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Solve a Rubik's cube: Difference between revisions
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Average time = 522 milliseconds
</pre>
=={{header|Nim}}==
{{trans|Kotlin}}
<lang Nim>#[
**********************************************************************
*
* A cube 'state' is a sequence of ints with 40 entries, the first
* 20 are a permutation of {0,...,19} and describe which cubie is
* at a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************
]#
import deques, os, strformat, strutils, tables, times
const
ApplicableMoves = [0, 262143, 259263, 74943, 74898]
AffectedCubies = [[0, 1, 2, 3, 0, 1, 2, 3], # U
[4, 7, 6, 5, 4, 5, 6, 7], # D
[0, 9, 4, 8, 0, 3, 5, 4], # F
[2, 10, 6, 11, 2, 1, 7, 6], # B
[3, 11, 7, 9, 3, 2, 6, 5], # L
[1, 8, 5, 10, 1, 0, 4, 7]] # R
type State = seq[int]
func initState(n: Natural = 0): State = newSeq[int](n)
var phase: Natural
proc slicetoState(s: openArray[int]): State =
result.setLen(40)
for i, val in s: result[i] = val
for i in s.len..39: result[i] = -1
proc id(state: State): State =
case phase
of 1: # Phase 1: Edge orientations.
result = sliceToState(state[20..31])
of 2: # Phase 2: Corner orientations, E slice edges.
var res = state[31..39]
for e in 0..11:
res[0] = res[0] or state[e] shr 3 shl e
result = sliceToState(res)
of 3: # Phase 3: Edge slices M and S, corner tetrads, overall parity.
var res = @[0, 0, 0]
for e in 0..11:
let temp = if state[e] > 7: 2 else: (state[e] and 1) shl (2 * e)
res[0] = res[0] or temp
for c in 0..7:
res[1] = res[1] or ((state[c + 12] - 12) and 5) shl (3 * c)
for i in 12..18:
for j in (i + 1)..19:
res[2] = res[2] xor ord(state[i] > state[j])
result = sliceToState(res)
else: # Phase 4: The rest.
result = state
proc applyMove(move: int; state: State): State =
result = state
var turns = move mod 3 + 1
let face = move div 3
while turns != 0:
dec turns
var oldState = result
for i in 0..7:
let isCorner = ord(i > 3)
let target = AffectedCubies[face][i] + isCorner * 12
let temp = if (i and 3) == 3: i - 3 else: i + 1
let killer = AffectedCubies[face][temp] + isCorner * 12
let orientationDelta =
if i < 4: ord(face in 2..3)
elif face < 2: 0
else: 2 - (i and 1)
result[target] = oldState[killer]
result[target + 20] = oldState[killer + 20] + orientationDelta
if turns == 0:
result[target + 20] = result[target + 20] mod (2 + isCorner)
func inverse(move: int): int = move + 2 - 2 * (move mod 3)
let startTime = cpuTime()
var aggregateMoves = 0
# Define the goal.
const Goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]
# Load dataset (file name should be passed as a command line argument).
if paramCount() == 0: quit "Missing file name", QuitFailure
var lineCount = 0
for line in paramStr(1).lines():
let inputs = line.splitWhitespace()
inc lineCount
var totalMoves = 0
# Prepare current (start) and goal state.
var currentState, goalState = initState(40)
for i in 0..19:
# Goal state.
goalState[i] = i
# Current (start) state.
var cubie = inputs[i]
while true:
let idx = Goal.find(cubie)
currentState[i] = if idx >= 0: idx else: 20
if currentState[i] != 20: break
cubie = cubie[1..^1] & cubie[0]
inc currentState[i + 20]
# Dance the funky Thistlethwaite...
phase = 1
while phase < 5:
block doPhase:
# Compute ids for current and goal state, skip phase if equal.
let currentId = id(currentState)
let goalId = id(goalState)
if currentId == goalId: break doPhase
# Initialize the BFS queue.
var q = [currentState, goalState].toDeque
# Initialize the BFS tables.
var predecessor: Table[State, State]
var direction, lastMove: Table[State, int]
direction[currentId] = 1
direction[goalId] = 2
# Dance the funky bidirectional BFS.
while true:
# Get state from queue, compute its ID and get its direction.
let oldState = q.popFirst()
var oldId = id(oldState)
let oldDir = direction[oldId]
# Apply all applicable moves to it and handle the new state.
var move = 0
while move < 18:
if (ApplicableMoves[phase] and (1 shl move)) != 0:
# Apply the move.
let newState = applyMove(move, oldState)
var newId = id(newState)
let newDir = direction.getOrDefault(newId, 0)
