題目： LeetCode - 51. N-Queens

解題思路

列為單位，上而下 DFS 模擬。

參考解法

C++

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class Solution {
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> results;
        vector<string> queens(n, string(n, '.'));
        dfs(n, 0, queens, results);
        return results;
    }

    void dfs(int n, int currRow, vector<string>& queens, vector<vector<string>>& results) {
        if (currRow == n) {
            results.push_back(queens);
            return;
        }

        for (int i = 0; i < n; ++i) {
            if (isValid(n, queens, currRow, i)) {
                queens[currRow][i] = 'Q';
                dfs(n, currRow + 1, queens, results);
                queens[currRow][i] = '.';
            }
        }
    }

    // row, col: new queen's position
    bool isValid(int n, vector<string>& queens, int row, int col) {
        // check if queen on the same columns
        for (int i = 0; i < row; ++i) {
            if (queens[i][col] == 'Q') {
                return false;
            }
        }
        
        // check if queen on left-top
        for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; --i, --j) {
            if (queens[i][j] == 'Q') {
                return false;
            }
        }
        
        // check if queen on right-top
        for (int i = row - 1, j = col + 1; i >= 0 && j < n; --i, ++j) {
            if (queens[i][j] == 'Q') {
                return false;
            }
        }

        return true;
    }
};

Python

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class Solution:
    def solveNQueens(self, n: int) -> List[List[str]]:
        results = []
        queens = [['.'] * n for _ in range(n)]
        self.dfs(n, 0, queens, results)
        return results

    def dfs(self, n, currRow, queens, results):
        if currRow == n:
            results.append([''.join(i) for i in queens])
            return
        
        for i in range(n):
            if self.isValid(n, queens, currRow, i):
                queens[currRow][i] = 'Q'
                self.dfs(n, currRow + 1, queens, results)
                queens[currRow][i] = '.'

    def isValid(self, n, queens, row, col):
        """
        row, col: new queen's position
        """
        # check if queen on the same columns
        for i in range(row):
            if queens[i][col] == 'Q':
                return False
        
        # check if queen on left-top
        i, j = row - 1, col - 1
        while i >= 0 and j >= 0:
            if queens[i][j] == 'Q':
                return False
            i -= 1
            j -= 1
        
        # check if queen on right-top
        i, j = row - 1, col + 1
        while i >= 0 and j < n:
            if queens[i][j] == 'Q':
                return False
            i -= 1
            j += 1
        
        return True