mirror of
https://github.com/krahets/hello-algo.git
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Ikko Eltociear Ashimine
954c45864b
* docs: add Japanese documents (`ja/docs`) * docs: add Japanese documents (`ja/codes`) * docs: add Japanese documents * Remove pythontutor blocks in ja/ * Add an empty at the end of each markdown file. * Add the missing figures (use the English version temporarily). * Add index.md for Japanese version. * Add index.html for Japanese version. * Add missing index.assets * Fix backtracking_algorithm.md for Japanese version. * Add avatar_eltociear.jpg. Fix image links on the Japanese landing page. * Add the Japanese banner. --------- Co-authored-by: krahets <krahets@163.com>
62 lines
2.1 KiB
Python
62 lines
2.1 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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"""バックトラッキングアルゴリズム：n クイーン"""
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# すべての行が配置されたら、解を記録
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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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# すべての列を走査
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for col in range(n):
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# セルに対応する主対角線と副対角線を計算
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diag1 = row - col + n - 1
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diag2 = row + col
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# 枝刈り：セルの列、主対角線、副対角線にクイーンを配置しない
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if not cols[col] and not diags1[diag1] and not diags2[diag2]:
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# 試行：セルにクイーンを配置
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state[row][col] = "Q"
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cols[col] = diags1[diag1] = diags2[diag2] = True
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# 次の行を配置
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backtrack(row + 1, n, state, res, cols, diags1, diags2)
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# 撤回：セルを空のスポットに復元
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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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"""n クイーンを解く"""
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# n*n サイズのチェスボードを初期化、'Q' はクイーンを表し、'#' は空のスポットを表す
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state = [["#" for _ in range(n)] for _ in range(n)]
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cols = [False] * n # クイーンがある列を記録
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diags1 = [False] * (2 * n - 1) # クイーンがある主対角線を記録
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diags2 = [False] * (2 * n - 1) # クイーンがある副対角線を記録
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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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"""ドライバーコード"""
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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"チェスボードの寸法入力：{n}")
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print(f"クイーン配置解の総数は {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) |