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* Retranslate the complete English edition from Simplified Chinese * Polish three English explanations after reader-focused review
63 lines
2.0 KiB
Python
63 lines
2.0 KiB
Python
"""
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File: n_queens.py
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Created Time: 2023-04-26
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Author: krahets (krahets@163.com)
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"""
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def backtrack(
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row: int,
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n: int,
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state: list[list[str]],
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res: list[list[list[str]]],
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cols: list[bool],
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diags1: list[bool],
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diags2: list[bool],
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):
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"""Backtracking: n-queens"""
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# Record a solution when a queen has been placed in every row
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if row == n:
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res.append([list(row) for row in state])
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return
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# Iterate over all columns
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for col in range(n):
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# Calculate the main-diagonal and anti-diagonal indices for this square
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diag1 = row - col + n - 1
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diag2 = row + col
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# Prune: the square must have no queen in its column, main diagonal, or anti-diagonal
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if not cols[col] and not diags1[diag1] and not diags2[diag2]:
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# Try: place a queen on this square
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state[row][col] = "Q"
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cols[col] = diags1[diag1] = diags2[diag2] = True
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# Place a queen in the next row
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backtrack(row + 1, n, state, res, cols, diags1, diags2)
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# Backtrack: restore this square to empty
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state[row][col] = "#"
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cols[col] = diags1[diag1] = diags2[diag2] = False
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def n_queens(n: int) -> list[list[list[str]]]:
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"""Solve the n-queens problem"""
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# Initialize an n*n board, where 'Q' represents a queen and '#' represents an empty square
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state = [["#" for _ in range(n)] for _ in range(n)]
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cols = [False] * n # Track whether a column contains a queen
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diags1 = [False] * (2 * n - 1) # Track whether a main diagonal contains a queen
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diags2 = [False] * (2 * n - 1) # Track whether an anti-diagonal contains a queen
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res = []
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backtrack(0, n, state, res, cols, diags1, diags2)
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return res
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"""Driver code"""
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if __name__ == "__main__":
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n = 4
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res = n_queens(n)
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print(f"The input board has width and height {n}")
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print(f"Number of ways to place the queens: {len(res)}")
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for state in res:
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print("--------------------")
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for row in state:
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print(row)
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