Solve a Rubik's cube
Solve a Rubik's cube is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- 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.
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.
/**********************************************************************
*
* 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")
}
- Output:
Same as Kotlin entry apart, of course, from the timings.
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")
- Output:
Using the 100-line database:
(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
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.
// 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")
}
- Output:
Using the original dataset of 100 lines, the results were as follows (time doesn't mean much but is typical for my modest machine):
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 = 127 milliseconds
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:
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
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"
- Output:
We compiled the program with command nim c -d:danger --gc:arc -d:lto, which means no runtime checks, ARC memory management and link time optimization.
When run with the original dataset of 100 lines, we got:
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 = 52.03 milliseconds
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:
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
Phix
cfop
Uses brute-force (width/highscore-first) Fridrich-steps (ie cross,f2l,oll,pll).
Not the fastest (see THRESHOLD) or shortest results (see thistlethwaite) but the code is pretty easy to follow.
The final stage (pll) would probably benefit the most from being replaced with standard algorithms.
While technically this works under pwa/p2js, you should expect a blank screen for nearly 3 minutes.
-- -- 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. -- with javascript_semantics constant THRESHOLD = 100000 -- 100000 -- very slow (100s), best results -- 10000 -- 10000 -- slow (10s), reasonable results -- 1000 -- fast (1s), fairly poor results -- 100 -- (counter-productive/slower) string init =""" ---YYY-------- ---YYY-------- ---YYY-------- BBBRRRGGGOOO-- BBBRRRGGGOOO-- BBBRRRGGGOOO-- ------WWW----- ------WWW----- ------WWW----- """ -- 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 if length(init)!=136 then ?9/0 end if -- -- TIP: Wrap a cube with blank paper, and write -- the numbers on it, to derive these sets. -- constant centres = {20,62,65,68,71,113} constant edges = {{ 4, 5, 6,57,56,55}, -- ie YYY/OOO { 6, 21, 36,54,53,52}, -- YYY/GGG { 34, 35, 36,49,50,51}, -- YYY/RRR { 4, 19, 34,46,47,48}, -- YYY/BBB { 51, 66, 81,52,67,82}, -- RRR/GGG { 54, 69, 84,55,70,85}, -- GGG/OOO { 57, 72, 87,46,61,76}, -- OOO/BBB { 48, 63, 78,49,64,79}, -- BBB/RRR { 97, 98, 99,82,83,84}, -- WWW/GGG { 99,114,129,85,86,87}, -- WWW/OOO {127,128,129,78,77,76}, -- WWW/BBB { 97,112,127,81,80,79}} -- WWW/RRR constant corners = {{ 4, 57,46},{34,48, 49},{36,51,52},{ 6,54,55}, -- YOB/UBL YBR/UFL YRG/UFR YGO/UBL {76,129,87},{78,79,127},{81,82,97},{84,85,99}} -- BWO/DBL BRW/DFL RGW/DFR GOW/DFL constant facing_corners = {-16,-14,16,14}, -- (nb not 14,16) facing_edges = {-15, 1,15,-1}, fce = facing_corners&facing_edges, rotations = { -- up (clockwise): {{57,54,51,48}, -- clockwise corners {46,55,52,49}, -- anticlockwise corners {47,56,53,50}}, -- middle edges -- left {{ 4,49,127, 87}, {57,34, 79,129}, {19,64,128, 72}}, -- front {{34,52, 97, 78}, {48,36, 82,127}, {35,67,112, 63}}, -- right {{36,55,99,81}, {51, 6,85,97}, {21,70,98,66}}, -- back {{ 6,46,129,84}, {54, 4, 76,99}, { 5,61,114,69}}, -- down {{82,85,76,79}, {81,84,87,78}, {83,86,77,80}}} --Up/Left/Front/Right/Back/Down enum U=1,L=2,F=3,R=4,B=5,D=6,Dbl=#08,Shift=#10 constant U2 = U+Dbl, F2 = F+Dbl, /*R2 = R+Dbl, B2 = B+Dbl,*/ D2 = D+Dbl, Us = U+Shift, Fs = F+Shift, Bs = B+Shift, Rs = R+Shift, Ds = D+Shift enum CROSS,F2L,OLL,PLL integer f2l = 0 -- (28==done) integer edge_score = 0 -- (0..12 for f2l [as U cleared], -- 0..24 for oll and pll stages) function score(string cube, integer stage) integer res = 0, c, cc, k f2l = 0 for i=1 to length(centres) do c = centres[i] cc = cube[c] for j=1 to length(fce) do -- (the 8 next to c) k = c+fce[j] if cube[k]=cc then res += 1 f2l += (stage>CROSS and k>=61) end if end for end for -- give extra credit for edges paired with corners edge_score = 0 -- += (0|1|2) for the 12 edges: if stage>CROSS then for i=1 to length(edges) do sequence ei = edges[i] -- as 123 -- -- 456 -- then if {1,4}=={2,5} then edge_score += 1, -- plus if {2,5}=={3,6} then edge_score += 1. edge_score += (cube[ei[1]]=cube[ei[2]] and cube[ei[4]]=cube[ei[5]]) + (cube[ei[2]]=cube[ei[3]] and cube[ei[5]]=cube[ei[6]]) end for end if return res end function function oll_score(string cube) -- (should only be invoked if f2l==28) integer res = 0 -- (true if res=8) integer cu = centres[U] if cube[cu]!='Y' then ?9/0 end if for i=1 to length(fce) do integer fcei = fce[i] res += (cube[cu+fcei]='Y') end for return res end function function rotate_face(string cube, integer face) -- -- face is 1..6 for clockwise (ULFRBD), -- plus #08(Dbl) for a 180 (clockwise), -- plus #10(Shift) for anti-clockwise. -- integer dbl = 1+(and_bits(face,Dbl)=Dbl) bool cw = 1-floor(face/Shift) face = remainder(face,Dbl) integer cf = centres[face] sequence rf = {sq_add(facing_corners,cf), sq_add(facing_edges,cf)} &rotations[face] for d=1 to dbl do for i=1 to length(rf) do sequence rfi = rf[i] if cw then rfi = reverse(rfi) end if integer rfi1 = cube[rfi[1]] for j=1 to 3 do cube[rfi[j]] = cube[rfi[j+1]] end for cube[rfi[4]] = rfi1 end for end for return cube end function function apply_moves(string cube, sequence moves) for i=1 to length(moves) do cube = rotate_face(cube,moves[i]) end for return cube end function constant ULFRBD = "ULFRBD" function moves_to_string(sequence moves) -- convert eg {1,20,11} to "UR'F2" string res = "" integer l = length(moves) for i=1 to l do integer face = moves[i] integer dbl = and_bits(face,Dbl)=Dbl bool anticw = floor(face/Shift) face = remainder(face,Dbl) res &= ULFRBD[face] if dbl then res &= '2' elsif anticw then res &= '\'' end if end for res &=sprintf(" (%d move%s) ",{l,iff(l=1?"":"s")}) return res end function -- -- 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) -- integer seen = new_dict() function solve_stage(string cube, integer stage) atom t1 = time()+1 string moves = "", moves2 sequence workspace, w2, init integer wslen, high = 1, s, c2c = 0, o = 0 bool done if stage=CROSS then -- -- first, blank out all corners, and -- all edges without a white on them. -- for i=1 to length(rotations) do for j=1 to 2 do -- (just corners) for k=1 to 4 do cube[rotations[i][j][k]]='-' end for end for end for for i=1 to length(edges) do integer {?,m1,?,?,m2,?} = edges[i] if cube[m1]!='W' and cube[m2]!='W' then cube[m1] = '-' cube[m2] = '-' end if end for wslen = 8 s = score(cube,CROSS) done = (s=8) elsif stage=F2L then -- -- first, blank out all pieces with a yellow -- for i=1 to length(corners) do integer {c1,c2,c3} = corners[i] if cube[c1]='Y' or cube[c2]='Y' or cube[c3]='Y' then cube[c1] = '-' cube[c2] = '-' cube[c3] = '-' end if end for for i=1 to length(edges) do integer {?,m1,?,?,m2,?} = edges[i] if cube[m1]='Y' and cube[m2]='Y' then cube[m1] = '-' cube[m2] = '-' end if end for wslen = 57+12 s = score(cube,F2L) done = (f2l=28) else wslen = 77+24 s = score(cube,stage) if f2l!=28 then ?9/0 end if if stage=OLL then done = (oll_score(cube)=8) else -- (stage=PLL) done = (s=48) end if end if if not done then workspace = repeat({},wslen) w2 = deep_copy(workspace) init = cube workspace[high] = {""} destroy_dict(seen,justclear:=1) integer move_count = 1 while 1 do if workspace[high]={} then while high and workspace[high]={} do high -= 1 end while if high=0 or (stage!=CROSS and c2c>THRESHOLD) then move_count += 1 workspace = w2 w2 = repeat({},wslen) c2c = 0 high = wslen while workspace[high]={} do high -= 1 end while end if end if moves = workspace[high][1] workspace[high] = workspace[high][2..