************************************=#
const applicablemoves = [0, 262143, 259263, 74943, 74898]
const affectedcubies = [
0 1 2 3 0 1 2 3; # U
4 7 6 5 4 5 6 7; # D
0 9 4 8 0 3 5 4; # F
2 10 6 11 2 1 7 6; # B
3 11 7 9 3 2 6 5; # L
1 8 5 10 1 0 4 7] # R
function applymove(move, state)
state2, oldstate2 = deepcopy(state), zeros(Int, length(state))
face, turns = divrem(move, 3) .+ 1
while turns != 0
turns -= 1
oldstate2 .= state2
for i in 1:8
iscorner = i > 4
target = affectedcubies[face, i] + iscorner * 12 + 1
temp = ((i-1) & 3) == 3 ? i - 3 : i + 1
killer = affectedcubies[face, temp] + iscorner * 12 + 1
orientationdelta = i < 5 ? Int(face in [3, 4]) : face < 3 ? 0 : 2 - ((i-1) & 1)
state2[target] = oldstate2[killer]
state2[target + 20] = oldstate2[killer + 20] + orientationdelta
(turns == 0) && (state2[target + 20] %= 2 + iscorner)
end
end
return state2
end
inverse(move) = move + 2 - 2 * (move % 3)
function id(state::Vector{Int}, phase::Int)
#--- Phase 1: Edge orientations.
if phase < 2
return state[21:32]
elseif phase < 3
#-- Phase 2: Corner orientations, E slice edges.
result = state[32:40]
for e in 0:11
result[1] |= ((state[e + 1] ÷ 8) << e)
end
return result
elseif phase < 4
#--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
result = zeros(Int, 3)
for e in 0:11
result[1] |= state[e + 1] > 7 ? 2 : (state[e + 1] & 1) << (2 * e)
end
for c in 0:7
result[2] |= ((state[c + 12 + 1] - 12) & 5) << (3 * c)
end
for i in 13:19, j in i+1:20
result[3] ⊻= Int(state[i] > state[j])
end
return result
end
#--- Phase 4: The rest.
return state
end
function pochmann(fname)
starttime = time_ns() ÷ 1000000
aggregatemoves = 0
#--- Define the goal.
goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]
#--- Load dataset (file name should be passed as a command line argument).
file = read(fname, String)
linecount = 0
for line in split(strip(file), "\n")
inputs = split(line)
linecount += 1
totalmoves = 0
#--- Prepare current (start) and goal state.
state, goalstate, phase = zeros(Int, 40), zeros(Int, 40), 0
for i in 1:20
#--- Goal state.
goalstate[i] = i - 1
#--- Current (start) state.
cubie = inputs[i]
while true
state[i] = something(findfirst(x -> x .== cubie, goal), 21) - 1
(state[i] != 20) && break
cubie = cubie[2:end] * cubie[1]
state[i + 20] += 1
end
end
#--- Dance the funky Thistlethwaite...
@label nextphase # preserves phase value, but restarts while loop
while (phase += 1) < 5
#--- Compute ids for current and goal state, skip phase if equal.
currentid = id(state, phase)
goalid = id(goalstate, phase)
currentid == goalid && continue
#--- Initialize the BFS queue.
q = [state, goalstate]
#--- Initialize the BFS tables.
predecessor = Dict{Vector{Int}, Vector{Int}}()
direction = Dict{Vector{Int}, Int}()
lastmove = Dict{Vector{Int}, Int}()
direction[currentid] = 1
direction[goalid] = 2
#--- Dance the funky bidirectional BFS...
while true
#--- Get state from queue, compute its ID and get its direction.
oldstate = popfirst!(q)
oldid = id(oldstate, phase)
olddir = get!(direction, oldid, 0)
#--- Apply all applicable moves to it and handle the new state.
for move in 0:17
if applicablemoves[phase + 1] & (1 << UInt(move)) != 0
#--- Apply the move.
newstate = applymove(move, oldstate)
newid = id(newstate, phase)
newdir = get!(direction, newid, 0)
#--- Have we seen this state (id) from the other direction already?
#--- I.e. have we found a connection?
if (newdir != 0) && (newdir != olddir)
#--- Make oldid represent the forwards
#--- and newid the backwards search state.
if olddir > 1
newid, oldid = oldid, newid
move = inverse(move)
end
#--- Reconstruct the connecting algorithm.
algorithm = [move]
while oldid != currentid
pushfirst!(algorithm, get(lastmove, oldid, 0))
oldid = get!(predecessor, oldid, Int[])
end
while newid != goalid
push!(algorithm, inverse(get!(lastmove, newid, 0)))
newid = get!(predecessor, newid, Int[])
end
#--- Print and apply the algorithm.
for i in 1:length(algorithm)
print("UDFBLR"[algorithm[i] ÷ 3 + 1])
print(algorithm[i] % 3 + 1)
print(" ")
totalmoves += 1
state = applymove(algorithm[i], state)
end
#--- Jump to the next phase.
@goto nextphase
end
#--- If we've never seen this state (id) before, visit it.
if newdir == 0
push!(q, newstate)
direction[newid] = olddir
lastmove[newid] = move
predecessor[newid] = oldid
end
end
move += 1
end
end
end
println(" (moves $totalmoves)")
aggregatemoves += totalmoves
end
elapsedtime = time_ns() ÷ 1000000 - starttime
println("\nAverage number of moves = $(aggregatemoves / linecount)")
println("\nAverage time = $(elapsedtime / linecount) milliseconds")
end
pochmann("rubikdata.txt")
</syntaxhighlight>{{out}}
Using the 100-line database:
<pre style="height:45ex">
(moves 0)
U1 U2 (moves 2)
U2 (moves 1)
U1 (moves 1)
F1 F2 (moves 2)
F2 (moves 1)
F1 (moves 1)
R1 R2 (moves 2)
R2 (moves 1)
R1 (moves 1)
D1 D2 (moves 2)
D2 (moves 1)
D1 (moves 1)
B1 B2 (moves 2)
B2 (moves 1)
B1 (moves 1)
L1 L2 (moves 2)
L2 (moves 1)
L1 (moves 1)
U2 B3 B2 (moves 3)
L2 U3 (moves 2)
R1 U1 (moves 2)
D3 L3 (moves 2)
D3 L2 (moves 2)
D2 F3 F2 (moves 3)
R2 F3 (moves 2)
R1 F2 F2 R2 F2 (moves 5)
D1 D2 U2 (moves 3)
L1 B2 F2 L2 R2 B2 F2 (moves 7)
L1 L2 D3 (moves 3)
D1 F2 (moves 2)
U2 R3 (moves 2)
L1 L2 U3 (moves 3)
U1 R2 (moves 2)
U1 R3 (moves 2)
F1 U2 (moves 2)
U2 R3 R2 (moves 3)
F2 D1 F3 (moves 3)
F2 D3 D2 U2 (moves 4)
L3 D2 R3 (moves 3)
D2 R3 R2 D3 (moves 4)
F1 R1 B2 B2 R2 B2 (moves 6)
L1 B2 F2 (moves 3)
U1 R2 B3 B2 (moves 4)
R2 F3 R2 (moves 3)
L2 D3 R3 R2 (moves 4)
L2 F3 L2 L2 F2 L2 (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2 (moves 29)
L1 L2 U3 R2 (moves 4)
L3 B3 B2 R3 R2 (moves 5)
B2 U1 R3 R2 (moves 4)
L3 B3 L2 (moves 3)
D1 B2 L3 L2 (moves 4)
B1 B2 R3 F2 F2 R2 F2 (moves 7)
D1 F3 D1 D2 (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2 (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2 (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2 (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2 (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2 (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2 (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2 (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2 (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2 (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2 (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2 (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2 (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2 (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2 (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2 (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2 (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2 (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2 (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2 (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2 (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2 (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2 (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2 (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2 (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2 (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2 (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2 (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2 (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2 (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2 (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2 (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2 (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2 (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2 (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2 (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2 (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2 (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2 (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2 (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2 (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2 (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2 (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2 (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2 (moves 36)
Average number of moves = 16.38
Average time = 65.71 milliseconds
</pre>
=={{header|Kotlin}}==
This is a translation of Stefan Pochmann's C++ entry in the 2004 competition which was linked to by the author of the Phix entry. This program won the Judge's prize, finished second overall and (as in the case of the winner) is based on Thistlethwaite's algorithm.
I've adjusted the code to accept input from a file whose name is supplied via a command line argument and, as in the case of the original competition, to calculate the average number of moves for each line in the file and the average time to process each one.
To aid readability I've also inserted spaces between each move in the results and added the total moves needed for each line.
