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* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.4.10 → v0.5.0](https://github.com/astral-sh/ruff-pre-commit/compare/v0.4.10...v0.5.0) - [github.com/pre-commit/mirrors-mypy: v1.10.0 → v1.10.1](https://github.com/pre-commit/mirrors-mypy/compare/v1.10.0...v1.10.1) * Fix ruff issues * Fix ruff issues --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
102 lines
2.4 KiB
Python
102 lines
2.4 KiB
Python
# Knight Tour Intro: https://www.youtube.com/watch?v=ab_dY3dZFHM
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from __future__ import annotations
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def get_valid_pos(position: tuple[int, int], n: int) -> list[tuple[int, int]]:
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"""
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Find all the valid positions a knight can move to from the current position.
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>>> get_valid_pos((1, 3), 4)
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[(2, 1), (0, 1), (3, 2)]
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"""
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y, x = position
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positions = [
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(y + 1, x + 2),
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(y - 1, x + 2),
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(y + 1, x - 2),
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(y - 1, x - 2),
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(y + 2, x + 1),
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(y + 2, x - 1),
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(y - 2, x + 1),
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(y - 2, x - 1),
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]
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permissible_positions = []
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for inner_position in positions:
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y_test, x_test = inner_position
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if 0 <= y_test < n and 0 <= x_test < n:
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permissible_positions.append(inner_position)
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return permissible_positions
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def is_complete(board: list[list[int]]) -> bool:
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"""
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Check if the board (matrix) has been completely filled with non-zero values.
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>>> is_complete([[1]])
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True
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>>> is_complete([[1, 2], [3, 0]])
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False
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"""
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return not any(elem == 0 for row in board for elem in row)
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def open_knight_tour_helper(
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board: list[list[int]], pos: tuple[int, int], curr: int
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) -> bool:
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"""
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Helper function to solve knight tour problem.
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"""
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if is_complete(board):
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return True
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for position in get_valid_pos(pos, len(board)):
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y, x = position
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if board[y][x] == 0:
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board[y][x] = curr + 1
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if open_knight_tour_helper(board, position, curr + 1):
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return True
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board[y][x] = 0
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return False
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def open_knight_tour(n: int) -> list[list[int]]:
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"""
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Find the solution for the knight tour problem for a board of size n. Raises
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ValueError if the tour cannot be performed for the given size.
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>>> open_knight_tour(1)
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[[1]]
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>>> open_knight_tour(2)
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Traceback (most recent call last):
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...
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ValueError: Open Knight Tour cannot be performed on a board of size 2
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"""
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board = [[0 for i in range(n)] for j in range(n)]
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for i in range(n):
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for j in range(n):
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board[i][j] = 1
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if open_knight_tour_helper(board, (i, j), 1):
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return board
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board[i][j] = 0
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msg = f"Open Knight Tour cannot be performed on a board of size {n}"
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raise ValueError(msg)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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