51. N-Queens

https://leetcode.com/problems/n-queens/description/

N * N格子要求每行每列放置一个元素，同行同列以及斜着不能有其它元素，问所有的放置方法。找所有可能，DFS。对当前row, 选择好每个可能的col后，DFS下一行。 配合三个visited set排除已经flag过不能再走的，分别是已经有过的列，45°斜和135°斜。

/*
 * @lc app=leetcode id=51 lang=cpp
 *
 * [51] N-Queens
 */
class Solution {
public:
    void dfs(const int n, int r, vector<bool> &cols, vector<bool> &diags1, vector<bool> &diags2, vector<string> &path, vector<vector<string>> &res) {
        if (r == n) {
            res.push_back(path);
            return;
        }
        for (int c = 0; c < n; ++c) {
            const int diag1 = r + c, diag2 = c - r + n - 1;
            if (cols[c] || diags1[diag1] || diags2[diag2]) continue;
            cols[c] = true;
            diags1[diag1] = true;
            diags2[diag2] = true;
            const string q = string(c, '.') + "Q" + string(n - 1 - c, '.');
            path.push_back(q);
            dfs(n, r + 1, cols, diags1, diags2, path, res);
            cols[c] = false;
            diags1[diag1] = false;
            diags2[diag2] = false;
            path.pop_back();
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<bool> cols(n), diags1(2 * n - 1), diags2(diags1);
        vector<string> path;
        vector<vector<string>> res;
        dfs(n, 0, cols, diags1, diags2, path, res);
        return res;
    }
};