<syntaxhighlight lang="scala">// version 1.2.21
/**********************************************************************
*
* A cube 'state' is a vector<int> with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************/
import java.util.ArrayDeque
import java.io.File
fun Boolean.toInt() = if (this) 1 else 0
typealias AI = ArrayList<Int>
val applicableMoves = intArrayOf(0, 262143, 259263, 74943, 74898)
val affectedCubies = listOf(
intArrayOf(0, 1, 2, 3, 0, 1, 2, 3), // U
intArrayOf(4, 7, 6, 5, 4, 5, 6, 7), // D
intArrayOf(0, 9, 4, 8, 0, 3, 5, 4), // F
intArrayOf(2, 10, 6, 11, 2, 1, 7, 6), // B
intArrayOf(3, 11, 7, 9, 3, 2, 6, 5), // L
intArrayOf(1, 8, 5, 10, 1, 0, 4, 7) // R
)
fun applyMove(move: Int, state: AI): AI {
val state2 = AI(state) // avoids mutating original 'state'.
var turns = move % 3 + 1
val face = move / 3
while (turns-- != 0) {
val oldState2 = AI(state2)
for (i in 0..7) {
val isCorner = (i > 3).toInt()
val target = affectedCubies[face][i] + isCorner * 12
val temp = if ((i and 3) == 3) i - 3 else i + 1
val killer = affectedCubies[face][temp] + isCorner * 12
val orientationDelta =
if (i < 4) (face in 2..3).toInt()
else if (face < 2) 0
else 2 - (i and 1)
state2[target] = oldState2[killer]
state2[target + 20] = oldState2[killer + 20] + orientationDelta
if (turns == 0) state2[target + 20] %= 2 + isCorner
}
}
return state2
}
fun inverse(move: Int) = move + 2 - 2 * (move % 3)
var phase = 0
fun id(state: AI): AI {
//--- Phase 1: Edge orientations.
if (phase < 2) return AI(state.subList(20, 32))
//-- Phase 2: Corner orientations, E slice edges.
if (phase < 3) {
val result = AI(state.subList(31, 40))
for (e in 0..11) result[0] = result[0] or ((state[e] / 8) shl e)
return result
}
//--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
if (phase < 4) {
val result = AI(3)
repeat(3) { result.add(0) }
for (e in 0..11) {
val temp = (if (state[e] > 7) 2 else (state[e] and 1)) shl (2 * e)
result[0] = result[0] or temp
}
for (c in 0..7) {
val temp = ((state[c + 12] - 12) and 5) shl (3 * c)
result[1] = result[1] or temp
}
for (i in 12..18) {
for (j in (i + 1)..19) {
result[2] = result[2] xor (state[i] > state[j]).toInt()
}
}
return result
}
//--- Phase 4: The rest.
return state
}
fun main(args: Array<String>) {
val startTime = System.currentTimeMillis()
var aggregateMoves = 0
//--- Define the goal.
val goal = listOf(
"UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"
)
//--- Load dataset (file name should be passed as a command line argument).
val file = File(args[0])
var lineCount = 0
file.forEachLine { line ->
val inputs = line.split(' ')
lineCount++
phase = 0
var totalMoves = 0
//--- Prepare current (start) and goal state.
var currentState = AI(40)
repeat(40) { currentState.add(0) }
val goalState = AI(40)
repeat(40) { goalState.add(0) }
for (i in 0..19) {
//--- Goal state.
goalState[i] = i
//--- Current (start) state.
var cubie = inputs[i]
while (true) {
val idx = goal.indexOf(cubie)
currentState[i] = if (idx >= 0) idx else 20
if (currentState[i] != 20) break
cubie = cubie.substring(1) + cubie[0]
currentState[i + 20]++
}
}
//--- Dance the funky Thistlethwaite...
nextPhase@ while (++phase < 5) {
//--- Compute ids for current and goal state, skip phase if equal.
val currentId = id(currentState)
val goalId = id(goalState)
if (currentId == goalId) continue
//--- Initialize the BFS queue.
val q = ArrayDeque<AI>()
q.addLast(currentState)
q.addLast(goalState)
//--- Initialize the BFS tables.
val predecessor = mutableMapOf<AI, AI>()
val direction = mutableMapOf<AI, Int>()
val lastMove = mutableMapOf<AI, Int>()
direction[currentId] = 1
direction[goalId] = 2
//--- Dance the funky bidirectional BFS...
while (true) {
//--- Get state from queue, compute its ID and get its direction.
val oldState = q.peek()
q.pop()
var oldId = id(oldState)
val oldDir = direction.getOrPut(oldId) { 0 }
//--- Apply all applicable moves to it and handle the new state.
var move = 0
while (move < 18) {
if ((applicableMoves[phase] and (1 shl move)) != 0) {
//--- Apply the move.
val newState = applyMove(move, oldState)
var newId = id(newState)
var newDir = direction.getOrPut(newId) { 0 }
//--- Have we seen this state (id) from the other direction already?
//--- I.e. have we found a connection?
if ((newDir != 0) && (newDir != oldDir)) {
//--- Make oldId represent the forwards
//--- and newId the backwards search state.
if (oldDir > 1) {
val temp = newId
newId = oldId
oldId = temp
move = inverse(move)
}
//--- Reconstruct the connecting algorithm.
val algorithm = AI()
algorithm.add(move)
while (oldId != currentId) {
val tempI = lastMove.getOrPut(oldId) { 0 }
algorithm.add(0, tempI)
val tempAI = predecessor.getOrPut(oldId) { AI() }
oldId = tempAI
}
while (newId != goalId) {
val tempI = lastMove.getOrPut(newId) { 0 }
algorithm.add(inverse(tempI))
val tempAI = predecessor.getOrPut(newId) { AI() }
newId = tempAI
}
//--- Print and apply the algorithm.
for (i in 0 until algorithm.size) {
print("UDFBLR"[algorithm[i] / 3])
print(algorithm[i] % 3 + 1)
print(" ")
totalMoves++
currentState = applyMove(algorithm[i], currentState)
}
//--- Jump to the next phase.
continue@nextPhase
}
//--- If we've never seen this state (id) before, visit it.
if (newDir == 0) {
q.addLast(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
}
}
move++
}
}
}
println(" (moves $totalMoves)")
aggregateMoves += totalMoves
}
val elapsedTime = System.currentTimeMillis() - startTime
println("\nAverage number of moves = ${aggregateMoves.toDouble() / lineCount}")
println("\nAverage time = ${elapsedTime / lineCount} milliseconds")
}</syntaxhighlight>
{{out}}
Using the original dataset of 100 lines, the results were as follows (time doesn't mean much but is typical for my modest machine):
<pre style="height:45ex">
U1 U2 (moves 2)
U2 (moves 1)
U1 (moves 1)
F1 F2 (moves 2)
F2 (moves 1)
F1 (moves 1)
R1 R2 (moves 2)
R2 (moves 1)
R1 (moves 1)
D1 D2 (moves 2)
D2 (moves 1)
D1 (moves 1)
B1 B2 (moves 2)
B2 (moves 1)
B1 (moves 1)
L1 L2 (moves 2)
L2 (moves 1)
L1 (moves 1)
U2 B3 B2 (moves 3)
L2 U3 (moves 2)
R1 U1 (moves 2)
D3 L3 (moves 2)
D3 L2 (moves 2)
D2 F3 F2 (moves 3)
R2 F3 (moves 2)
R1 F2 F2 R2 F2 (moves 5)
D1 D2 U2 (moves 3)
L1 B2 F2 L2 R2 B2 F2 (moves 7)
L1 L2 D3 (moves 3)
D1 F2 (moves 2)
U2 R3 (moves 2)
L1 L2 U3 (moves 3)
U1 R2 (moves 2)
U1 R3 (moves 2)
F1 U2 (moves 2)
U2 R3 R2 (moves 3)
F2 D1 F3 (moves 3)
F2 D3 D2 U2 (moves 4)
L3 D2 R3 (moves 3)
D2 R3 R2 D3 (moves 4)
F1 R1 B2 B2 R2 B2 (moves 6)
L1 B2 F2 (moves 3)
U1 R2 B3 B2 (moves 4)
R2 F3 R2 (moves 3)
L2 D3 R3 R2 (moves 4)
L2 F3 L2 L2 F2 L2 (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2 (moves 29)
L1 L2 U3 R2 (moves 4)
L3 B3 B2 R3 R2 (moves 5)
B2 U1 R3 R2 (moves 4)
L3 B3 L2 (moves 3)
D1 B2 L3 L2 (moves 4)
B1 B2 R3 F2 F2 R2 F2 (moves 7)
D1 F3 D1 D2 (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2 (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2 (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2 (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2 (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2 (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2 (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2 (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2 (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2 (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2 (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2 (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2 (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2 (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2 (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2 (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2 (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2 (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2 (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2 (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2 (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2 (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2 (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2 (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2 (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2 (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2 (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2 (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2 (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2 (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2 (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2 (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2 (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2 (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2 (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2 (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2 (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2 (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2 (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2 (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2 (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2 (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2 (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2 (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2 (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2 (moves 34)
</pre>
<pre>
Average number of moves = 16.72
Average time = 127 milliseconds
</pre>
When run with a file containing the single line:
UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL
a typical result was:
<pre>
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
Average number of moves = 29.0
Average time = 522 milliseconds
</pre>
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">#[
**********************************************************************
*
* A cube 'state' is a sequence of ints with 40 entries, the first
* 20 are a permutation of {0,...,19} and describe which cubie is
* at a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************
]#
import deques, os, strformat, strutils, tables, times
const
ApplicableMoves = [0, 262143, 259263, 74943, 74898]
AffectedCubies = [[0, 1, 2, 3, 0, 1, 2, 3], # U
[4, 7, 6, 5, 4, 5, 6, 7], # D
[0, 9, 4, 8, 0, 3, 5, 4], # F
[2, 10, 6, 11, 2, 1, 7, 6], # B
[3, 11, 7, 9, 3, 2, 6, 5], # L
[1, 8, 5, 10, 1, 0, 4, 7]] # R
type State = seq[int]
func initState(n: Natural = 0): State = newSeq[int](n)
var phase: Natural
proc slicetoState(s: openArray[int]): State =
result.setLen(40)
for i, val in s: result[i] = val
for i in s.len..39: result[i] = -1
proc id(state: State): State =
case phase
of 1: # Phase 1: Edge orientations.
