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DXPowerDXPower
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Added a Pentominos Solver.
Works by brute force DFS.
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Diff for: ‎puzzles/Pentominos Solver/Python/pentominos.py

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import os
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from colorama import init, deinit, Fore, Back, Style
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clear = lambda: os.system('cls')
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clear()
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init()
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colors = [Fore.BLACK, Fore.WHITE, Fore.WHITE + Style.BRIGHT, Fore.RED + Style.DIM, Style.BRIGHT + Fore.GREEN, Fore.YELLOW, Fore.BLUE, Fore.MAGENTA, Fore.CYAN, Fore.RED + Style.BRIGHT, Fore.BLUE + Style.BRIGHT, Fore.MAGENTA + Style.BRIGHT, Fore.YELLOW + Style.BRIGHT]
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# Shapes
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shapes = [
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{ "variations":
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("OOOO\n" # L
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"O..."),
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"used": False },
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{ "variations":
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("..OO\n" # N
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"OOO."),
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"used": False },
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{ "variations":
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("OOO\n" # P
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".OO"),
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"used": False },
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{ "variations":
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("OOO\n" # T
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".O.\n"
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".O."),
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"used": False },
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{ "variations":
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("O.O\n" # U
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"OOO"),
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"used": False },
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{ "variations":
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("O..\n" # V
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"O..\n"
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"OOO"),
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"used": False },
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{ "variations":
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("..O\n" # W
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".OO\n"
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"OO."),
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"used": False },
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{ "variations":
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(".O.\n" # X
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"OOO\n"
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".O."),
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"used": False },
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{ "variations":
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("OOOO\n" # Y
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".O.."),
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"used": False },
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{ "variations":
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("OO.\n" # Z
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".O.\n"
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".OO"),
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"used": False },
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{ "variations":
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("OOOOO"),
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"used": False
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}, # I
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{ "variations":
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(".OO\n" # F
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"OO.\n"
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".O."),
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"used": False }
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]
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# Interpret shape strings above
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for i in range(0, len(shapes)):
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variations = []
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shape = shapes[i]["variations"].split("\n")
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# Turn the list of strings of the shape into list of lists of 0's and 1's representing shape
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for j in range(0, len(shape)):
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shape[j] = list(shape[j])
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shape[j] = [0 if c == "." else 1 for c in shape[j]]
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mirror = [list(reversed(row)) for row in shape]
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for _ in range(0, 4):
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shape = [list(elem) for elem in zip(*shape[::-1])] # Rotate clockwise
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mirror = [list(elem) for elem in zip(*mirror[::-1])]
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if not shape in variations:
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variations.append(shape)
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if not mirror in variations:
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variations.append(mirror)
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shapes[i]["variations"] = variations
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input_string = input("Enter width and height in format 'w h'. Only multiples of 5 work.: \n").split(" ")
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width = int(input_string[0])
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height = int(input_string[1])
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pieces_needed = (width * height) / 5
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board = [[0 for i in range(0, width)] for j in range(0, height)]
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num_steps = 0
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def print_board():
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global num_steps
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for r in board:
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s = ""
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for c in r:
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s += colors[c] + "██" + Style.RESET_ALL
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print(s + Style.RESET_ALL + "|")
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print("----------------------------")
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print(num_steps)
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def try_place_shape(shape, x, y, id, adj):
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if y + len(shape) > height or x + len(shape[0]) > width:
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return False
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foundAdj = False
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for j, r in enumerate(shape):
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by = y + j
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for i, c in enumerate(r):
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bx = x + i
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if c == 1:
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if board[by][bx] > 0:
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return False
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elif adj and not foundAdj: # Some shapes may not touch another when placed in their spot. It's useless to place those
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if bx > 0 and board[by][bx - 1] > 0:
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foundAdj = True
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elif bx + 1 < width and board[by][bx + 1] > 0:
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foundAdj = True
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elif by > 0 and board[by - 1][bx] > 0:
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foundAdj = True
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elif by + 1 < height and board[by + 1][bx] > 0:
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foundAdj = True
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else:
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foundAdj = False
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if adj and not foundAdj:
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return False
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for j, r in enumerate(shape):
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by = y + j
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for i, c in enumerate(r):
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bx = x + i
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if c == 1:
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board[by][bx] = id
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# Check for impossible areas. Done in one scan by combining areas it sees above with area's it's created by traveling from left to right
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areas = {}
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combines = {}
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ai = -1
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for j, r in enumerate(board):
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for i, c in enumerate(r):
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if c == 0:
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left = 1
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up = 1
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if i > 0:
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left = board[j][i - 1]
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if j > 0:
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up = board[j - 1][i]
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elif i == 0 and j == 0:
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areas[ai] = 1
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board[j][i] = ai
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ai -= 1
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continue
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if left < 0 and up < 0:
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if left == up:
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areas[left] += 1
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else:
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areas[left] += 1
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combines[left] = up
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board[j][i] = left
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elif left < 0:
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areas[left] += 1
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board[j][i] = left
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elif up < 0:
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areas[up] += 1
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board[j][i] = up
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else:
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ai -= 1
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areas[ai] = 1
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board[j][i] = ai
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# Reset our math
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for j, r in enumerate(board):
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for i, c in enumerate(r):
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if c < 0:
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board[j][i] = 0
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# Combine all areas
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for key, value in combines.items():
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v = value # Sometimes chains of areas may exist
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while v in combines:
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v = combines[v]
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areas[v] += areas[key]
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del areas[key]
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# Check if any areas are "cutoff". This is a slight optimization that sometimes prevents the contuation of a search that has an obvious "hole" that can only be filled by
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# an already used piece
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if len(areas) > 1:
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remove_shape(shape, x, y)
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return False
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# If the area left is not a multiple of 5, then it is unsolvable.
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for key, value in areas.items():
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if value < 5 or value % 5 != 0:
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remove_shape(shape, x, y)
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return False
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return True
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def remove_shape(shape, x, y):
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for j, r in enumerate(shape):
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for i, c in enumerate(r):
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if c == 1:
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board[y + j][x + i] = 0
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solution_stack = []
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# It's safe to use a recursive search because the max depth we can go is 12.
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def recursive_search():
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global num_steps
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for i, shape in enumerate(shapes):
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if shape["used"]:
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continue
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for j, variation in enumerate(shape["variations"]):
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for x in range(0, width):
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for y in range(0, height):
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if try_place_shape(variation, x, y, i + 1, len(solution_stack) != 0):
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shape["used"] = True
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solution_stack.append({ "shape": variation, "x": x, "y": y})
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num_steps += 1
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print_board()
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clear()
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if len(solution_stack) == pieces_needed:
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return True
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elif recursive_search():
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return True
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else:
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shape["used"] = False
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solution_stack.pop()
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remove_shape(variation, x, y)
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recursive_search()
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print_board()
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input()
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deinit()

Diff for: ‎puzzles/Pentominos Solver/README.md

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# ABOUT PENTOMINOS
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Pentominos is a simple puzzle game where the goal is to fit several varying shapes of area 5 units into another shape. There are 12 unique "pentominos" that can be placed. The largest version of the game can fit 12 pentominos into a 6x10 box with a total of 2339 solutions.
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https://en.wikipedia.org/wiki/Pentomino

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