洞悉算法思维，破解经典 N 皇后难题

前端

2023-11-14 04:41:54

N 皇后难题：破解经典算法谜题的思维之旅

回溯法的利器：剖析破解 N 皇后难题的奥秘

踏入 N 皇后难题的殿堂，我们将开启一场探索算法思维和回溯法魅力的智力冒险。N 皇后难题是一个经久不衰的算法经典，它要求我们在一个 N×N 的棋盘上摆放 N 个皇后，使得任意两个皇后都不处在同一行、同一列或同一斜线上。

算法思维：问题的抽象与解决之道

算法思维是一种解决问题的强大工具，它通过将问题抽象成一系列步骤来寻求最优解。回溯法正是算法思维的典型代表，它通过系统地枚举所有可能的情况，逐一尝试并排除不满足条件的方案，最终找到满足约束条件的解。

Python 实现：将思维转化为代码

为了更深入地理解 N 皇后难题及其回溯法解法，让我们使用 Python 语言进行编码实践：

def solve_n_queens(n):
    """
    Solves the N Queens problem using backtracking.

    Args:
        n: The size of the chessboard.

    Returns:
        A list of all solutions to the N Queens problem.
    """

    # Initialize the chessboard.
    board = [[0 for _ in range(n)] for _ in range(n)]

    # Function to check if a queen can be placed at a given position.
    def is_safe(board, row, col):
        # Check if there is a queen in the same column above.
        for i in range(row):
            if board[i][col] == 1:
                return False

        # Check if there is a queen in the same diagonal above.
        for i, j in zip(range(row, -1, -1), range(col, -1, -1)):
            if board[i][j] == 1:
                return False

        # Check if there is a queen in the same diagonal above.
        for i, j in zip(range(row, -1, -1), range(col, n)):
            if board[i][j] == 1:
                return False

        # If no queen is found, it is safe to place a queen at the given position.
        return True

    # Function to solve the N Queens problem using backtracking.
    def solve(board, row):
        # If all rows have been filled with queens, we have found a solution.
        if row == n:
            return True

        # Try to place a queen in each column of the current row.
        for col in range(n):
            # If it is safe to place a queen at the current position, do so.
            if is_safe(board, row, col):
                board[row][col] = 1

                # Recursively solve the problem for the next row.
                if solve(board, row + 1):
                    return True

                # If no solution is found for the next row, remove the queen from the current position.
                board[row][col] = 0

        # If no solution is found for the current row, return False.
        return False

    # Solve the N Queens problem.
    if solve(board, 0):
        # Print the solution.
        print_solution(board)
        return True
    else:
        # No solution found.
        return False

# Function to print the solution.
def print_solution(board):
    """
    Prints the solution to the N Queens problem.

    Args:
        board: The chessboard with the queens placed.
    """

    for row in board:
        print(row)

# Solve the 8 Queens problem.
solve_n_queens(8)