result = sliceToState(state[20..31])
of 2: # Phase 2: Corner orientations, E slice edges.
var res = state[31..39]
for e in 0..11:
res[0] = res[0] or state[e] shr 3 shl e
result = sliceToState(res)
of 3: # Phase 3: Edge slices M and S, corner tetrads, overall parity.
var res = @[0, 0, 0]
for e in 0..11:
let temp = if state[e] > 7: 2 else: (state[e] and 1) shl (2 * e)
res[0] = res[0] or temp
for c in 0..7:
res[1] = res[1] or ((state[c + 12] - 12) and 5) shl (3 * c)
for i in 12..18:
for j in (i + 1)..19:
res[2] = res[2] xor ord(state[i] > state[j])
result = sliceToState(res)
else: # Phase 4: The rest.
result = state
proc applyMove(move: int; state: State): State =
result = state
var turns = move mod 3 + 1
let face = move div 3
while turns != 0:
dec turns
var oldState = result
for i in 0..7:
let isCorner = ord(i > 3)
let target = AffectedCubies[face][i] + isCorner * 12
let temp = if (i and 3) == 3: i - 3 else: i + 1
let killer = AffectedCubies[face][temp] + isCorner * 12
let orientationDelta =
if i < 4: ord(face in 2..3)
elif face < 2: 0
else: 2 - (i and 1)
result[target] = oldState[killer]
result[target + 20] = oldState[killer + 20] + orientationDelta
if turns == 0:
result[target + 20] = result[target + 20] mod (2 + isCorner)
func inverse(move: int): int = move + 2 - 2 * (move mod 3)
let startTime = cpuTime()
var aggregateMoves = 0
# Define the goal.
const Goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]
# Load dataset (file name should be passed as a command line argument).
if paramCount() == 0: quit "Missing file name", QuitFailure
var lineCount = 0
for line in paramStr(1).lines():
let inputs = line.splitWhitespace()
inc lineCount
var totalMoves = 0
# Prepare current (start) and goal state.
var currentState, goalState = initState(40)
for i in 0..19:
# Goal state.
goalState[i] = i
# Current (start) state.
var cubie = inputs[i]
while true:
let idx = Goal.find(cubie)
currentState[i] = if idx >= 0: idx else: 20
if currentState[i] != 20: break
cubie = cubie[1..^1] & cubie[0]
inc currentState[i + 20]
# Dance the funky Thistlethwaite...
phase = 1
while phase < 5:
block doPhase:
# Compute ids for current and goal state, skip phase if equal.
let currentId = id(currentState)
let goalId = id(goalState)
if currentId == goalId: break doPhase
# Initialize the BFS queue.
var q = [currentState, goalState].toDeque
# Initialize the BFS tables.
var predecessor: Table[State, State]
var direction, lastMove: Table[State, int]
direction[currentId] = 1
direction[goalId] = 2
# Dance the funky bidirectional BFS.
while true:
# Get state from queue, compute its ID and get its direction.
let oldState = q.popFirst()
var oldId = id(oldState)
let oldDir = direction[oldId]
# Apply all applicable moves to it and handle the new state.
var move = 0
while move < 18:
if (ApplicableMoves[phase] and (1 shl move)) != 0:
# Apply the move.
let newState = applyMove(move, oldState)
var newId = id(newState)
let newDir = direction.getOrDefault(newId, 0)
# Have we seen this state (id) from the other direction already?
# I.e. have we found a connection?
if newDir != 0 and newDir != oldDir:
# Make oldId represent the forwards and newId the backwards search state.
if oldDir > 1:
swap newId, oldId
move = inverse(move)
# Reconstruct the connecting algorithm.
var algorithm: State = @[move]
while oldId != currentId:
algorithm.insert(lastMove.mgetOrPut(oldId, 0), 0)
oldId = predecessor.mgetOrPut(oldId, initState())
while newId != goalId:
algorithm.add inverse(lastMove.mgetOrPut(newId, 0))
newId = predecessor.mgetOrPut(newId, initState())
# Print and apply the algorithm.
for step in algorithm:
stdout.write "UDFBLR"[step div 3], step mod 3 + 1, ' '
inc totalMoves
currentState = applyMove(step, currentState)
# Jump to the next phase.
break doPhase
# If we've never seen this state (id) before, visit it.
if newdir == 0:
q.addLast(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
inc move
inc phase
echo &" (moves {totalMoves})"
inc aggregateMoves, totalMoves
let elapsedTime = cpuTime() - startTime
echo &"\nAverage number of moves = {aggregateMoves / lineCount}"
echo &"\nAverage time = {elapsedTime * 1000 / lineCount.toFloat:.2f} milliseconds"</syntaxhighlight>
{{out}}
We compiled the program with command <code>nim c -d:danger --gc:arc -d:lto</code>, which means no runtime checks, ARC memory management and link time optimization.
When run with the original dataset of 100 lines, we got:
<pre style="height:45ex">U1 U2 (moves 2)
U2 (moves 1)
U1 (moves 1)
F1 F2 (moves 2)
F2 (moves 1)
F1 (moves 1)
R1 R2 (moves 2)
R2 (moves 1)
R1 (moves 1)
D1 D2 (moves 2)
D2 (moves 1)
D1 (moves 1)
B1 B2 (moves 2)
B2 (moves 1)
B1 (moves 1)
L1 L2 (moves 2)
L2 (moves 1)
L1 (moves 1)
U2 B3 B2 (moves 3)
L2 U3 (moves 2)
R1 U1 (moves 2)
D3 L3 (moves 2)
D3 L2 (moves 2)
D2 F3 F2 (moves 3)
R2 F3 (moves 2)
R1 F2 F2 R2 F2 (moves 5)
D1 D2 U2 (moves 3)
L1 B2 F2 L2 R2 B2 F2 (moves 7)
L1 L2 D3 (moves 3)
D1 F2 (moves 2)
U2 R3 (moves 2)
L1 L2 U3 (moves 3)
U1 R2 (moves 2)
U1 R3 (moves 2)
F1 U2 (moves 2)
U2 R3 R2 (moves 3)
F2 D1 F3 (moves 3)
F2 D3 D2 U2 (moves 4)
L3 D2 R3 (moves 3)
D2 R3 R2 D3 (moves 4)
F1 R1 B2 B2 R2 B2 (moves 6)
L1 B2 F2 (moves 3)
U1 R2 B3 B2 (moves 4)
R2 F3 R2 (moves 3)
L2 D3 R3 R2 (moves 4)
L2 F3 L2 L2 F2 L2 (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2 (moves 29)
L1 L2 U3 R2 (moves 4)
L3 B3 B2 R3 R2 (moves 5)
B2 U1 R3 R2 (moves 4)
L3 B3 L2 (moves 3)
D1 B2 L3 L2 (moves 4)
B1 B2 R3 F2 F2 R2 F2 (moves 7)
D1 F3 D1 D2 (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2 (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2 (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2 (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2 (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2 (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2 (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2 (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2 (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2 (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2 (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2 (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2 (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2 (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2 (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2 (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2 (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2 (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2 (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2 (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2 (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2 (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2 (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2 (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2 (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2 (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2 (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2 (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2 (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2 (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2 (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2 (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2 (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2 (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2 (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2 (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2 (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2 (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2 (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2 (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2 (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2 (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2 (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2 (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2 (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2 (moves 34)</pre>
<pre>Average number of moves = 16.72
Average time = 52.03 milliseconds</pre>
When run with a file containing the single line:
UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL
a typical result was:
<pre>U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
Average number of moves = 29.0
Average time = 69.01 milliseconds</pre>
=={{header|Phix}}==
===cfop===
Uses brute-force (width/highscore-first) Fridrich-steps (ie cross,f2l,oll,pll).<br>
Not the fastest (see THRESHOLD) or shortest results (see thistlethwaite) but the code is pretty easy to follow.<br>
The final stage (pll) would probably benefit the most from being replaced with standard algorithms.<br>
While technically this works under pwa/p2js, you should expect a blank screen for nearly 3 minutes.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\rubik_cfop.exw
--
-- Each stage uses a workspace of moves tried so far, ranked by score.
