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* Add the intial translation of code of all the languages * test * revert * Remove * Add Python and Java code for EN version
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 algorithm: n queens"""
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# When all rows are placed, record the solution
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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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# Traverse all columns
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for col in range(n):
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# Calculate the main and minor diagonals corresponding to the cell
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diag1 = row - col + n - 1
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diag2 = row + col
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# Pruning: do not allow queens on the column, main diagonal, or minor diagonal of the cell
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if not cols[col] and not diags1[diag1] and not diags2[diag2]:
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# Attempt: place the queen in the cell
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state[row][col] = "Q"
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cols[col] = diags1[diag1] = diags2[diag2] = True
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# Place the next row
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backtrack(row + 1, n, state, res, cols, diags1, diags2)
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# Retract: restore the cell to an empty spot
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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 n queens"""
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# Initialize an n*n size chessboard, where 'Q' represents the queen and '#' represents an empty spot
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state = [["#" for _ in range(n)] for _ in range(n)]
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cols = [False] * n # Record columns with queens
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diags1 = [False] * (2 * n - 1) # Record main diagonals with queens
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diags2 = [False] * (2 * n - 1) # Record minor diagonals with queens
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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"Input chessboard dimensions as {n}")
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print(f"The total number of queen placement solutions is {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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