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solutions.py
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# solutions.py
# Chris Barker
# CMU S13 15-112 Term Project
# solutions.beginner3Layer(state) takes a CubeState (see cube.py)
# and returns a list of moves.
from geometry import *
import time
import datetime
SOLVED_STATE = [[[ ( 1, 210), ( 2, 210), ( 3, 210) ],
[ ( 4, 210), ( 5, 210), ( 6, 210) ],
[ ( 7, 210), ( 8, 210), ( 9, 210) ]],
[[ (10, 210), (11, 210), (12, 210) ],
[ (13, 210), (14, 210), (15, 210) ],
[ (16, 210), (17, 210), (18, 210) ]],
[[ (19, 210), (20, 210), (21, 210) ],
[ (22, 210), (23, 210), (24, 210) ],
[ (25, 210), (26, 210), (27, 210) ]]]
CUBE_DIMENSION = 3
MOVE_CODES = { K_HAT: 'U',
-K_HAT: 'D',
-I_HAT: 'L',
I_HAT: 'R',
J_HAT: 'F',
-J_HAT: 'B'}
COLOR_CODES = { I_HAT : 'green',
-I_HAT : 'blue',
J_HAT : 'red',
-J_HAT : 'orange',
K_HAT : 'yellow',
-K_HAT : 'white'}
def valueAtPos(vec, state):
(x, y, z) = vec.components
(x, y, z) = (int(x+1), int(y+1), int(z+1))
return state.state[z][y][x]
def solutionAtPos(vec):
(x, y, z) = vec.components
(x, y, z) = (int(x+1), int(y+1), int(z+1))
return SOLVED_STATE[z][y][x]
def posOfVal(val, state):
for z in xrange(CUBE_DIMENSION):
for y in xrange(CUBE_DIMENSION):
for x in xrange(CUBE_DIMENSION):
if hasattr(state, 'state'):
if state.state[z][y][x][0] == val:
return Vector(x-1, y-1, z-1)
else:
if state[z][y][x][0] == val:
return Vector(x-1, y-1, z-1)
def makeMoves(axes, state, moves, status='Solving'):
for axis in axes:
move = MOVE_CODES[axis[0]]
if axis[1]: move += "'"
state.rotate(state.rotationInfo(move))
move = (move, status)
moves.append(move)
class Struct(): pass
def getPerpendicular(vec):
if vec // K_HAT:
val = +J_HAT
else: val = +K_HAT
return val
def refine(L):
while True:
for i in xrange(len(L) - 1):
if i+2 != len(L) and L[i][0] == L[i+1][0] == L[i+2][0]:
if "'" in L[i][0]:
L[i:i+3] = [(L[i][0][0], L[i][1])]
else:
L[i:i+3] = [(L[i][0] + "'", L[i][1])]
break
if L[i][0] == L[i+1][0] + "'" or L[i+1][0] == L[i][0] + "'":
L[i:i+2] = []
break
else:
break
def determineFixTXB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
orientation = info.orientation
posOfValue = info.posOfValue
if desiredValue == currentValue:
# Correct location
if desiredOrientation == currentOrientation:
return retain
else:
return flipTopCrossBeginner
else:
# Incorrect location
if posOfValue ** topLayer > 0:
# Elsewhere on the top layer
if orientation / 100 == desiredOrientation / 100:
# Same color facing upward
return relocateTopLayerTXB
else:
# Top-layer color not facing up
return reorientTopLayerTXB
elif posOfValue ** topLayer == 0:
return secondLayerTXB
else:
if orientation / 100 == desiredOrientation / 100:
return relocateBottomLayerTXB
else:
return reorientBottomLayerTXB
def determineFixTCB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
if desiredValue == currentValue:
if desiredOrientation == currentOrientation:
# Already where we want it
return retain
else:
return flipTopTCB
else:
if posOfValue ** topLayer > 0:
# Elsewhere on the top layer
return moveCornerDown
else:
# On the bottom layer
return moveCornerUp
def determineFixSLB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
if desiredValue == currentValue:
desO = list(str(desiredOrientation))
curO = list(str(currentOrientation))
desO.remove('2')