$] cube = apply_moves(init,moves) for face=U to D do -- (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.) for m=0 to Shift by Shift do integer mi = face+m sequence cube2 = rotate_face(cube,mi) if getd_index(cube2,seen)=0 then putd(cube2,0,seen) s = score(cube2,stage) if stage=CROSS then done = (s=8) elsif stage=F2L then done = (f2l=28) else if f2l=28 then o = oll_score(cube2) else o = 0 end if if stage=OLL then done = (o=8) else done = (s=48) end if end if moves2 = moves if length(moves2) and moves2[$]=mi then moves2[$] = face+Dbl else moves2 &= mi end if if done then destroy_dict(seen,justclear:=1) return moves2 end if s += 1+edge_score*2+o w2[s] = append(w2[s],moves2) c2c += 1 end if end for end for if time()>t1 and platform()!=JS then printf(1,"working... %d moves, %d positions\r",{move_count,dict_size(seen)}) t1 = time()+1 if get_key()=#1B then exit end if end if end while end if return "" -- (already solved case) end function constant stage_desc = { "make cross", "solve first two layers", "orientate last layer", "permute last layer" } procedure main() string cube sequence moves integer total_moves = 0 atom t0 = time() -- "hardest case" from http://www.cube20.org moves = {F, Us, F2, Ds, B, U, Rs, Fs, L, Ds, Rs, Us, L, U, Bs, D2, Rs, F, U2, D2} cube = apply_moves(init,moves) if length(moves)<=20 then printf(1,"scramble: %s\n",{moves_to_string(moves)}) end if puts(1,substitute(cube,"-"," ")) for stage=CROSS to PLL do moves = solve_stage(cube, stage) total_moves += length(moves) cube = apply_moves(cube,moves) printf(1,"%s: %s\n",{stage_desc[stage],moves_to_string(moves)}) if length(moves) then puts(1,substitute(cube,"-"," ")) end if end for printf(1,"\nsolution of %d total moves found in %3.2fs\n",{total_moves,time()-t0}) end procedure main()
- Output:
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!
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
thistlethwaite
Translation/de-golf(hrumph) of Tomas Sirgedas' winning entry from http://tomas.rokicki.com/cubecontest as held in 2004.
Faster and shorter solutions (in most cases) than cfop, however probably nigh on impossible to debug/enhance...
-- -- demo\rosetta\rubik_tomas.exw -- with javascript_semantics function xor_string(string s) return xor_bits(s[1],xor_bits(s[2],iff(length(s)=3?s[3]:'!'))) end function function xor_all(sequence s) for i=1 to length(s) do s[i] = xor_string(s[i]) end for return s end function constant d1 = xor_all(split("UF DF UB DB UR DR UL DL FR FL BR BL UFR DBR UBL DFL DLB ULF DRF URB")) -- 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. constant d2 = {18,12,17,15,0, 9,1,8,16,14,19,13,2,10,3,11,12,18,13,19,4,8,5,10, 14,16,15,17,6,11,7,9,17,12,19,14,6, 0,4, 2,18,15,16,13,1,7,3, 5} --?sort(d2): (0..11 appear twice, 12..19 appear thrice - edges/corners is pretty much all I can say) constant d3 = {13,16,15,1,3, 19,18,17,4,6} -- these apppear to be swapped during initialisation, dunno why... integer cur_phase, search_mode, history_idx sequence history_mov = repeat(0,48), history_rpt = repeat(0,48), depth_to_go, hash_table = repeat(repeat(6,6912),48) -- (hash_table can/should be preserved for different problems) sequence cubelet_pos = repeat(0,48), cubelet_twi = repeat(0,48) procedure rot(integer cur_phase) if cur_phase<4 then for i=0 to 3 do integer di = cur_phase*8+i+1, j = d2[di]+1, k = d2[di+4]+1 cubelet_twi[j] = mod(cubelet_twi[j]+2-mod(i,2),3) cubelet_twi[k] = xor_bits(cubelet_twi[k],cur_phase<2) end for end if for i=0 to 6 do integer di = cur_phase*8+i+1, j = d2[di+(i!