-- We repeatedly take the best scoring so far and try more moves, storing
-- those results in a second/new workspace. The THRESHOLD value below
-- determines the minimum number we should examine before discarding a
-- workspace and switching to the new (one move longer) one. We only ever
-- switch on change of score, and obviously the first workspace is empty,
-- and the next new workspace has a maximum of 12 entries (+/-90 by 6),
-- both of which will force earlier switches.
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">THRESHOLD</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100000</span> <span style="color: #000080;font-style:italic;">-- 100000 -- very slow (100s), best results
-- 10000 -- 10000 -- slow (10s), reasonable results
-- 1000 -- fast (1s), fairly poor results
-- 100 -- (counter-productive/slower)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">init</span> <span style="color: #0000FF;">=</span><span style="color: #008000;">"""
---YYY--------
---YYY--------
---YYY--------
BBBRRRGGGOOO--
BBBRRRGGGOOO--
BBBRRRGGGOOO--
------WWW-----
------WWW-----
------WWW-----
"""</span>
<span style="color: #000080;font-style:italic;">-- numbering:
-- 1..15: ---456--------\n
-- 16..30: ---901--------\n -- U
-- 31..45: ---456--------\n
-- 46..60: 678901234567--\n
-- 61..75: 123456789012--\n -- LFRB
-- 76..90: 678901234567--\n
-- 91..105: ------789-----\n
-- 106..120:------234-----\n -- D
-- 121..136:------789-----\n\n</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">init</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">136</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">--
-- TIP: Wrap a cube with blank paper, and write
-- the numbers on it, to derive these sets.
--</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">centres</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">62</span><span style="color: #0000FF;">,</span><span style="color: #000000;">65</span><span style="color: #0000FF;">,</span><span style="color: #000000;">68</span><span style="color: #0000FF;">,</span><span style="color: #000000;">71</span><span style="color: #0000FF;">,</span><span style="color: #000000;">113</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">edges</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">56</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- ie YYY/OOO</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">,</span><span style="color: #000000;">54</span><span style="color: #0000FF;">,</span><span style="color: #000000;">53</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- YYY/GGG</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">34</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">35</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">36</span><span style="color: #0000FF;">,</span><span style="color: #000000;">49</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">51</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- YYY/RRR</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">46</span><span style="color: #0000FF;">,</span><span style="color: #000000;">47</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- YYY/BBB</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">51</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">66</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">81</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span><span style="color: #000000;">67</span><span style="color: #0000FF;">,</span><span style="color: #000000;">82</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- RRR/GGG</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">54</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">69</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">84</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">85</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- GGG/OOO</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">57</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">72</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">87</span><span style="color: #0000FF;">,</span><span style="color: #000000;">46</span><span style="color: #0000FF;">,</span><span style="color: #000000;">61</span><span style="color: #0000FF;">,</span><span style="color: #000000;">76</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- OOO/BBB</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">48</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">63</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">78</span><span style="color: #0000FF;">,</span><span style="color: #000000;">49</span><span style="color: #0000FF;">,</span><span style="color: #000000;">64</span><span style="color: #0000FF;">,</span><span style="color: #000000;">79</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- BBB/RRR</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">97</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">98</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">99</span><span style="color: #0000FF;">,</span><span style="color: #000000;">82</span><span style="color: #0000FF;">,</span><span style="color: #000000;">83</span><span style="color: #0000FF;">,</span><span style="color: #000000;">84</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- WWW/GGG</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">99</span><span style="color: #0000FF;">,</span><span style="color: #000000;">114</span><span style="color: #0000FF;">,</span><span style="color: #000000;">129</span><span style="color: #0000FF;">,</span><span style="color: #000000;">85</span><span style="color: #0000FF;">,</span><span style="color: #000000;">86</span><span style="color: #0000FF;">,</span><span style="color: #000000;">87</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- WWW/OOO</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">127</span><span style="color: #0000FF;">,</span><span style="color: #000000;">128</span><span style="color: #0000FF;">,</span><span style="color: #000000;">129</span><span style="color: #0000FF;">,</span><span style="color: #000000;">78</span><span style="color: #0000FF;">,</span><span style="color: #000000;">77</span><span style="color: #0000FF;">,</span><span style="color: #000000;">76</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- WWW/BBB</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">97</span><span style="color: #0000FF;">,</span><span style="color: #000000;">112</span><span style="color: #0000FF;">,</span><span style="color: #000000;">127</span><span style="color: #0000FF;">,</span><span style="color: #000000;">81</span><span style="color: #0000FF;">,</span><span style="color: #000000;">80</span><span style="color: #0000FF;">,</span><span style="color: #000000;">79</span><span style="color: #0000FF;">}}</span> <span style="color: #000080;font-style:italic;">-- WWW/RRR</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">corners</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">46</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">49</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">36</span><span style="color: #0000FF;">,</span><span style="color: #000000;">51</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">},{</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">54</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">},</span>
<span style="color: #000080;font-style:italic;">-- YOB/UBL YBR/UFL YRG/UFR YGO/UBL</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">76</span><span style="color: #0000FF;">,</span><span style="color: #000000;">129</span><span style="color: #0000FF;">,</span><span style="color: #000000;">87</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">78</span><span style="color: #0000FF;">,</span><span style="color: #000000;">79</span><span style="color: #0000FF;">,</span><span style="color: #000000;">127</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">81</span><span style="color: #0000FF;">,</span><span style="color: #000000;">82</span><span style="color: #0000FF;">,</span><span style="color: #000000;">97</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">84</span><span style="color: #0000FF;">,</span><span style="color: #000000;">85</span><span style="color: #0000FF;">,</span><span style="color: #000000;">99</span><span style="color: #0000FF;">}}</span>
<span style="color: #000080;font-style:italic;">-- BWO/DBL BRW/DFL RGW/DFR GOW/DFL</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">facing_corners</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- (nb not 14,16)</span>
<span style="color: #000000;">facing_edges</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">fce</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">facing_corners</span><span style="color: #0000FF;">&</span><span style="color: #000000;">facing_edges</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">rotations</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>
<span style="color: #000080;font-style:italic;">-- up (clockwise):</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">54</span><span style="color: #0000FF;">,</span><span style="color: #000000;">51</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- clockwise corners</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">46</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span><span style="color: #000000;">49</span><span style="color: #0000FF;">},</span> <span style="color: #000080;font-style:italic;">-- anticlockwise corners</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">47</span><span style="color: #0000FF;">,</span><span style="color: #000000;">56</span><span style="color: #0000FF;">,</span><span style="color: #000000;">53</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">}},</span> <span style="color: #000080;font-style:italic;">-- middle edges
-- left</span>
<span style="color: #0000FF;">{{</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">49</span><span style="color: #0000FF;">,</span><span style="color: #000000;">127</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">87</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">57</span><span style="color: #0000FF;">,</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">79</span><span style="color: #0000FF;">,</span><span style="color: #000000;">129</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">64</span><span style="color: #0000FF;">,</span><span style="color: #000000;">128</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">72</span><span style="color: #0000FF;">}},</span>
<span style="color: #000080;font-style:italic;">-- front</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">97</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">78</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">48</span><span style="color: #0000FF;">,</span><span style="color: #000000;">36</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">82</span><span style="color: #0000FF;">,</span><span style="color: #000000;">127</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">35</span><span style="color: #0000FF;">,</span><span style="color: #000000;">67</span><span style="color: #0000FF;">,</span><span style="color: #000000;">112</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">63</span><span style="color: #0000FF;">}},</span>
<span style="color: #000080;font-style:italic;">-- right</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">36</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">99</span><span style="color: #0000FF;">,</span><span style="color: #000000;">81</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">51</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">85</span><span style="color: #0000FF;">,</span><span style="color: #000000;">97</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">21</span><span style="color: #0000FF;">,</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">98</span><span style="color: #0000FF;">,</span><span style="color: #000000;">66</span><span style="color: #0000FF;">}},</span>
<span style="color: #000080;font-style:italic;">-- back</span>
<span style="color: #0000FF;">{{</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">46</span><span style="color: #0000FF;">,</span><span style="color: #000000;">129</span><span style="color: #0000FF;">,</span><span style="color: #000000;">84</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">54</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">76</span><span style="color: #0000FF;">,</span><span style="color: #000000;">99</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">61</span><span style="color: #0000FF;">,</span><span style="color: #000000;">114</span><span style="color: #0000FF;">,</span><span style="color: #000000;">69</span><span style="color: #0000FF;">}},</span>
<span style="color: #000080;font-style:italic;">-- down</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">82</span><span style="color: #0000FF;">,</span><span style="color: #000000;">85</span><span style="color: #0000FF;">,</span><span style="color: #000000;">76</span><span style="color: #0000FF;">,</span><span style="color: #000000;">79</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">81</span><span style="color: #0000FF;">,</span><span style="color: #000000;">84</span><span style="color: #0000FF;">,</span><span style="color: #000000;">87</span><span style="color: #0000FF;">,</span><span style="color: #000000;">78</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">83</span><span style="color: #0000FF;">,</span><span style="color: #000000;">86</span><span style="color: #0000FF;">,</span><span style="color: #000000;">77</span><span style="color: #0000FF;">,</span><span style="color: #000000;">80</span><span style="color: #0000FF;">}}}</span>
<span style="color: #000080;font-style:italic;">--Up/Left/Front/Right/Back/Down</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">U</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">L</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">F</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">R</span><span style="color: #0000FF;">=</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">B</span><span style="color: #0000FF;">=</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">D</span><span style="color: #0000FF;">=</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">=</span><span style="color: #000000;">#08</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">=</span><span style="color: #000000;">#10</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">U2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">U</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">F2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">F</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">/*R2 = R+Dbl, B2 = B+Dbl,*/</span> <span style="color: #000000;">D2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">D</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">Us</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">U</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Fs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">F</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Bs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">B</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Rs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">R</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Ds</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">D</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Shift</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">CROSS</span><span style="color: #0000FF;">,</span><span style="color: #000000;">F2L</span><span style="color: #0000FF;">,</span><span style="color: #000000;">OLL</span><span style="color: #0000FF;">,</span><span style="color: #000000;">PLL</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">f2l</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (28==done)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">edge_score</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (0..12 for f2l [as U cleared],
