【LeetCode】051. N-Queens

题目：

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

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens‘ placement, where ‘Q‘ and ‘.‘ both indicate a queen and an empty space respectively.

For example,
There exist two distinct solutions to the 4-queens puzzle:

[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

题解：

class Solution {
public:
    void dfs(vector<vector<string>>& res, vector<string>& v, int n, vector<int>& pos, int row) {
         if(row >= n) {
             res.push_back(v);
             return;
         }
         for(int col=0; col<n; ++col) {
            if (!isValid(pos, row, col)) {
                continue;
            }
            v[row][col] = ‘Q‘;
            pos[row] = col;
            dfs(res, v, n, pos, row + 1);
            pos[row] = -1;
            v[row][col] = ‘.‘;
         }
    }
    bool isValid(vector<int>& pos, int row, int col) {
        for (int i = 0; i < row; ++i) {
            if (pos[i] == col || abs(row - i) == abs(col - pos[i])) {
                return false;
            }
        }
        return true;
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> res;
        vector<string> v(n, string(n, ‘.‘));
        vector<int> pos(n, -1);
        dfs(res, v, n, pos, 0);
        return res;
    }
};