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{{draft task}}
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 = [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") }
{{out}}
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.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") }
{{out}} Using the original dataset of 100 lines, the results were as follows (time doesn't mean much but is typical for my modest machine):
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)
```
```txt
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:
```txt
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.
```Phix
--
-- 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/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 = 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 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()
```
{{Out}}
The "hardest case" from http://www.cube20.org with a high threshold. You can try this manually.
Disclaimer: the results are not always quite as good as this!
```txt
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...
```Phix
--
-- demo\rosetta\rubik_tomas.exw
--
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, 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[1]
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[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"))
```
{{out}}
```txt
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.