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from board import Board, generate_orientations
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from typing import Tuple, List
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import pieces
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import numpy as np
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import colorama
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def backtrack(board: Board, pieces_list: List[str], piece_index: int,
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orientations: dict, solutions: List[np.ndarray]) -> None:
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"""
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Backtracking to place each piece in the board in all possible ways.
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"""
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# if full, check if solution
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if piece_index == len(pieces_list):
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if board.is_full():
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solutions.append(board.grid.copy())
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return
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piece_name = pieces_list[piece_index]
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all_orientations = orientations[piece_name]
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for orientation in all_orientations:
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rows, cols = orientation.shape
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for row in range(board.rows - rows + 1):
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for col in range(board.cols - cols + 1):
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if board.placeable(orientation, (row, col)):
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board.place(orientation, (row, col), piece_index + 1)
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backtrack(board, pieces_list, piece_index + 1, orientations, solutions)
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board.remove(orientation, (row, col))
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def colorful_solution(solution: np.ndarray) -> str:
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"""
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Return a colorful representation of the solution.
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"""
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rows, cols = solution.shape
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result = ""
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piece_id_to_color = {
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-1: colorama.Back.BLACK,
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1: colorama.Back.GREEN,
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2: colorama.Back.BLUE,
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3: colorama.Back.YELLOW,
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4: colorama.Back.MAGENTA,
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5: colorama.Back.CYAN,
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6: colorama.Back.RED,
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}
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for r in range(rows):
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for c in range(cols):
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piece_id = solution[r, c]
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if piece_id == 0:
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result += colorama.Back.LIGHTWHITE_EX + " "
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else:
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result += piece_id_to_color[piece_id] + " "
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result += colorama.Back.RESET
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result += "\n"
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return result
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def solve(xPin: Tuple[int, int], yPin: Tuple[int, int], zPin: Tuple[int, int]):
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"""
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solve the puzzle, avoiding the pins at the specified positions.
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Args:
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xPin (Tuple[int, int]): row, col of the 'x' pin
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yPin (Tuple[int, int]): row, col of the 'y' pin
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zPin (Tuple[int, int]): row, col of the 'z' pin
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"""
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board = Board((5, 5))
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pinned_positions = [xPin, yPin, zPin]
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for (pr, pc) in pinned_positions:
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board.grid[pr, pc] = -1
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orientations_map = {}
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for piece_name, piece_matrix in pieces.all_pieces.items():
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orientations_map[piece_name] = generate_orientations(piece_matrix)
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piece_names = list(pieces.all_pieces.keys())
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solutions = []
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backtrack(board, piece_names, 0, orientations_map, solutions)
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if solutions:
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print(f"Found {len(solutions)} solution(s).")
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for idx, sol in enumerate(solutions, start=1):
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print(f"Solution #{idx}:")
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print(colorful_solution(sol))
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print("------------------")
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print(f"Total: {len(solutions)} solution{"s" if len(solutions) else ""}.")
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return
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print("No solution found.")
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if __name__ == "__main__":
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solve((0, 2), (2, 0), (3, 3))
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@ -99,11 +99,11 @@ def try_all_pegs():
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all_solutions = []
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# Solution entry {x: (row, col), y: (row, col), z: (row, col), solution_count: int}
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for xPinA in tqdm(range(5)):
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for xPinA in (range(5)):
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for yPinA in range(5):
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for xPinB in range(5):
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for yPinB in range(5):
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for xPinC in range(5):
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for xPinC in tqdm(range(5)):
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for yPinC in range(5):
