# 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.

Create a program that is capable of solving a Rubik's Cube as efficiently as possible.

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 = int var applicableMoves = int{0, 262143, 259263, 74943, 74898} var phase = 0 var affectedCubies = 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 |= (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 |= temp << (2 * e)        }        for c := uint(0); c < 8; c++ {            result |= ((state[c+12] - 12) & 5) << (3 * c)        }        for i := 12; i < 19; i++ {            for j := i + 1; j < 20; j++ {                result ^= 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 := 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)    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                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 = 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.
```

## 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.ArrayDequeimport 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 = result 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 = result or temp        }        for (c in 0..7) {            val temp =  ((state[c + 12] - 12) and 5) shl (3 * c)            result = result or temp        }        for (i in 12..18) {            for (j in (i + 1)..19) {                result = result 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)    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                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
```

## 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.

`---- 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.--constant THRESHOLD = 100000 -- 100000 -- very slow (100s), best results                            --  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/Downenum U=1,L=2,F=3,/*R=4,*/B=5,D=6,Dbl=#08,Shift=#10constant 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]=cube[ei] and                           cube[ei]=cube[ei]) +                          (cube[ei]=cube[ei] and                           cube[ei]=cube[ei])        end for    end if    return resend 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 resend 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]            for j=1 to 3 do                cube[rfi[j]] = cube[rfi[j+1]]            end for            cube[rfi] = rfi1        end for    end for    return cubeend function function apply_moves(string cube, sequence moves)    for i=1 to length(moves) do        cube = rotate_face(cube,moves[i])    end for    return cubeend 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 resend 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()+1string moves = "", moves2sequence workspace, w2,         initinteger wslen, high = 1,        s, c2c = 0, o = 0bool 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 = 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]            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 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 cubesequence movesinteger total_moves = 0atom 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 proceduremain()`
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--function xor_string(string s)    return xor_bits(s,xor_bits(s,iff(length(s)=3?s:'!')))end function function xor_all(sequence s)    for i=1 to length(s) do        s[i] = xor_string(s[i])    end for    return send 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_idxsequence 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 forend 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],inva[b+1])*2,                        ib3 = xor_bits(inva[b+1],inva[b+1]),                        ib4 = xor_bits(inva[b+1],inva[b+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 0end function function pack_moves()string moves = ""integer n = 0, this, 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        last_rpt = 0        for i=1 to history_idx do            this = history_mov[i]            if this!=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 = this                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>'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.