51. N-Queens

Problem:

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.

Solution (C++):

public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> res;
        vector<string> ans(n, string(n, '.'));
        solveNQueens(res, ans, 0, n);
        
        return res;
    }
private:
    void solveNQueens(vector<vector<string>> &res, vector<string> &ans, int row, int n) {
        if (row == n)  {
            res.push_back(ans);
            return;
        }
        
        for (int col = 0; col < n; ++col) {
            if (isValid(ans, row, col, n)) {
                ans[row][col] = 'Q';
                solveNQueens(res, ans, row+1, n);
                ans[row][col] = '.';
            }
        }
    }
    bool isValid(vector<string> ans, int row, int col, int n) {
        for (int i = 0; i < row; ++i) {             //判断列是否有'Q'
            if (ans[i][col] == 'Q')  return false;
        }
        for (int i = row-1, j = col-1; i >= 0 && j >= 0; --i, --j) {             //判断45°方向是否有'Q'
            if (ans[i][j] == 'Q')  return false;
        }
        for (int i = row-1, j = col+1; i >= 0 && j <= n-1; --i, ++j) {           //判断135°方向是否有'Q'
            if (ans[i][j] == 'Q')  return false;
        }
        return true;
    }