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if (xPinA, yPinA) == (xPinB, yPinB) or (xPinA, yPinA) == (xPinC, yPinC) or (xPinB, yPinB) == (xPinC, yPinC):
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continue
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62
out.json
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62
out.json
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@ -0,0 +1,62 @@
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[
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{ "x": [0, 0], "y": [1, 4], "z": [2, 2], "solution_count": 12 },
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{ "x": [0, 0], "y": [1, 4], "z": [3, 2], "solution_count": 15 },
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{ "x": [0, 0], "y": [1, 4], "z": [4, 2], "solution_count": 12 },
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{ "x": [0, 0], "y": [2, 4], "z": [1, 2], "solution_count": 21 },
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{ "x": [0, 0], "y": [2, 4], "z": [3, 2], "solution_count": 20 },
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{ "x": [0, 0], "y": [2, 4], "z": [4, 2], "solution_count": 28 },
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{ "x": [0, 0], "y": [3, 4], "z": [1, 2], "solution_count": 24 },
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{ "x": [0, 0], "y": [3, 4], "z": [2, 2], "solution_count": 16 },
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{ "x": [0, 0], "y": [3, 4], "z": [4, 2], "solution_count": 26 },
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{ "x": [0, 0], "y": [4, 4], "z": [1, 2], "solution_count": 31 },
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{ "x": [0, 0], "y": [4, 4], "z": [2, 2], "solution_count": 52 },
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{ "x": [0, 0], "y": [4, 4], "z": [3, 2], "solution_count": 31 },
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{ "x": [1, 0], "y": [0, 4], "z": [2, 2], "solution_count": 12 },
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{ "x": [1, 0], "y": [0, 4], "z": [3, 2], "solution_count": 15 },
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{ "x": [1, 0], "y": [0, 4], "z": [4, 2], "solution_count": 12 },
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{ "x": [1, 0], "y": [2, 4], "z": [0, 2], "solution_count": 9 },
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{ "x": [1, 0], "y": [2, 4], "z": [3, 2], "solution_count": 14 },
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{ "x": [1, 0], "y": [2, 4], "z": [4, 2], "solution_count": 5 },
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{ "x": [1, 0], "y": [3, 4], "z": [0, 2], "solution_count": 7 },
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{ "x": [1, 0], "y": [3, 4], "z": [2, 2], "solution_count": 6 },
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{ "x": [1, 0], "y": [3, 4], "z": [4, 2], "solution_count": 7 },
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{ "x": [1, 0], "y": [4, 4], "z": [0, 2], "solution_count": 26 },
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{ "x": [1, 0], "y": [4, 4], "z": [2, 2], "solution_count": 16 },
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{ "x": [1, 0], "y": [4, 4], "z": [3, 2], "solution_count": 24 },
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{ "x": [2, 0], "y": [0, 4], "z": [1, 2], "solution_count": 21 },
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{ "x": [2, 0], "y": [0, 4], "z": [3, 2], "solution_count": 20 },
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{ "x": [2, 0], "y": [0, 4], "z": [4, 2], "solution_count": 28 },
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{ "x": [2, 0], "y": [1, 4], "z": [0, 2], "solution_count": 9 },
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{ "x": [2, 0], "y": [1, 4], "z": [3, 2], "solution_count": 14 },
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{ "x": [2, 0], "y": [1, 4], "z": [4, 2], "solution_count": 5 },
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{ "x": [2, 0], "y": [3, 4], "z": [0, 2], "solution_count": 5 },
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{ "x": [2, 0], "y": [3, 4], "z": [1, 2], "solution_count": 14 },
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{ "x": [2, 0], "y": [3, 4], "z": [4, 2], "solution_count": 9 },
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{ "x": [2, 0], "y": [4, 4], "z": [0, 2], "solution_count": 28 },
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{ "x": [2, 0], "y": [4, 4], "z": [1, 2], "solution_count": 20 },
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{ "x": [2, 0], "y": [4, 4], "z": [3, 2], "solution_count": 21 },
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{ "x": [3, 0], "y": [0, 4], "z": [1, 2], "solution_count": 24 },
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{ "x": [3, 0], "y": [0, 4], "z": [2, 2], "solution_count": 16 },
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{ "x": [3, 0], "y": [0, 4], "z": [4, 2], "solution_count": 26 },
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{ "x": [3, 0], "y": [1, 4], "z": [0, 2], "solution_count": 7 },
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{ "x": [3, 0], "y": [1, 4], "z": [2, 2], "solution_count": 6 },
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{ "x": [3, 0], "y": [1, 4], "z": [4, 2], "solution_count": 7 },
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{ "x": [3, 0], "y": [2, 4], "z": [0, 2], "solution_count": 5 },
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{ "x": [3, 0], "y": [2, 4], "z": [1, 2], "solution_count": 14 },
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{ "x": [3, 0], "y": [2, 4], "z": [4, 2], "solution_count": 9 },
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{ "x": [3, 0], "y": [4, 4], "z": [0, 2], "solution_count": 12 },
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{ "x": [3, 0], "y": [4, 4], "z": [1, 2], "solution_count": 15 },
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{ "x": [3, 0], "y": [4, 4], "z": [2, 2], "solution_count": 12 },
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{ "x": [4, 0], "y": [0, 4], "z": [1, 2], "solution_count": 31 },
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{ "x": [4, 0], "y": [0, 4], "z": [2, 2], "solution_count": 52 },
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{ "x": [4, 0], "y": [0, 4], "z": [3, 2], "solution_count": 31 },
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{ "x": [4, 0], "y": [1, 4], "z": [0, 2], "solution_count": 26 },
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{ "x": [4, 0], "y": [1, 4], "z": [2, 2], "solution_count": 16 },
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{ "x": [4, 0], "y": [1, 4], "z": [3, 2], "solution_count": 24 },
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{ "x": [4, 0], "y": [2, 4], "z": [0, 2], "solution_count": 28 },
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{ "x": [4, 0], "y": [2, 4], "z": [1, 2], "solution_count": 20 },
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{ "x": [4, 0], "y": [2, 4], "z": [3, 2], "solution_count": 21 },
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{ "x": [4, 0], "y": [3, 4], "z": [0, 2], "solution_count": 12 },
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{ "x": [4, 0], "y": [3, 4], "z": [1, 2], "solution_count": 15 },
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{ "x": [4, 0], "y": [3, 4], "z": [2, 2], "solution_count": 12 }
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]
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