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somasolver.py
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somasolver.py
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from locale import normalize
import numpy as np
from copy import copy, deepcopy
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
# Rotation matrices
Rx = np.array([[ 1, 0, 0],
[ 0, 0,-1],
[ 0, 1, 0]])
Ry = np.array([[ 0, 0, 1],
[ 0, 1, 0],
[-1, 0, 0]])
Rz = np.array([[ 0,-1, 0],
[ 1, 0, 0],
[ 0, 0, 1]])
class Block:
def __init__(self, coords, name):
self.coord_len = len(coords)
self.coords = np.array(coords).T
self.origin = np.array([0,0,0])
self.unique_rotations = self.generate_unique_rotations()
# self.direction = np.array([[1],[0],[0]])
self.bounding_box = np.max(self.coords, axis=1)
self.name = name
def __len__(self):
return self.coord_len
def __getitem__(self, i):
return self.coords[:,i]
def set_coords(self, new_coords):
self.coords = new_coords
self.bounding_box = np.max(self.coords, axis=1)
def set_origin(self, origin_coords):
self.origin = np.array(origin_coords)
def roll(self):
self.coords = Rx @ self.coords
# self.direction = Rx @ self.direction
def turn(self):
self.coords = Rz @ self.coords
# self.direction = Rz @ self.direction
@staticmethod
def equivalent_coords(coord1, coord2):
if coord1.shape != coord2.shape:
return False
n = coord1.shape[1]
for i in range(n):
c1 = coord1[:,i]
c1_in_coord2 = False
for j in range(n):
c2 = coord2[:,j]
if (c1 == c2).all():
c1_in_coord2 = True
if not c1_in_coord2:
return False
return True
def _get_all_rotations(self):
"""Return a list of the 24 3d rotations"""
rotations = []
for cycle in range(2):
for step in range(3):
self.roll()
rotations.append(copy(self.coords))
for i in range(3):
self.turn()
rotations.append(copy(self.coords))
self.roll()
self.turn()
self.roll()
return rotations
def normalize_rotations(self, rotations):
normalized_rotations = []
for coords in rotations:
normalized_rotations.append(coords - np.min(coords, axis=1)[:,None])
return normalized_rotations
def generate_unique_rotations(self):
"""Return a list of unique 3d rotations with duplicates due to symmetry removed"""
all_rotations = self._get_all_rotations()
normalized_rotations = self.normalize_rotations(all_rotations)
unique_rotations = []
for new_rot in normalized_rotations:
is_duplicate = False
for unique_rot in unique_rotations:
# if (new_rot == unique_rot).all():
if self.equivalent_coords(new_rot, unique_rot):
is_duplicate = True
break
if not is_duplicate:
unique_rotations.append(new_rot)
return unique_rotations
def rotations(self):
for rot in self.unique_rotations:
self_copy = deepcopy(self)
self_copy.set_coords(rot)
yield(self_copy)
# def rotations(self):
# """Generator for the 24 unique 3d rotations"""
# for cycle in range(2):
# for step in range(3):
# self.roll()
# yield(self.coords)
# for i in range(3):
# self.turn()
# yield(self.coords)
# self.roll()
# self.turn()
# self.roll()
class Box:
def __init__(self):
self.filled = np.zeros((3, 3, 3), dtype=int)
@property
def is_filled(self):
return (self.filled == 1).all()
@property
def num_filled(self):
return np.sum(self.filled)
def coord_is_filled(self, i, j, k):
return self.filled[i, j, k]
def validate_placement(self, block, origin):
for offset in block:
cube_coord = origin + offset
if (cube_coord < 0).any() or (cube_coord > 2).any():
raise IndexError('Block placement is out of bounds.')
if self.filled[tuple(cube_coord)]:
raise IndexError('Space is already filled.')
def place(self, block, origin):
self.validate_placement(block, origin)
for offset in block:
cube_coord = origin + offset
self.filled[tuple(cube_coord)] = 1
class GameState:
def __init__(self, block_list):
self.block_candidates = [Block(b, f'B{i}') for i, b in enumerate(block_list)]
self.placed_blocks = []
self.box = Box()
@property
def is_solved(self):
return self.box.is_filled
def print(self):
print(f'Places filled: {self.box.num_filled}')
print('Candidate blocks: ', end='')
for bc in self.block_candidates:
print(bc.name, end=' ')
print('\nPlaced blocks: ', end='')
for pb in self.placed_blocks:
print(pb.name, end=' ')
print()
def solve(game):
game.print()
if not game.is_solved and len(game.block_candidates) > 0:
placement_block = game.block_candidates.pop()
for i in range(3):
for j in range(3):
for k in range(3):
if game.box.coord_is_filled(i, j, k):
continue
placement_block.set_origin([i, j, k])
for block_rotation in placement_block.rotations():
game_copy = deepcopy(game)
try:
game_copy.box.place(block_rotation, [i, j, k])
game_copy.placed_blocks.append(block_rotation)
# placement_block_copy = deepcopy(placement_block)
# game_copy.box.place(placement_block_copy, [i, j, k])
# game_copy.placed_blocks.append(placement_block_copy)
game_copy = solve(game_copy)
if game_copy.is_solved:
return game_copy
except IndexError:
pass
return game
def plot_solution(game):
fig = plt.figure()
ax = plt.axes(projection='3d')
plt.title('Cube solution')
for c, b in enumerate(game.placed_blocks):
coords = b.coords + b.origin[:,None]
ax.scatter(coords[0], coords[1], coords[2], color=f'C{c}', s=200, alpha=1)
for cube1 in b:
for cube2 in b:
c1 = cube1 + b.origin
c2 = cube2 + b.origin
if np.sum((c1 - c2)**2) == 1:
ax.plot3D((c1[0], c2[0]), (c1[1], c2[1]), (c1[2], c2[2]), color=f'C{c}', lw=10)
plt.show()
B1 = [[0, 0, 0],
[1, 0, 0],
[2, 0, 0],
[2, 1, 0]]
B2 = [[0, 0, 0],
[1, 0, 0],
[2, 0, 0],
[1, 1, 0]]
B3 = [[0, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 1, 1]]
B4 = [[0, 0, 0],
[1, 0, 0],
[2, 0, 0],
[1, 1, 0],
[1, 1, 1]]
B5 = [[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[1, 0, 1],
[2, 0, 1]]
B6 = [[0, 0, 0],
[1, 0, 0],
[2, 0, 0],
[1, 1, 0],
[2, 0, 1]]
block_list = [B1, B2, B3, B4, B5, B6]
def main():
game = GameState(block_list)
game_solved = solve(game)
if game_solved.is_solved:
print('yay!')
print(len(game_solved.placed_blocks))
for b in game_solved.placed_blocks:
print(b.name)
print(b.coords + b.origin[:,None])
plot_solution(game_solved)
else:
print('Found no solution :\'(')
if __name__ == "__main__":
main()