"""
@author Thomas Lehmann
@file four_cubes_problem.py
There are four cubes with concrete colors on their sides and the goal
is to place each cube in one row that way, that along the row each side
presents four different colors:
- - - -
|W| |R| |G| |B| (front view)
- - - -
Of course four different colors are also required at the top view
at the bottom view and at the back view.
Background: I have those four cubes in real and I have been seeking
for the solution without manual try.
"""
import random
class Color:
""" represents a kind of enum for all used colors """
GREEN = 0
RED = 1
WHITE = 2
BLUE = 3
MAX = 4
@staticmethod
def name(value):
return ["GREEN", "RED", "WHITE", "BLUE"][value]
class Cube:
def __init__(self, front, back, left, right, top, bottom):
""" initializes all sides of a cube with colors """
self.front = front
self.back = back
self.left = left
self.right = right
self.top = top
self.bottom = bottom
def __eq__(self, other):
""" compares this cube and another for to be equal """
return self.front == other.front \
and self.back == other.back \
and self.left == other.left \
and self.right == other.right \
and self.top == other.top \
and self.bottom == other.bottom
def __hash__(self):
""" unique key for this instance """
return hash((self.front, self.back, self.left, self.right, self.top, self.bottom))
def clone(self):
""" provides a copy of this instance """
return Cube(self.front, self.back, self.left, self.right, self.top, self.bottom)
def __str__(self):
""" does print the current cube setup (colors) """
return "front:" + Color.name(self.front) + "," + \
"back:" + Color.name(self.back) + "," + \
"left:" + Color.name(self.left) + "," + \
"right:" + Color.name(self.right) + "," + \
"top:" + Color.name(self.top) + "," + \
"bottom:" + Color.name(self.bottom)
def getCombinations(self):
""" I know: there should be 24 combinations """
cubes = set()
cubes.add(self.clone())
cube = self.clone()
while not len(cubes) == 24:
mode = random.randint (0, 4)
if 0 == mode: cube.rotateLeft()
elif 1 == mode: cube.rotateRight()
elif 2 == mode: cube.rotateTop()
elif 3 == mode: cube.rotateBottom()
cubes.add(cube.clone())
return cubes
def rotateLeft(self):
""" does rotate the cube to the left """
help = self.left
self.left = self.front
self.front = self.right
self.right = self.back
self.back = help
return self
def rotateRight(self):
""" does rotate the cube to the right """
help = self.right
self.right = self.front
self.front = self.left
self.left = self.back
self.back = help
return self
def rotateTop(self):
""" does rotate the cube to the top """
help = self.top
self.top = self.front
self.front = self.bottom
self.bottom = self.back
self.back = help
return self
def rotateBottom(self):
""" does rotate the cube to the bottom """
help = self.bottom
self.bottom = self.front
self.front = self.top
self.top = self.back
self.back = help
return self
class CubesChecker:
def __init__(self, cubes):
self.originalCubes = cubes
@staticmethod
def isValidState(cubes):
""" ensure the rule: four different colors on each side """
frontColors = set()
backColors = set()
topColors = set()
bottomColors = set()
for cube in cubes:
frontColors.add(cube.front)
backColors.add(cube.back)
topColors.add(cube.top)
bottomColors.add(cube.bottom)
return len(frontColors) == Color.MAX \
and len(backColors) == Color.MAX \
and len(topColors) == Color.MAX \
and len(bottomColors) == Color.MAX
def calculate(self, position = 0, cubes = []):
""" find the cubes final state """
if len(cubes) == Color.MAX:
if CubesChecker.isValidState(cubes):
for cube in cubes:
print(cube)
return True
else:
return False
for cube in self.originalCubes[position].getCombinations():
if self.calculate(position+1, cubes + [cube]):
return True
return False
def main():
""" there are four cubes with concrete colors on their sides and the goal
is to place each cube in one row that way that along the row each side
presents four different colors """
# ----------- ----------- ----------- ----------- ----------- -----------
# front back left right top bottom
# ----------- ----------- ----------- ----------- ----------- -----------
cubes = [ Cube(Color.GREEN, Color.WHITE, Color.GREEN, Color.RED, Color.WHITE, Color.BLUE),
Cube(Color.WHITE, Color.RED , Color.WHITE, Color.GREEN, Color.BLUE, Color.RED),
Cube(Color.RED, Color.RED, Color.RED , Color.GREEN, Color.BLUE, Color.WHITE),
Cube(Color.BLUE, Color.RED, Color.GREEN, Color.GREEN, Color.WHITE, Color.BLUE) ]
cubesChecker = CubesChecker(cubes)
cubesChecker.calculate()
if __name__ == "__main__":
main()