curO.remove('2')
if desO == curO:
return retain
else:
return moveSecondLayerDown
else:
if posOfValue ** topLayer < 0:
return moveSecondLayerUp
else:
return moveSecondLayerDown
def retain(info): return
def named(pieceId):
pos = posOfVal(pieceId, SOLVED_STATE)
colors = [COLOR_CODES[k] for k in COLOR_CODES if k**pos > 0]
if len(colors) == 2:
return 'the %s and %s edge piece' % (colors[0], colors[1])
elif len(colors) == 3:
msg = 'the %s, %s, and %s corner piece'
return msg % (colors[0], colors[1], colors[2])
else:
return str(colors)
def flipTopCrossBeginner(info):
axesToRotate = [
# Put the piece on the second layer
(info.pos - (info.pos > info.topLayer), False),
(info.topLayer, True), # Rotate the top layer
# Put the piece back on the top layer
(info.pos * info.topLayer, False),
(info.topLayer, False) # Put the top layer back
]
msg = "Flipping %s on the first layer." % (named(info.desiredValue))
makeMoves(axesToRotate, info.state, info.moves, msg)
def relocateTopLayerTXB(info):
desiredAxis = info.pos - (info.pos > info.topLayer)
currentAxis = info.posOfValue - (info.posOfValue > info.topLayer)
if desiredAxis // currentAxis: # Opposite side
numRotations = 2
elif (desiredAxis * currentAxis) ** info.topLayer < 0:
numRotations = -1
else:
numRotations = 1
axesToRotate = [ ]
axesToRotate.append((currentAxis, False))
for i in xrange(abs(numRotations)):
axesToRotate.append((info.topLayer, numRotations < 0))
axesToRotate.append((currentAxis, True))
for i in xrange(abs(numRotations)):
axesToRotate.append((info.topLayer, numRotations > 0))
msg = 'Moving %s into place.' % named(info.desiredValue)
makeMoves(axesToRotate, info.state, info.moves, msg)
def reorientTopLayerTXB(info):
desiredAxis = info.pos - (info.pos > info.topLayer)
currentAxis = info.posOfValue - (info.posOfValue > info.topLayer)
if desiredAxis // currentAxis: # Opposite side
numRotations = 1
elif (desiredAxis * currentAxis) ** info.topLayer < 0:
numRotations = 2
else:
numRotations = 0
axesToRotate = [ ]
axesToRotate.append((currentAxis, False))
for i in xrange(abs(numRotations)):
axesToRotate.append((info.topLayer, numRotations < 0))
axesToRotate.append((currentAxis * info.topLayer, False))
for i in xrange(abs(numRotations)):
axesToRotate.append((info.topLayer, numRotations > 0))
msg = "Relocating %s on the first layer." % (named(info.desiredValue))
makeMoves(axesToRotate, info.state, info.moves, msg)
def secondLayerTXB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
orientation = str(orientation)
orientation = list(orientation)
orientation.remove('2')
if len(orientation) == 2: # The top-facing is on the y-face
rotating = +I_HAT
else: rotating = +J_HAT
if rotating ** posOfValue < 0:
rotating = rotating * -1
cclock = False
if (rotating * topLayer) ** posOfValue > 0:
cclock = True
desiredAxis = pos - (pos > topLayer)
currentAxis = rotating
if desiredAxis // currentAxis:
if desiredAxis ** currentAxis > 0:
numRotations = 0
else:
numRotations = 2
elif (desiredAxis * currentAxis) ** topLayer < 0:
numRotations = 1
else:
numRotations = -1
axesToRotate = [ ]
for i in xrange(abs(numRotations)):
axesToRotate.append((topLayer, numRotations > 0))
axesToRotate.append((currentAxis, cclock))
for i in xrange(abs(numRotations)):
axesToRotate.append((topLayer, numRotations < 0))
task = 'Moving %s from the second layer to the first layer.'
