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import copy
import random
def area(tile):
return tile[0] * tile[1]
def factors(n):
return [i for i in range(1,n+1) if n%i == 0]
assert(factors(1) == [1])
assert(factors(6) == [1,2,3,6])
def possible_dimensions(tiles):
max_height = max(tile[0] for tile in tiles)
max_width = max(tile[1] for tile in tiles)
min_constraint = min(max_height, max_width)
max_constraint = max(max_height, max_width)
total_area = sum([area(tile) for tile in tiles])
return [(f, total_area/f) for f in factors(total_area) if f >= max_constraint and total_area/f >= min_constraint and f >= total_area/f]
assert(possible_dimensions([(32, 11)]) == [(32, 11)])
assert(possible_dimensions([(32, 11), (32, 10), (28, 14),
(28, 7), (28, 6), (21, 18),
(21, 18), (21, 14), (21, 14),
(17, 14), (14, 4), (10, 7) ]) == [(56, 56), (64, 49), (98, 32), (112, 28)])
def x_capacity(x,y,board):
for i, element in enumerate(board[y][x:]):
if element is not None: return i
return i+1
assert(x_capacity(0, 0, [[None,'x',None],[None,None,None],[None,None,None]]) == 1)
assert(x_capacity(0, 0, [[None,None,None],[None,None,None],[None,None,None]]) == 3)
assert(x_capacity(0, 0, [[None,None,None],['x',None,None],[None,None,None]]) == 3)
assert(x_capacity(0, 2, [[None,None,None],[None,None,None],[None,None,'x']]) == 2)
assert(x_capacity(2, 1, [['x','x','x'],
['x','x',None],
[None,'x',None]]) == 1)
def y_capacity(x,y,board):
return x_capacity(y,x,zip(*board))
assert(y_capacity(0, 0, [[None,None,None],[None,None,None],[None,None,None]]) == 3)
assert(y_capacity(0, 0, [[None,'x',None],[None,None,None],[None,None,None]]) == 3)
assert(y_capacity(0, 0, [[None,None,None],['x',None,None],[None,None,None]]) == 1)
assert(y_capacity(2, 0, [['x','x',None],['x','x',None],[None,None,None]]) == 3)
assert(y_capacity(1, 0, [[None,None,None],['x','x',None],[None,None,None]]) == 1)
assert(y_capacity(2, 1, [['x','x','x'],
['x','x',None],
[None,'x',None]]) == 2)
def bottomleft_space(board):
for j, row in enumerate(board):
for i, el in enumerate(row):
if el is None: return (i, j)
assert(bottomleft_space([[None,None,None],[None,None,None],[None,None,None]]) == (0, 0))
assert(bottomleft_space([['x','x',None],[None,None,None],[None,None,None]]) == (2, 0))
assert(bottomleft_space([['x','x','x'],['x',None,None],[None,None,None]]) == (1, 1))
assert(bottomleft_space([['x','x','x'],
['x','x',None],
[None,'x',None]]) == (2, 1))
def place(l, w, x, y, board):
"""return a new state
which is the result of placing the tile
at (x,y)"""
new_board = copy.deepcopy(board)
for i in range(l):
for j in range(w):
if i == 0 or i == l-1 or j == 0 or j == w-1:
new_board[y+i][x+j] = '.'
else:
new_board[y+i][x+j] = 'x'
return new_board
assert(place(1, 2, 1, 0, [[None,None,None],[None,None,None],[None,None,None]]) == [[None, '.', '.'],[None,None,None],[None,None,None]])
assert(place(1, 1, 0, 0, [[None,None,None],[None,None,None],[None,None,None]]) == [['.',None,None],[None,None,None],[None,None,None]])
assert(place(2, 2, 0, 0, [[None,None,None],[None,None,None],[None,None,None]]) == [['.','.',None],['.','.',None],[None,None,None]])
def print_board(board):
for row in board: print ' '.join([str(e or ' ') for e in row])
def solve_puzzle(tiles, board):
if random.randint(0, 1000) == 1000: print '.'
if not tiles:
# if there are no tiles to place, we're done!
return board
else:
# figure out where we ought to place the tile (bottom left space)
# and how much room we have to the right and above
x, y = bottomleft_space(board)
max_width = x_capacity(x, y, board)
max_length = y_capacity(x, y, board)
# for each remaining tile
for i, tile in enumerate(tiles):
remaining_tiles = tiles[:i] + tiles[i+1:]
# for both of its rotations
for width, length in [tile, reversed(tile)]:
if width <= max_width and length <= max_length:
# place the tile and try to solve the puzzle from the resulting state
new_board = place(length, width, x, y, board)
result = solve_puzzle(remaining_tiles, new_board)
if result:
return result
# if we can't solve the puzzle from this board configuration,
# no matter which tile we place, then there are no solutions this way
return None
def calibron(tiles):
for dimensions in possible_dimensions(tiles):
print "Trying to solve for", dimensions
starting_board = [[None for i in range(dimensions[0])] for j in range(dimensions[1])]
board = solve_puzzle(tiles, starting_board)
if board:
print "DONE!"
print_board(board)
break
else:
print "Unable to solve for", dimensions
calibron([
(32, 11),
(32, 10),
(28, 14),
(28, 7),
(28, 6),
(21, 18),
(21, 18),
(21, 14),
(21, 14),
(17, 14),
(14, 4),
(10, 7),
])
"""
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"""