-- 0..24 for oll and pll stages)</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">score</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cc</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span>
<span style="color: #000000;">f2l</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">centres</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">centres</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">cc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fce</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (the 8 next to c)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">fce</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">cc</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">f2l</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">stage</span><span style="color: #0000FF;">></span><span style="color: #000000;">CROSS</span> <span style="color: #008080;">and</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">61</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">-- give extra credit for edges paired with corners</span>
<span style="color: #000000;">edge_score</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- += (0|1|2) for the 12 edges:</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">></span><span style="color: #000000;">CROSS</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">edges</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ei</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">edges</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- as 123
-- -- 456
-- then if {1,4}=={2,5} then edge_score += 1,
-- plus if {2,5}=={3,6} then edge_score += 1.</span>
<span style="color: #000000;">edge_score</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]=</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]]</span> <span style="color: #008080;">and</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]]=</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]])</span> <span style="color: #0000FF;">+</span>
<span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]]=</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]]</span> <span style="color: #008080;">and</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]]=</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ei</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">oll_score</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- (should only be invoked if f2l==28)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (true if res=8)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">cu</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">centres</span><span style="color: #0000FF;">[</span><span style="color: #000000;">U</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cu</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'Y'</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fce</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">fcei</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fce</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cu</span><span style="color: #0000FF;">+</span><span style="color: #000000;">fcei</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'Y'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">rotate_face</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">face</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- face is 1..6 for clockwise (ULFRBD),
-- plus #08(Dbl) for a 180 (clockwise),
-- plus #10(Shift) for anti-clockwise.
--</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">dbl</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">+(</span><span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">face</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">cw</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">face</span><span style="color: #0000FF;">/</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">face</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">face</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">cf</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">centres</span><span style="color: #0000FF;">[</span><span style="color: #000000;">face</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rf</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">facing_corners</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cf</span><span style="color: #0000FF;">),</span>
<span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">facing_edges</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cf</span><span style="color: #0000FF;">)}</span>
<span style="color: #0000FF;">&</span><span style="color: #000000;">rotations</span><span style="color: #0000FF;">[</span><span style="color: #000000;">face</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">dbl</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rf</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">rfi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rf</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cw</span> <span style="color: #008080;">then</span> <span style="color: #000000;">rfi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rfi</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">rfi1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rfi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rfi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rfi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rfi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rfi1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">cube</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">apply_moves</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">cube</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate_face</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">cube</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">ULFRBD</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"ULFRBD"</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">moves_to_string</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- convert eg {1,20,11} to "UR'F2"</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">face</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">moves</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">dbl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">face</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">Dbl</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">anticw</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">face</span><span style="color: #0000FF;">/</span><span style="color: #000000;">Shift</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">face</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">face</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Dbl</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">ULFRBD</span><span style="color: #0000FF;">[</span><span style="color: #000000;">face</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">dbl</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">'2'</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">anticw</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;"><nowiki>'\''</nowiki></span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" (%d move%s) "</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"s"</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">--
-- The seen dictionary.
-- Without this, since it uses a breadth/highscore-first
-- algorithm, after f2l (for instance) it would probably
-- just do U and U' as the new high scores, forever.
-- (The THRESHOLD constant mitigates that to some extent)
--</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">seen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">new_dict</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">solve_stage</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">moves</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">moves2</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">workspace</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">w2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">init</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">wslen</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">high</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c2c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">done</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">CROSS</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--
-- first, blank out all corners, and
-- all edges without a white on them.
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rotations</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (just corners)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">rotations</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">j</span><span style="color: #0000FF;">][</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]]=</span><span style="color: #008000;">'-'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">edges</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{?,</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">,?,?,</span><span style="color: #000000;">m2</span><span style="color: #0000FF;">,?}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">edges</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'W'</span>
<span style="color: #008080;">and</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m2</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">'W'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">wslen</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">8</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">score</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #000000;">CROSS</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">F2L</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--
-- first, blank out all pieces with a yellow
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">corners</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">c1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">corners</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'Y'</span>
<span style="color: #008080;">or</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'Y'</span>
<span style="color: #008080;">or</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'Y'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">edges</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{?,</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">,?,?,</span><span style="color: #000000;">m2</span><span style="color: #0000FF;">,?}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">edges</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'Y'</span>
<span style="color: #008080;">and</span> <span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'Y'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #000000;">cube</span><span style="color: #0000FF;">[</span><span style="color: #000000;">m2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">'-'</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">wslen</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">57</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">score</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #000000;">F2L</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">f2l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">wslen</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">77</span><span style="color: #0000FF;">+</span><span style="color: #000000;">24</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">score</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #000000;">stage</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f2l</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">28</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">OLL</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">oll_score</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span> <span style="color: #000080;font-style:italic;">-- (stage=PLL)</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">48</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">done</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">workspace</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">wslen</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">w2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">workspace</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">init</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cube</span>
<span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">""</span><span style="color: #0000FF;">}</span>
<span style="color: #7060A8;">destroy_dict</span><span style="color: #0000FF;">(</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">,</span><span style="color: #000000;">justclear</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">move_count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">]={}</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">high</span> <span style="color: #008080;">and</span> <span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">]={}</span> <span style="color: #008080;">do</span> <span style="color: #000000;">high</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">high</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">stage</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">CROSS</span> <span style="color: #008080;">and</span> <span style="color: #000000;">c2c</span><span style="color: #0000FF;">></span><span style="color: #000000;">THRESHOLD</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">move_count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">workspace</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">w2</span>
<span style="color: #000000;">w2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">({},</span><span style="color: #000000;">wslen</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">c2c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">high</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">wslen</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">]={}</span> <span style="color: #008080;">do</span> <span style="color: #000000;">high</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">moves</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">workspace</span><span style="color: #0000FF;">[</span><span style="color: #000000;">high</span><span style="color: #0000FF;">][</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">cube</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">apply_moves</span><span style="color: #0000FF;">(</span><span style="color: #000000;">init</span><span style="color: #0000FF;">,</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">face</span><span style="color: #0000FF;">=</span><span style="color: #000000;">U</span> <span style="color: #008080;">to</span> <span style="color: #000000;">D</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- (originally this loop did 180s as well, but that
-- gave them far too much dominance, esp during pll.