msg = task % (named(info.desiredValue))
makeMoves(axesToRotate, state, moves, msg)
def relocateBottomLayerTXB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
desiredAxis = pos - (pos > topLayer)
currentAxis = posOfValue - (posOfValue > topLayer)
if desiredAxis // currentAxis:
if desiredAxis ** currentAxis > 0:
numRotations = 0
else:
numRotations = 2
elif (desiredAxis * currentAxis) ** topLayer < 0:
numRotations = 1
else:
numRotations = -1
axesToRotate = [ ]
for i in xrange(abs(numRotations)):
axesToRotate.append(( -1 * topLayer, numRotations > 0))
axesToRotate.append((desiredAxis, True))
axesToRotate.append((desiredAxis, True))
task = 'Moving %s from the third layer to the first layer.'
msg = task % (named(info.desiredValue))
makeMoves(axesToRotate, state, moves, msg)
def reorientBottomLayerTXB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
desiredAxis = pos - (pos > topLayer)
currentAxis = posOfValue - (posOfValue > topLayer)
if desiredAxis // currentAxis:
if desiredAxis ** currentAxis > 0:
numRotations = 0
else:
numRotations = 2
elif (desiredAxis * currentAxis) ** topLayer < 0:
numRotations = 1
else:
numRotations = -1
axesToRotate = [ ]
for i in xrange(abs(numRotations)):
# Rotate top to correct position
axesToRotate.append(( topLayer, numRotations > 0))
# Move piece up to second layer
axesToRotate.append((currentAxis, False))
# Move open space on top layer accordingly
axesToRotate.append((topLayer, False))
axesToRotate.append((topLayer * currentAxis, True))
axesToRotate.append((topLayer, True))
for i in xrange(abs(numRotations)):
axesToRotate.append(( topLayer, numRotations < 0))
task = 'Moving %s from the third layer to the first layer.'
msg = task % (named(info.desiredValue))
makeMoves(axesToRotate, state, moves, msg)
def flipTopTCB(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
orientation = str(orientation)
orientation = list(orientation)
if len(orientation) == 2:
orientation = ['0'] + orientation
if orientation[0] == '0': # The top-facing is on the x-face
(rotating, other) = (+I_HAT, +J_HAT)
else: (rotating, other) = (+J_HAT, +I_HAT)
if rotating ** posOfValue < 0:
rotating = rotating * -1
if other ** posOfValue < 0:
other = other * -1
cclock = (rotating * other) ** topLayer > 0
axesToRotate = [ ]
axesToRotate.append((rotating, cclock))
axesToRotate.append((topLayer * -1, cclock))
axesToRotate.append((rotating, not cclock))
axesToRotate.append((topLayer * -1, not cclock))
axesToRotate.append((rotating, cclock))
axesToRotate.append((topLayer * -1, cclock))
axesToRotate.append((rotating, not cclock))
msg = 'Rotating %s on the first layer.' % named(info.desiredValue)
makeMoves(axesToRotate, state, moves, msg)
def moveCornerDown(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
(axis0, axis1) = (+I_HAT, +J_HAT)
if axis0 ** posOfValue < 0:
axis0 = axis0 * -1
if axis1 ** posOfValue < 0:
axis1 = axis1 * -1
if (axis1 * axis0) ** topLayer < 0:
(axis1, axis0) = (axis0, axis1)
axesToRotate = [ ]
axesToRotate.append((axis1, True))
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis1, False))
task = 'Moving %s from the first layer to the third layer.'