=3)]+1, k = d2[di]+1 -- swap(cubelet[j]], cubelet[k]); {cubelet_pos[j],cubelet_pos[k]} = {cubelet_pos[k],cubelet_pos[j]} {cubelet_twi[j],cubelet_twi[k]} = {cubelet_twi[k],cubelet_twi[j]} end for end procedure function hashf() int ret = 0; switch cur_phase do case 0: for i=0 to 10 do ret += ret + cubelet_twi[i+1] end for return ret; case 1: for i=0 to 6 do ret = ret*3 + cubelet_twi[i+12+1] end for for i=0 to 10 do ret += ret + (cubelet_pos[i+1]>7) end for return ret-7; case 2: sequence inva = repeat(0,48), b = repeat(0,48) for i=0 to 7 do integer ci12p = cubelet_pos[i+12+1], ci12p3 = and_bits(ci12p,3) if ci12p<16 then inva[ci12p3+1] = ret ret += 1 else b[i-ret+1] = ci12p3 end if end for for i=0 to 6 do ret += ret + (cubelet_pos[i+1]>3); end for for i=0 to 6 do ret += ret + (cubelet_pos[i+12+1]>15); end for integer ib2 = xor_bits(inva[b[1]+1],inva[b[2]+1])*2, ib3 = xor_bits(inva[b[1]+1],inva[b[3]+1]), ib4 = xor_bits(inva[b[1]+1],inva[b[4]+1]) return ret*54 + ib2 + (ib3 > ib4) - 3587708 end switch for i=0 to 4 do ret *= 24; for cp=0 to 3 do for k=0 to cp-1 do if cubelet_pos[i*4+cp+1] < cubelet_pos[i*4+k+1] then ret += cp + iff(cp=3?cp:0) end if end for end for end for return floor(ret/2) end function function do_search(integer dpt) integer h = hashf(), q = (floor(cur_phase/2)*19+8)*power(2,7), hmq = mod(h,q)+1, hfq = floor(h/q)+1, d = (dpt < hash_table[cur_phase+1][hmq] or dpt < hash_table[cur_phase+4+1][hfq]) if d xor search_mode then if search_mode then if dpt <= depth_to_go[h+1] then return not h; else depth_to_go[h+1] = dpt; end if end if hash_table[cur_phase+1][hmq] = min(hash_table[cur_phase+1][hmq],dpt); hash_table[cur_phase+5][hfq] = min(hash_table[cur_phase+5][hfq],dpt); for k=0 to 5 do for i=0 to 3 do rot(k) if (k>=cur_phase*2 or i=1) and i<=2 then history_idx += 1 history_mov[history_idx] = k history_rpt[history_idx] = i if do_search(dpt-search_mode*2+1) then return 1 end if history_idx -= 1 end if end for end for end if return 0 end function function pack_moves() string moves = "" integer n = 0, curr, last, last_rpt if history_idx!=0 then -- add a dummy move to trigger the last move print: last = xor_bits(history_mov[history_idx],1) -- F<->B, etc history_idx += 1 history_mov[history_idx] = last history_rpt[history_idx] = 0 last = history_mov[1] last_rpt = 0 for i=1 to history_idx do curr = history_mov[i] if curr!=last then -- coalesce eg F1F2 to F' (unless you wanna fix do_search()!) if last_rpt then moves &= "FBRLUD"[last+1] & {"","2","'"}[last_rpt] n += 1 end if last = curr last_rpt = history_rpt[i]+1 else last_rpt = mod(last_rpt+history_rpt[i]+1,4) end if end for end if return {moves,n,iff(n=1?"":"s")} end function function tomas(sequence args) search_mode = 0 history_idx = 0 depth_to_go = repeat(0,5*power(2,20)) for i=0 to 19 do cubelet_pos[i+1] = i end for for i=0 to 3 do cur_phase = i {} = do_search(0) end for args = split(args) for i=0 to 19 do string s = args[i+1] -- (may be rotated, eg RU or UR) integer p = find(xor_string(s),d1) if p=0 then ?9/0 end if -- sensible message(bad args)? cubelet_pos[i+1] = p-1 int x = max(find('U',s), find('D',s)); cubelet_twi[i+1] = iff(x!=0 ? x-1 : s[1]>'F') end for for i=0 to 4 do integer j = d3[i+1]+1, k = d3[i+6]+1 -- swap(cubelet[j], cubelet[k]); {cubelet_pos[j],cubelet_pos[k]} = {cubelet_pos[k],cubelet_pos[j]} {cubelet_twi[j],cubelet_twi[k]} = {cubelet_twi[k],cubelet_twi[j]} end for search_mode = 1; for cp=0 to 3 do cur_phase = cp for i=0 to 19 do if do_search(i) then exit end if end for end for return pack_moves() end function printf(1,"%s (%d move%s)\n",tomas("UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL"))
- Output:
UF'R'FB2R2B2LD2L2DLR2U'F2UF2U2F2L2UF2DF2U2R2U2R2B2D2R2F2L2B2D2 (35 moves)
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.
Raku
This is a translation of the Perl competition code, by Stefan Pochmann.
# 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";
- Output:
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
Wren
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.
/**********************************************************************
*
* 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")- Output:
Using the original dataset of 100 lines, the results were as follows:
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
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:
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