-- instead we now coalese those that survive a 90.)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">Shift</span> <span style="color: #008080;">by</span> <span style="color: #000000;">Shift</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">mi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">face</span><span style="color: #0000FF;">+</span><span style="color: #000000;">m</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">cube2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rotate_face</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mi</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">getd_index</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">putd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">score</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">stage</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">CROSS</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">F2L</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">f2l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">f2l</span><span style="color: #0000FF;">=</span><span style="color: #000000;">28</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">oll_score</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">OLL</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">o</span><span style="color: #0000FF;">=</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">done</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">48</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">moves2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">moves</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">moves2</span><span style="color: #0000FF;">[$]=</span><span style="color: #000000;">mi</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">moves2</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">face</span><span style="color: #0000FF;">+</span><span style="color: #000000;">Dbl</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">moves2</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">mi</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">done</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">destroy_dict</span><span style="color: #0000FF;">(</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">,</span><span style="color: #000000;">justclear</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">moves2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">s</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">edge_score</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">+</span><span style="color: #000000;">o</span>
<span style="color: #000000;">w2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">],</span><span style="color: #000000;">moves2</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">c2c</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()></span><span style="color: #000000;">t1</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"working... %d moves, %d positions\r"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">move_count</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">dict_size</span><span style="color: #0000FF;">(</span><span style="color: #000000;">seen</span><span style="color: #0000FF;">)})</span>
<span style="color: #000000;">t1</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">get_key</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">#1B</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #008000;">""</span> <span style="color: #000080;font-style:italic;">-- (already solved case)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">stage_desc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #008000;">"make cross"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"solve first two layers"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"orientate last layer"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"permute last layer"</span> <span style="color: #0000FF;">}</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">cube</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">moves</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">total_moves</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000080;font-style:italic;">-- "hardest case" from http://www.cube20.org</span>
<span style="color: #000000;">moves</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">F</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Us</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">F2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Ds</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">B</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">U</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Rs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Fs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">L</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Ds</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">Rs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Us</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">L</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">U</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Bs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">D2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Rs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">F</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">U2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">D2</span><span style="color: #0000FF;">}</span>
<span style="color: #000000;">cube</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">apply_moves</span><span style="color: #0000FF;">(</span><span style="color: #000000;">init</span><span style="color: #0000FF;">,</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)<=</span><span style="color: #000000;">20</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"scramble: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">moves_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">=</span><span style="color: #000000;">CROSS</span> <span style="color: #008080;">to</span> <span style="color: #000000;">PLL</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">moves</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solve_stage</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stage</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">total_moves</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cube</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">apply_moves</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">stage_desc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">stage</span><span style="color: #0000FF;">],</span><span style="color: #000000;">moves_to_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cube</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nsolution of %d total moves found in %3.2fs\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">total_moves</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{Out}}
The "hardest case" from http://www.cube20.org with a high threshold. You can try this manually.
Disclaimer: the results are not always quite as good as this!
<pre>
scramble: FU'F2D'BUR'F'LD'R'U'LUB'D2R'FU2D2 (20 moves)
ROB
BYG
GRO
YYOYYBYYRYYG
RBOBRGOGRGOB
WWOWWBWWRWWG
OGB
RWO
GBR
make cross: DLBRFL (6 moves)
BRB
YYG
YYY
ROBRBRGOYOGW
OBRBRYRGYGOB
RBYORGOGOBOW
WWW
WWW
GWG
solve first two layers: FUL'R'FLRF'LRB'R'U'BU'B'U'B (18 moves)
RYG
OYR
YYY
BYRGGOBYOYBY
BBBRRRGGGOOO
BBBRRRGGGOOO
WWW
WWW
WWW
orientate last layer: R'F'U'FUR (6 moves)
YYY
YYY
YYY
GGBRRGOOOBBR
BBBRRRGGGOOO
BBBRRRGGGOOO
WWW
WWW
WWW
permute last layer: RU'L'UR'U2LU'L'U2LU' (12 moves)
YYY
YYY
YYY
BBBRRRGGGOOO
BBBRRRGGGOOO
BBBRRRGGGOOO
WWW
WWW
WWW
solution of 42 total moves found in 81.33s
</pre>
===thistlethwaite===
Translation/de-golf(hrumph) of Tomas Sirgedas' winning entry from http://tomas.rokicki.com/cubecontest as held in 2004.<br>
Faster and shorter solutions (in most cases) than cfop, however probably nigh on impossible to debug/enhance...
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\rubik_tomas.exw
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">xor_string</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">?</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]:</span><span style="color: #008000;">'!'</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">xor_all</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xor_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">d1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">xor_all</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"UF DF UB DB UR DR UL DL FR FL BR BL UFR DBR UBL DFL DLB ULF DRF URB"</span><span style="color: #0000FF;">))</span>
<span style="color: #000080;font-style:italic;">-- This is Mike Reid's notation, 12 sides then 8 corners, which may be rotated - hence we xor the
-- characters for fast lookup. The above string represents a cube in the solved state.</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">d2</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">}</span>
<span style="color: #000080;font-style:italic;">--?sort(d2): (0..11 appear twice, 12..19 appear thrice - edges/corners is pretty much all I can say)</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">d3</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}</span>
<span style="color: #000080;font-style:italic;">-- these apppear to be swapped during initialisation, dunno why...</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">search_mode</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">history_idx</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">history_mov</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">history_rpt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">depth_to_go</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">hash_table</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6912</span><span style="color: #0000FF;">),</span><span style="color: #000000;">48</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- (hash_table can/should be preserved for different problems)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">cubelet_pos</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">cubelet_twi</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">rot</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cur_phase</span><span style="color: #0000FF;"><</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">di</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">*</span><span style="color: #000000;">8</span><span style="color: #0000FF;">+</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">di</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">di</span><span style="color: #0000FF;">+</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;"><</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">di</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">*</span><span style="color: #000000;">8</span><span style="color: #0000FF;">+</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">di</span><span style="color: #0000FF;">+(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d2</span><span style="color: #0000FF;">[</span><span style="color: #000000;">di</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
<span style="color: #000080;font-style:italic;">-- swap(cubelet[j]], cubelet[k]);</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">hashf</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">int</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">cur_phase</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ret</span><span style="color: #0000FF;">*</span><span style="color: #000000;">3</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]></span><span style="color: #000000;">7</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span><span style="color: #0000FF;">-</span><span style="color: #000000;">7</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">:</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">inva</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">48</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">7</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ci12p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">ci12p3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ci12p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ci12p</span><span style="color: #0000FF;"><</span><span style="color: #000000;">16</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ci12p3</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ret</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">ret</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ci12p3</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]></span><span style="color: #000000;">3</span><span style="color: #0000FF;">);</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">ret</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]></span><span style="color: #000000;">15</span><span style="color: #0000FF;">);</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ib2</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">ib3</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]),</span>