msg = task % named(info.desiredValue)
makeMoves(axesToRotate, state, moves, msg)
def moveCornerUp(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
(axis0, axis1) = (+I_HAT, +J_HAT)
if axis0 ** pos < 0:
axis0 = axis0 * -1
if axis1 ** pos < 0:
axis1 = axis1 * -1
if (axis1 * axis0) ** topLayer < 0:
(axis1, axis0) = (axis0, axis1)
pos = pos - (pos > topLayer)
posOfValue = posOfValue - (posOfValue > topLayer)
if (pos * posOfValue) ** topLayer > 0:
numRotations = 1
elif (pos * posOfValue) ** topLayer < 0:
numRotations = -1
else:
if pos ** posOfValue > 0:
numRotations = 0
else:
numRotations = 2
axesToRotate = [ ]
for i in xrange(abs(numRotations)):
axesToRotate.append((topLayer * -1, numRotations < 0))
axesToRotate.append((axis1, True))
axesToRotate.append((topLayer * -1, True))
axesToRotate.append((axis1, False))
task = 'Moving %s from the third layer to the first layer.'
msg = task % named(info.desiredValue)
makeMoves(axesToRotate, state, moves, msg)
def moveSecondLayerDown(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
(axis0, axis1) = (+I_HAT, +J_HAT)
if axis0 ** posOfValue < 0:
axis0 = axis0 * -1
if axis1 ** posOfValue < 0:
axis1 = axis1 * -1
if (axis1 * axis0) ** topLayer < 0:
(axis1, axis0) = (axis0, axis1)
axesToRotate = [ ]
axesToRotate.append((axis1, True))
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis1, False))
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis0, False))
axesToRotate.append((topLayer * -1, True))
axesToRotate.append((axis0, True))
task = 'Moving %s from the second layer to the third layer temporarily.'
msg = task % named(info.desiredValue)
makeMoves(axesToRotate, state, moves, msg)
def moveSecondLayerUp(info):
pos = info.pos
desiredValue = info.desiredValue
desiredOrientation = info.desiredOrientation
currentValue = info.currentValue
currentOrientation = info.currentOrientation
topLayer = info.topLayer
state = info.state
moves = info.moves
orientation = info.orientation
posOfValue = info.posOfValue
currentAxis = posOfValue - (posOfValue > topLayer)
(axis0, axis1) = (+I_HAT, +J_HAT)
if axis0 ** pos < 0:
axis0 = axis0 * -1
if axis1 ** pos < 0:
axis1 = axis1 * -1
if (axis1 * axis0) ** topLayer < 0:
(axis1, axis0) = (axis0, axis1)
orientation = list(str(orientation))
# what matters is whether z comes first or not
if len(orientation) == 2:
orientation = ['0'] + orientation
if posOfValue ** I_HAT == 0:
orientation.remove('0')
if posOfValue ** J_HAT == 0:
orientation.remove('1')
if orientation[0] == '2':
# The Y value is displayed on the Z axis
# So the X value is displayed above
setupAxis = pos > I_HAT
else:
setupAxis = pos > J_HAT
if setupAxis // currentAxis:
if setupAxis ** currentAxis > 0:
numRotations = 0
else:
numRotations = 2
elif (setupAxis * currentAxis) ** topLayer < 0:
numRotations = 1
else:
numRotations = -1
axesToRotate = [ ]
for i in xrange(abs(numRotations)):
axesToRotate.append((-1 * topLayer, numRotations > 0))
if (setupAxis * pos) ** topLayer > 0:
# Right side
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis0, False))
axesToRotate.append((topLayer * -1, True))
axesToRotate.append((axis0, True))
axesToRotate.append((topLayer * -1, True))
axesToRotate.append((axis1, True))
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis1, False))
else:
# Left side
axesToRotate.append((topLayer * -1, True))
axesToRotate.append((axis1, True))
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis1, False))
axesToRotate.append((topLayer * -1, False))
axesToRotate.append((axis0, False))
axesToRotate.append((topLayer * -1, True))
axesToRotate.append((axis0, True))
msg = 'Moving %s from the third layer to the second layer.' % (
named(info.desiredValue))
makeMoves(axesToRotate, state, moves, msg)
def topCrossBeginner(state, topLayer, log):
moves = [ ]
axis0 = getPerpendicular(topLayer)