# Have we seen this state (id) from the other direction already?
# I.e. have we found a connection?
if newDir != 0 and newDir != oldDir:
# Make oldId represent the forwards and newId the backwards search state.
if oldDir > 1:
swap newId, oldId
move = inverse(move)
# Reconstruct the connecting algorithm.
var algorithm: State = @[move]
while oldId != currentId:
algorithm.insert(lastMove.mgetOrPut(oldId, 0), 0)
oldId = predecessor.mgetOrPut(oldId, initState())
while newId != goalId:
algorithm.add inverse(lastMove.mgetOrPut(newId, 0))
newId = predecessor.mgetOrPut(newId, initState())
# Print and apply the algorithm.
for step in algorithm:
stdout.write "UDFBLR"[step div 3], step mod 3 + 1, ' '
inc totalMoves
currentState = applyMove(step, currentState)
# Jump to the next phase.
break doPhase
# If we've never seen this state (id) before, visit it.
if newdir == 0:
q.addLast(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
inc move
inc phase
echo &" (moves {totalMoves})"
inc aggregateMoves, totalMoves
let elapsedTime = cpuTime() - startTime
echo &"\nAverage number of moves = {aggregateMoves / lineCount}"
echo &"\nAverage time = {elapsedTime * 1000 / lineCount.toFloat:.2f} milliseconds"</lang>
{{out}}
We compiled the program with command <code>nim c -d:danger --gc:arc -d:lto</code>, which means no runtime checks, ARC memory management and link time optimization.
When run with the original dataset of 100 lines, we got:
<pre style="height:45ex">U1 U2 (moves 2)
U2 (moves 1)
U1 (moves 1)
F1 F2 (moves 2)
F2 (moves 1)
F1 (moves 1)
R1 R2 (moves 2)
R2 (moves 1)
R1 (moves 1)
D1 D2 (moves 2)
D2 (moves 1)
D1 (moves 1)
B1 B2 (moves 2)
B2 (moves 1)
B1 (moves 1)
L1 L2 (moves 2)
L2 (moves 1)
L1 (moves 1)
U2 B3 B2 (moves 3)
L2 U3 (moves 2)
R1 U1 (moves 2)
D3 L3 (moves 2)
D3 L2 (moves 2)
D2 F3 F2 (moves 3)
R2 F3 (moves 2)
R1 F2 F2 R2 F2 (moves 5)
D1 D2 U2 (moves 3)
L1 B2 F2 L2 R2 B2 F2 (moves 7)
L1 L2 D3 (moves 3)
D1 F2 (moves 2)
U2 R3 (moves 2)
L1 L2 U3 (moves 3)
U1 R2 (moves 2)
U1 R3 (moves 2)
F1 U2 (moves 2)
U2 R3 R2 (moves 3)
F2 D1 F3 (moves 3)
F2 D3 D2 U2 (moves 4)
L3 D2 R3 (moves 3)
D2 R3 R2 D3 (moves 4)
F1 R1 B2 B2 R2 B2 (moves 6)
L1 B2 F2 (moves 3)
U1 R2 B3 B2 (moves 4)
R2 F3 R2 (moves 3)
L2 D3 R3 R2 (moves 4)
L2 F3 L2 L2 F2 L2 (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2 (moves 29)
L1 L2 U3 R2 (moves 4)
L3 B3 B2 R3 R2 (moves 5)
B2 U1 R3 R2 (moves 4)
L3 B3 L2 (moves 3)
D1 B2 L3 L2 (moves 4)
B1 B2 R3 F2 F2 R2 F2 (moves 7)
D1 F3 D1 D2 (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2 (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2 (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2 (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2 (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2 (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2 (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2 (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2 (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2 (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2 (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2 (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2 (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2 (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2 (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2 (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2 (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2 (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2 (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2 (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2 (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2 (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2 (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2 (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2 (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2 (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2 (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2 (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2 (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2 (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2 (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2 (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2 (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2 (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2 (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2 (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2 (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2 (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2 (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2 (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2 (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2 (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2 (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2 (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2 (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2 (moves 34)</pre>
<pre>Average number of moves = 16.72
Average time = 52.03 milliseconds</pre>
When run with a file containing the single line:
UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL
a typical result was:
<pre>U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2 (moves 29)
Average number of moves = 29.0
Average time = 69.01 milliseconds</pre>
=={{header|Phix}}==
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