leetCode 30天

题太难了，就来一个N皇后吧
51. N 皇后

class Solution {
private:
    vector<vector<string>> res;
    void backtracking(int n, int row, vector<string>& chessboard){
        if (row == n){
            res.push_back(chessboard);
            return;
        }
        for (int col = 0; col<n; col++){
            if (isValid(row, col, chessboard, n)){
                chessboard[row][col] = 'Q';
                backtracking(n, row+1,chessboard);
                chessboard[row][col] = '.';
            }
        }
    }
    bool isValid(int row, int col, vector<string>& chessboard, int n){
        // 检查列
        for (int i = 0; i<row; i++){
            if (chessboard[i][col] == 'Q'){
                return false;
            }
        }
        // 检查45度角
        for (int i = row-1,j = col-1; i>=0 && j>=0; i--,j--){
            if (chessboard[i][j] == 'Q'){
                return false;
            }
        }
        // 检查135度
        for (int i = row-1,j = col+1; i>=0 && j<n; i--,j++){
            if (chessboard[i][j] == 'Q'){
                return false;
            }
        }
        return true;
    }

public:
    vector<vector<string>> solveNQueens(int n) {
        res.clear();
        vector<string> chessboard(n, string(n,'.'));
        backtracking(n, 0, chessboard);
        return res;
    }
};