axis1 = topLayer * axis0
topCross = [ topLayer + axis0 ,
topLayer - axis0 ,
topLayer + axis1 ,
topLayer - axis1]
for pos in topCross:
(desiredValue, desiredOrientation) = solutionAtPos(pos)
(currentValue, currentOrientation) = valueAtPos(pos, state)
posOfValue = posOfVal(desiredValue, state)
orientation = valueAtPos(posOfValue, state)[1]
info = Struct()
info.desiredValue = desiredValue
info.desiredOrientation = desiredOrientation
info.pos = pos
info.moves = moves
info.currentValue = currentValue
info.currentOrientation = currentOrientation
info.state = state
info.orientation = orientation
info.topLayer = topLayer
info.posOfValue = posOfValue
fix = determineFixTXB(info)
fix(info)
log.append('TXB:%d' % (len(moves)))
return moves
def topCornersBeginner(state, topLayer, log):
moves = [ ]
axis0 = getPerpendicular(topLayer)
axis1 = topLayer * axis0
topCorners = [ topLayer + axis0 + axis1,
topLayer + axis0 - axis1,
topLayer - axis0 + axis1,
topLayer - axis0 - axis1 ]
doneUp = done = False
while not done:
changedThisRound = False
for pos in topCorners:
fix = None
count = 0
(desiredValue, desiredOrientation) = solutionAtPos(pos)
(currentValue, currentOrientation) = valueAtPos(pos, state)
posOfValue = posOfVal(desiredValue, state)
orientation = valueAtPos(posOfValue, state)[1]
info = Struct()
info.desiredValue = desiredValue
info.desiredOrientation = desiredOrientation
info.pos = pos
info.moves = moves
info.currentValue = currentValue
info.currentOrientation = currentOrientation
info.state = state
info.orientation = orientation
info.topLayer = topLayer
info.posOfValue = posOfValue
fix = determineFixTCB(info)
if (((fix == flipTopTCB) or (fix == moveCornerDown))
and (not doneUp)):
continue
else:
fix(info)
changedThisRound = changedThisRound or fix != retain
done = (not changedThisRound) and doneUp
doneUp = not changedThisRound
log.append('TCB:%d' % (len(moves)))
return moves
def secondLayerBeginner(state, topLayer, log):
moves = [ ]
axis0 = getPerpendicular(topLayer)
axis1 = topLayer * axis0
secondLayer = [axis0 + axis1,
axis0 - axis1,
(-1 * axis0) + axis1,
(-1 * axis0) - axis1]
doneUp = False
done = False
while not done:
changedThisRound = False
for pos in secondLayer:
fix = None
count = 0
(desiredValue, desiredOrientation) = solutionAtPos(pos)
(currentValue, currentOrientation) = valueAtPos(pos, state)
posOfValue = posOfVal(desiredValue, state)
orientation = valueAtPos(posOfValue, state)[1]
info = Struct()
info.desiredValue = desiredValue
info.desiredOrientation = desiredOrientation
info.pos = pos
info.moves = moves
info.currentValue = currentValue
info.currentOrientation = currentOrientation
info.state = state
info.orientation = orientation
info.topLayer = topLayer
info.posOfValue = posOfValue
fix = determineFixSLB(info)
if fix == moveSecondLayerDown and not doneUp:
continue
else:
fix(info)
changedThisRound = changedThisRound or fix != retain
done = (not changedThisRound) and doneUp
doneUp = not changedThisRound
log.append('SLB:%d' % (len(moves)))
return moves
def thirdLayerCornerOrientation(state, topLayer, log):
moves = [ ]
axis0 = getPerpendicular(topLayer)
axis1 = topLayer * axis0
bottomLayer = topLayer * -1
bottomCorners = [ bottomLayer + axis0 + axis1,
bottomLayer + axis0 - axis1,
bottomLayer - axis0 + axis1,
bottomLayer - axis0 - axis1 ]
# Bottom, right, top, left
axes = [ axis0, axis1, -1 * axis0, -1 * axis1]
count = 50
while count > 0:
orientations = [valueAtPos(corner,state)[1] for
corner in bottomCorners]
facingDowns = [i for i in bottomCorners if valueAtPos(i,state)[1] > 200]
facingXs = [i for i in bottomCorners if valueAtPos(i,state)[1] < 100]
facingYs = [i for i in bottomCorners if 100 < valueAtPos(i,state)[1] < 200]
numFacingDown = len(facingDowns)
if numFacingDown == 4:
break
elif numFacingDown == 3:
raise ValueError('Impossible cube!')
