N-Queens DFS

思路：
典型的DFS。时间复杂度O(N!)，空间复杂度O(N)。

map[row] 表示第 i row行的皇后放置的位置。
每一层有n种放置方法，一共有n层。

//N-Queens : dfs
class Solution {
private:
vector<vector<string>> res;

void addSolution(vector<int> &map, int n) {
    vector<string> ans;
    for(int i = 0; i < n; ++i) {
        string row(n, '.');
        row[map[i]] = 'Q';
        ans.push_back(row);
    }
    res.push_back(ans);
}
bool canSet(vector<int> &map, int n, int row, int col) {
    //if(map[row] != 0) //row
    //    return false;
    int tmpcol = 0;
    for(int tmprow = 0; tmprow < row; ++tmprow) {
        tmpcol = map[tmprow];
        if(tmpcol == col) //col
            return false;
        if((tmpcol - col) == (tmprow - row)) //right slant line
            return false;
        if((tmpcol - col) == (row - tmprow)) //left slant line
            return false;
    }
    return true;
}
void nqueensSet(vector<int> &map, int n, int row) {
    for(int i = 0; i < n; ++i) {
        if(canSet(map, n, row, i)) {
            map[row] = i;
            if(row == n-1) {
                addSolution(map, n);
                map[row] = 0;
                return;
            }
            nqueensSet(map, n, row+1);
            map[row] = 0;
        }
    }
}
public:
    vector<vector<string>> solveNQueens(int n) {
        vector<int> map = vector<int>(n, 0);
        //judge and set
        nqueensSet(map, n, 0);
        return res;
    }
};