<span style="color: #000000;">ib4</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">inva</span><span style="color: #0000FF;">[</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">ret</span><span style="color: #0000FF;">*</span><span style="color: #000000;">54</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">ib2</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">ib3</span> <span style="color: #0000FF;">></span> <span style="color: #000000;">ib4</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">3587708</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">24</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">cp</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">cp</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">4</span><span style="color: #0000FF;">+</span><span style="color: #000000;">cp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">4</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">ret</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">cp</span> <span style="color: #0000FF;">+</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cp</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">?</span><span style="color: #000000;">cp</span><span style="color: #0000FF;">:</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ret</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">do_search</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">dpt</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hashf</span><span style="color: #0000FF;">(),</span>
<span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">19</span><span style="color: #0000FF;">+</span><span style="color: #000000;">8</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">hmq</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">hfq</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">/</span><span style="color: #000000;">q</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">dpt</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">hash_table</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">hmq</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">or</span>
<span style="color: #000000;">dpt</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">hash_table</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">+</span><span style="color: #000000;">4</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">hfq</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">d</span> <span style="color: #008080;">xor</span> <span style="color: #000000;">search_mode</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">search_mode</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">dpt</span> <span style="color: #0000FF;"><=</span> <span style="color: #000000;">depth_to_go</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">not</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">depth_to_go</span><span style="color: #0000FF;">[</span><span style="color: #000000;">h</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dpt</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">hash_table</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">hmq</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hash_table</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">hmq</span><span style="color: #0000FF;">],</span><span style="color: #000000;">dpt</span><span style="color: #0000FF;">);</span>
<span style="color: #000000;">hash_table</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">+</span><span style="color: #000000;">5</span><span style="color: #0000FF;">][</span><span style="color: #000000;">hfq</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hash_table</span><span style="color: #0000FF;">[</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">+</span><span style="color: #000000;">5</span><span style="color: #0000FF;">][</span><span style="color: #000000;">hfq</span><span style="color: #0000FF;">],</span><span style="color: #000000;">dpt</span><span style="color: #0000FF;">);</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">rot</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">cur_phase</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span> <span style="color: #008080;">or</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">history_idx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">history_mov</span><span style="color: #0000FF;">[</span><span style="color: #000000;">history_idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span>
<span style="color: #000000;">history_rpt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">history_idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">do_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dpt</span><span style="color: #0000FF;">-</span><span style="color: #000000;">search_mode</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">1</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">history_idx</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">pack_moves</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">moves</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">curr</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">last</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">last_rpt</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">history_idx</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- add a dummy move to trigger the last move print:</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">xor_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">history_mov</span><span style="color: #0000FF;">[</span><span style="color: #000000;">history_idx</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- F<->B, etc</span>
<span style="color: #000000;">history_idx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">history_mov</span><span style="color: #0000FF;">[</span><span style="color: #000000;">history_idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">last</span>
<span style="color: #000000;">history_rpt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">history_idx</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">history_mov</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">last_rpt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">history_idx</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">curr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">history_mov</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">curr</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">last</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- coalesce eg F1F2 to F' (unless you wanna fix do_search()!)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">last_rpt</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">moves</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">"FBRLUD"</span><span style="color: #0000FF;">[</span><span style="color: #000000;">last</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"2"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"'"</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">last_rpt</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">last</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">curr</span>
<span style="color: #000000;">last_rpt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">history_rpt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">last_rpt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">last_rpt</span><span style="color: #0000FF;">+</span><span style="color: #000000;">history_rpt</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">moves</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"s"</span><span style="color: #0000FF;">)}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">tomas</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">args</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">search_mode</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">history_idx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">depth_to_go</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">19</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">cur_phase</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">do_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">args</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">args</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">19</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">args</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- (may be rotated, eg RU or UR)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xor_string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span><span style="color: #000000;">d1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- sensible message(bad args)?</span>
<span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #004080;">int</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'U'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'D'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">));</span>
<span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #0000FF;">?</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #0000FF;">:</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]></span><span style="color: #008000;">'F'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">4</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">j</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d3</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d3</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">6</span><span style="color: #0000FF;">]+</span><span style="color: #000000;">1</span>
<span style="color: #000080;font-style:italic;">-- swap(cubelet[j], cubelet[k]); </span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_pos</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">cubelet_twi</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">search_mode</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">;</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">cp</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">cur_phase</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">cp</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">19</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">do_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">pack_moves</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s (%d move%s)\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tomas</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL"</span><span style="color: #0000FF;">))</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
UF'R'FB2R2B2LD2L2DLR2U'F2UF2U2F2L2UF2DF2U2R2U2R2B2D2R2F2L2B2D2 (35 moves)
</pre>
The distributed copy of demo\rosetta\rubik_cfop.exw also contains routines to convert between my 136-character cube and reid notation,
and demo\rosetta\rubik_tomas.exw also contains the full 100-long test set from the original competition.
=={{header|Raku}}==
This is a translation of the [https://tomas.rokicki.com/cubecontest/stefan2.txt Perl] [https://tomas.rokicki.com/cubecontest/ competition] code, by Stefan Pochmann.
<syntaxhighlight lang="raku" line># 20230401 Raku programming solution
my @data=<UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL>;
my @goal=<UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR>;
sub printAlg ($x) { #--- Algorithms.
my $algo = 'x0F0DN0EB0H00N0B0R0KB0L0QB0G1A1M11C1I1E1OFI2'~
'DN2IEOB2H22N2B2GRM2MKGB2GLM2QBK23D3EN3E3B3N33H3';
$algo ~~ s:g
!(\D*)(\d)!{
$0 ~ <ILOFCLKHRNQCL OBIRALOBIRAL CEJHPEIMIG DFNRHRDKMQ>[$1]
# ~ [~] reverse map { TR/G..R/M..X/ }, " $0".comb }!;
~ " $0".trans( ['G'..'R'] => ['M'..'X'] ).flip }!;
my @algo = $algo.split: ' ';
#`[[[ or use the following to save some CPU power and time # my @algo = <
xILOFCLKHRNQCLx FILOFCLKHRNQCLF DNILOFCLKHRNQCLTD EBILOFCLKHRNQCLBE
HILOFCLKHRNQCLN ILOFCLKHRNQCL NILOFCLKHRNQCLT BILOFCLKHRNQCLB
RILOFCLKHRNQCLX KBILOFCLKHRNQCLBQ LILOFCLKHRNQCLR QBILOFCLKHRNQCLBW
GOBIRALOBIRALM AOBIRALOBIRALA MOBIRALOBIRALS OBIRALOBIRAL
COBIRALOBIRALC IOBIRALOBIRALO EOBIRALOBIRALE OFICEJHPEIMIGOFU
DNCEJHPEIMIGTD IEOBCEJHPEIMIGBUEO HCEJHPEIMIGN CEJHPEIMIG
NCEJHPEIMIGT BCEJHPEIMIGB GRMCEJHPEIMIGSXM MKGBCEJHPEIMIGBMQS
GLMCEJHPEIMIGSRM QBKCEJHPEIMIGQBW DFNRHRDKMQ DDFNRHRDKMQD
ENDFNRHRDKMQTE EDFNRHRDKMQE BDFNRHRDKMQB NDFNRHRDKMQT
DFNRHRDKMQ HDFNRHRDKMQN >; #]]]
say [~] my @moves = map {
substr('UDFBLR', (my $ord=.ord-65) % 6, 1) ~ substr("2 '", $ord div 6, 1)
}, @algo[$x].comb;
return @moves.elems
}
my $total = 0;
for 1..18 -> $x { #--- Orient.
until @data[$x] ∈ @goal {
$total += printAlg $x;
@data[$x] ~~ s/(.)(.+)/$1$0/;
@data[$x < 12 ?? 0 !! 19] ~~ s/(.+)(.)/$1$0/;
}
}
for ^41 { #--- Permute.
for ^20 -> $w {
next if @data[$w] eq @goal[$w];
my $x = 0;
until @data[$w] eq @goal[$x] { $x++ };
$x < 12 ?? ( @data[0,$x,12,15] = @data[$x,0,15,12] )
!! ( @data[12,$x] = @data[$x,12] );
$total += printAlg $x+=18 and last
}
}
say "\nTotal number of moves : $total";</syntaxhighlight>
{{out}}
<pre>B2D'F R F'R2F2R L D R'D'L'F2R DB2
D F R F'R2F2R L D R'D'L'F2R D'
U F'D2F R'U2R F'D2F R'U2R U'
U2F'D2F R'U2R F'D2F R'U2R U2
U2F'D2F R'U2R F'D2F R'U2R U2
F2F'D2F R'U2R F'D2F R'U2R F2
F F'D2F R'U2R F'D2F R'U2R F'
F F'D2F R'U2R F'D2F R'U2R F'
L2F'D2F R'U2R F'D2F R'U2R L2
L2F'D2F R'U2R F'D2F R'U2R L2
F L2F'D2F2L2B D B'L2F U'F U D2FL2F'
B2D'F2L2B D B'L2F U'F U DB2
U R'U'F2L2B D B'L2F U'F U URU'
F2L2B D B'L2F U'F U
U R U'F2L2B D B'L2F U'F U UR'U'
L'D2L F2L2B D B'L2F U'F U L'D2L
U'L U D2F2L2B D B'L2F U'F U D2U'L'U
F'R2F F2L2B D B'L2F U'F U F'R2F
D2F2L2B D B'L2F U'F U D2
B2B2R2D'R'D R'B2L U'L'B2
L2D'B2R2D'R'D R'B2L U'L'DL2
B2R2D'R'D R'B2L U'L'
D B2R2D'R'D R'B2L U'L'D'
L2B2R2D'R'D R'B2L U'L'L2
D2B2R2D'R'D R'B2L U'L'D2
Total number of moves : 352</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
Wren has a similar problem to Go in that Lists cannot be used as Map keys. Worse still Wren doesn't support fixed size arrays so I've had to convert the Lists to space delimited Strings which is an expensive operation.
Despite this, the script is taking an average of just over a second to calculate the number of moves for each line which is probably not too bad for an interpreted language.