elif numFacingDown == 2:
pos0 = facingDowns[0]
pos1 = facingDowns[1]
if pos0 // pos1:
pos = facingDowns[0]
pos = pos - (pos > bottomLayer)
operator = ((bottomLayer * pos) + pos) / 2
else:
if len(facingXs) == 2:
if ((I_HAT ** facingXs[0]) *
(I_HAT ** facingXs[1]) > 0):
operator = (facingXs[0] > -I_HAT) ^ 1
else:
pos = facingXs[0] + facingXs[1]
operator = (bottomLayer * pos) ^ 1
elif len(facingYs) == 2:
if ((J_HAT ** facingYs[0]) *
(J_HAT ** facingYs[1]) > 0):
operator = (facingYs[0] > -J_HAT) ^ 1
else:
pos = facingYs[0] + facingYs[1]
operator = (bottomLayer * pos) ^ 1
else:
operator = +I_HAT
elif numFacingDown == 1:
pos = facingDowns[0]
pos = pos - (pos > bottomLayer)
operator = ((bottomLayer * pos) - pos) / 2
elif numFacingDown == 0:
if len(facingXs) == 4:
operator = +I_HAT
elif len(facingXs) == 0:
operator = +J_HAT
else:
if ((I_HAT ** facingXs[0]) *
(I_HAT ** facingXs[1]) > 0):
# The Xs are facing the same direction
unequals = (facingXs[0] > I_HAT) ^ 1
else:
unequals = (facingYs[0] > J_HAT) ^ 1
pos = unequals - (unequals > bottomLayer)
operator = ((pos * bottomLayer) ^ 1)
try:
s = MOVE_CODES[operator]
except:
print 'UNTREATED CASE.',
print 'numFacingDown = %d.' % (numFacingDown),
print 'facingXs=%s, facingYs%s, facingDowns%s' % (
facingXs, facingYs, facingDowns)
break
axesToRotate = [ (operator, True), (bottomLayer, True),
(operator, False), (bottomLayer, True),
(operator, True), (bottomLayer, True),
(bottomLayer, True), (operator, False) ]
msg = 'Orienting the third layer corners by rotating %s and %s.' % (
COLOR_CODES[operator], COLOR_CODES[bottomLayer])
makeMoves(axesToRotate, state, moves, msg)
count -= 1
else:
raise ValueError('Could not generate solution.')
log.append('BCO:%d' % (len(moves)))
return moves
def thirdLayerEdgeOrientation(state, topLayer, log):
moves = [ ]
axis0 = getPerpendicular(topLayer)
axis1 = topLayer * axis0
bottomLayer = topLayer * -1
bottomEdges = [ bottomLayer + axis0,
bottomLayer - axis0,
bottomLayer + axis1,
bottomLayer - axis1]
count = 50
while count > 0:
orientations = [valueAtPos(edge,state)[1] for edge in bottomEdges]
facingDowns = [ ]
facingXs = [ ]
facingYs = [ ]
for edge in bottomEdges:
(pos, orient) = valueAtPos(edge, state)
orient = list(str(orient))
if len(orient) == 2:
orient = ['0'] + orient
if edge ** I_HAT == 0:
orient.remove('0')
if edge ** J_HAT == 0:
orient.remove('1')
if edge ** K_HAT == 0:
orient.remove('2')
if orient[0] == '2':
facingDowns.append(edge)
elif orient[0] == '1':
facingYs.append(edge)
elif orient[0] == '0':
facingXs.append(edge)
numFacingDown = len(facingDowns)
if numFacingDown == 4:
break
elif numFacingDown == 3:
return
raise ValueError('Impossible cube! 3 down')
elif numFacingDown == 2:
if len(facingXs) == 1:
# Diagonal case
if (facingXs[0] * facingYs[0]) ** bottomLayer < 0:
operator = facingXs[0] > (-I_HAT)
else:
operator = facingYs[0] > (-J_HAT)
else:
if len(facingXs) == 2:
operator = +J_HAT
else:
operator = +I_HAT
elif numFacingDown == 1:
return
raise ValueError('Impossible cube! Only 1 down')
elif numFacingDown == 0:
operator = +I_HAT
axesToRotate = [ ]
front = operator
right = front * bottomLayer
axesToRotate.append((right, True))
axesToRotate.append((bottomLayer, True))
axesToRotate.append((front, True))
axesToRotate.append((bottomLayer, False))
axesToRotate.append((front, False))
axesToRotate.append((right, False))
msg = 'Orienting third layer edges.'
