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* Euler problem 551 sol 1: Reduce McCabe code complexity As discussed in #2128 * fixup! Format Python code with psf/black push Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
99 lines
2.3 KiB
Python
99 lines
2.3 KiB
Python
# Knight Tour Intro: https://www.youtube.com/watch?v=ab_dY3dZFHM
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from typing import List, Tuple
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def get_valid_pos(position: Tuple[int], n: int) -> List[Tuple[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 position in positions:
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y_test, x_test = position
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if 0 <= y_test < n and 0 <= x_test < n:
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permissible_positions.append(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(board: List[List[int]], pos: Tuple[int], curr: int) -> 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 Kight 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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raise ValueError(f"Open Kight Tour cannot be performed on a board of size {n}")
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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