<syntaxhighlight lang="wren">/**********************************************************************
*
* A cube 'state' is an int array with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************/
import "os" for Process
import "io" for File
var applicableMoves= [0, 262143, 259263, 74943, 74898]
var phase = 0
var affectedCubies = [
[0, 1, 2, 3, 0, 1, 2, 3], // U
[4, 7, 6, 5, 4, 5, 6, 7], // D
[0, 9, 4, 8, 0, 3, 5, 4], // F
[2, 10, 6, 11, 2, 1, 7, 6], // B
[3, 11, 7, 9, 3, 2, 6, 5], // L
[1, 8, 5, 10, 1, 0, 4, 7] // R
]
var btoi = Fn.new { |b| (b) ? 1 : 0 }
var applyMove = Fn.new { |move, origState|
var state = origState[0..-1] // make copy so don't mutate original
var turns = move%3 + 1
var face = (move/3).floor
while (turns != 0) {
turns = turns - 1
var oldState = state[0..-1] // make a copy prior to mutation
for (i in 0..7) {
var isCorner = btoi.call(i > 3)
var target = affectedCubies[face][i] + isCorner*12
var temp = (i&3 == 3) ? i - 3 : i + 1
var killer = affectedCubies[face][temp] + isCorner*12
var orientationDelta
if (i < 4) {
orientationDelta = btoi.call(face > 1 && face < 4)
} else if (face < 2) {
orientationDelta = 0
} else {
orientationDelta = 2 - (i&1)
}
state[target] = oldState[killer]
state[target+20] = oldState[killer+20] + orientationDelta
if (turns == 0) state[target+20] = state[target+20] % (2 + isCorner)
}
}
return state
}
var inverse = Fn.new { |move| move + 2 - 2*(move%3) }
var id = Fn.new { |state|
//--- Phase 1: Edge orientations.
if (phase < 2) return state[20...32]
//--- Phase 2: Corner orientations, E slice edges.
if (phase < 3) {
var result = state[31...40]
for (e in 0..11) result[0] = result[0] | ((state[e]/8).floor << e)
return result
}
//--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
if (phase < 4) {
var result = [0, 0, 0]
for (e in 0..11) {
var temp = ((state[e] > 7) ? 2 : state[e] & 1) << (2 * e)
result[0] = result[0] | temp
}
for (c in 0..7) {
var temp = ((state[c + 12] - 12) & 5) << (3 * c)
result[1] = result[1] | temp
}
for (i in 12..18) {
for (j in i+1..19) result[2] = result[2] ^ btoi.call(state[i] > state[j])
}
return result
}
//--- Phase 4: The rest.
return state
}
var startTime = System.clock
var aggregateMoves = 0
//--- Define the goal.
var goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]
//--- Load dataset (file name should be passed as a command line argument).
if (Process.arguments.count != 1) {
Fiber.abort("The file name should be passed as a command line argument.")
}
var lines = File.read(Process.arguments[0]).split("\n")
if (lines[-1] == "") lines.removeAt(-1) // if there's a final blank line remove it
var lineCount = lines.count
for (line in lines) {
var inputs = line.split(" ")
phase = 0
var totalMoves = 0
//--- Prepare current (start) and goal state.
var currentState = List.filled(40, 0)
var goalState = List.filled(40, 0)
for (i in 0..19) {
//--- Goal state.
goalState[i] = i
//--- Current (start) state.
var cubie = inputs[i]
while (true) {
var idx = -1
for (c in 0...goal.count) {
if (goal[c] == cubie) {
idx = c
break
}
}
currentState[i] = (idx >= 0) ? idx : 20
if (currentState[i] != 20) break
cubie = cubie[1..-1] + cubie[0]
currentState[i+20] = currentState[i+20] + 1
}
}
//--- Dance the funky Thistlethwaite..
phase = phase + 1
while (phase < 5) {
var nextPhase = false
//--- Compute ids for current and goal state, skip phase if equal.
var currentId = id.call(currentState).join(" ")
var goalId = id.call(goalState).join(" ")
if (currentId != goalId) {
//--- Initialize the BFS queue.
var q = [currentState, goalState]
//--- Initialize the BFS tables.
var predecessor = {}
var direction = {}
var lastMove = {}
direction[currentId] = 1
direction[goalId] = 2
//--- Dance the funky bidirectional BFS...
while (true) {
//--- Get state from queue, compute its ID and get its direction.
var oldState = q[0]
q = q[1..-1]
var oldId = id.call(oldState).join(" ")
var oldDir = direction[oldId]
if (oldDir == null) {
oldDir = 0
direction[oldId] = 0
}
//--- Apply all applicable moves to it and handle the new state.
var move = 0
while (move < 18) {
if ((applicableMoves[phase] & (1 << move)) != 0) {
//--- Apply the move.
var newState = applyMove.call(move, oldState)
var newId = id.call(newState).join(" ")
var newDir = direction[newId]
if (newDir == null) {
newDir = 0
direction[newId] = 0
}
//--- Have we seen this state (id) from the other direction already?
//--- I.e. have we found a connection?
if (newDir != 0 && newDir != oldDir) {
//--- Make oldId represent the forwards
//--- and newId the backwards search state.
if (oldDir > 1) {
var t = newId
newId = oldId
oldId = t
move = inverse.call(move)
}
//--- Reconstruct the connecting algorithm.
var algorithm = [move]
while (oldId != currentId) {
var t = lastMove[oldId]
if (t == null) {
t = 0
lastMove[oldId] = 0
}
algorithm.insert(0, t)
oldId = predecessor[oldId]
if (oldId == null) {
oldId = ""
predecessor[oldId] = ""
}
}
while (newId != goalId) {
var t = lastMove[newId]
if (t == null) {
t = 0
lastMove[newId] = 0
}
algorithm.add(inverse.call(t))
newId = predecessor[newId]
if (newId == null) {
newId = ""
predecessor[newId] = ""
}
}
//--- Print and apply the algorithm.
for (i in 0...algorithm.count) {
System.write("UDFBLR"[(algorithm[i]/3).floor])
System.write(algorithm[i]%3 + 1)
System.write(" ")
totalMoves = totalMoves + 1
currentState = applyMove.call(algorithm[i], currentState)
}
nextPhase = true
break
}
//--- If we've never seen this state (id) before, visit it.
if (newDir == 0) {
q.add(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
}
}
move = move + 1
}
if (nextPhase) break
}
}
phase = phase + 1
}
System.print(" (moves %(totalMoves))")
aggregateMoves = aggregateMoves + totalMoves
}
var endTime = System.clock
var elapsedTime = ((endTime - startTime) * 1000).round
System.print("\nAverage number of moves = %(aggregateMoves/lineCount)")
System.print("\nAverage time = %(elapsedTime/lineCount) milliseconds")</syntaxhighlight>
{{out}}
Using the original dataset of 100 lines, the results were as follows:
<pre style="height:45ex">
U1 U2 (moves 2)
U2 (moves 1)
U1 (moves 1)
F1 F2 (moves 2)
F2 (moves 1)
F1 (moves 1)
R1 R2 (moves 2)
R2 (moves 1)
R1 (moves 1)
D1 D2 (moves 2)
D2 (moves 1)
D1 (moves 1)
B1 B2 (moves 2)
B2 (moves 1)
B1 (moves 1)
L1 L2 (moves 2)
L2 (moves 1)
L1 (moves 1)
U2 B3 B2 (moves 3)
L2 U3 (moves 2)
R1 U1 (moves 2)
D3 L3 (moves 2)
D3 L2 (moves 2)
D2 F3 F2 (moves 3)
R2 F3 (moves 2)
R1 F2 F2 R2 F2 (moves 5)
D1 D2 U2 (moves 3)
L1 B2 F2 L2 R2 B2 F2 (moves 7)
L1 L2 D3 (moves 3)
D1 F2 (moves 2)
U2 R3 (moves 2)
L1 L2 U3 (moves 3)
U1 R2 (moves 2)
U1 R3 (moves 2)
F1 U2 (moves 2)
U2 R3 R2 (moves 3)
F2 D1 F3 (moves 3)
F2 D3 D2 U2 (moves 4)
L3 D2 R3 (moves 3)
D2 R3 R2 D3 (moves 4)
F1 R1 B2 B2 R2 B2 (moves 6)
L1 B2 F2 (moves 3)
U1 R2 B3 B2 (moves 4)
R2 F3 R2 (moves 3)
L2 D3 R3 R2 (moves 4)
L2 F3 L2 L2 F2 L2 (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2 (moves 29)
L1 L2 U3 R2 (moves 4)
L3 B3 B2 R3 R2 (moves 5)
B2 U1 R3 R2 (moves 4)
L3 B3 L2 (moves 3)
D1 B2 L3 L2 (moves 4)
B1 B2 R3 F2 F2 R2 F2 (moves 7)
D1 F3 D1 D2 (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2 (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2 (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2 (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2 (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2 (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2 (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2 (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2 (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2 (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2 (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2 (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2 (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2 (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2 (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2 (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2 (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2 (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2 (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2 (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2 (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2 (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2 (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2 (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2 (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2 (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2 (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2 (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2 (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2 (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2 (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2 (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2 (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2 (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2 (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2 (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2 (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2 (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2 (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2 (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2 (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2 (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2 (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2 (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2 (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2 (moves 34)
Average number of moves = 16.72
Average time = 1005.78 milliseconds
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When run with a file containing the single line:
UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL
a typical result was:
<pre>
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
Average number of moves = 29
Average time = 665 milliseconds
</pre>
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