makeMoves(axesToRotate, state, moves, msg)
count -= 1
else:
raise ValueError('Could not generate solution.')
log.append('BEO:%d' % (len(moves)))
return moves
def thirdLayerCornerPermutation(state, topLayer, log):
moves = [ ]
axis0 = getPerpendicular(topLayer)
axis1 = topLayer * axis0
bottomLayer = topLayer * -1
bottomCorners = [ bottomLayer + axis0 + axis1,
bottomLayer + axis0 - axis1,
bottomLayer - axis0 - axis1,
bottomLayer - axis0 + axis1 ]
count = 50
while count > 0:
adjacentPairs = [ ]
for i in xrange(len(bottomCorners)):
corner1 = bottomCorners[i]
corner2 = bottomCorners[(i+1) % (len(bottomCorners))]
# what we have at corner 1 right now
(currentValue1, currentOrientation1) = valueAtPos(corner1, state)
# where that piece should be
desired1 = posOfVal(currentValue1, SOLVED_STATE)
# what we have at corner 2 right now
(currentValue2, currentOrientation2) = valueAtPos(corner2, state)
# where that piece should be
desired2 = posOfVal(currentValue2, SOLVED_STATE)
if not ((desired1 - bottomLayer) // (desired2 - bottomLayer)):
# they are adjacent corners
if (((desired1 - bottomLayer) * (desired2 - bottomLayer)) **
((corner1 - bottomLayer) * (corner2 - bottomLayer))) > 0:
# correct orientation
adjacentPairs.append((corner1, corner2))
if len(adjacentPairs) == 4:
break
elif len(adjacentPairs) == 0:
operator = +I_HAT
elif len(adjacentPairs) == 1:
(corner1, corner2) = adjacentPairs[0]
nonOp = (corner1 - bottomLayer) + (corner2 - bottomLayer)
operator = (-1 * nonOp) / 2
else:
print adjacentPairs
print state
raise ValueError('bad corners')
top = bottomLayer
front = operator
back = operator * -1
right = operator * bottomLayer
axesToRotate = [ (right, True), (front, False), (right, True),
( back, True), ( back, True), (right, False),
(front, True), (right, True), ( back, True),
( back, True), (right, True), (right, True) ]
task = 'Permuting third layer corners.'
msg='%s. So far, %d %s permuted correctly.' % (
task, len(adjacentPairs), 'pair is' if
len(adjacentPairs) == 1 else 'pairs are')
makeMoves(axesToRotate, state, moves, msg)
count -= 1
else:
raise ValueError('Could not generate solution.')
posOfValue = bottomCorners[0]
val = valueAtPos(posOfValue, state)
solvedPos = posOfVal(val[0], SOLVED_STATE)
if (solvedPos * posOfValue) ** topLayer > 0:
numRotations = 1
elif (solvedPos * posOfValue) ** topLayer < 0:
numRotations = -1
else:
if solvedPos ** posOfValue > 0:
numRotations = 0