[LintCode] N-Queens

N-Queens

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.

 

Example

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

[

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

"...Q",

"Q...",

"..Q."],

["..Q.", // Solution 2

"Q...",

"...Q",

".Q.."]

]

 class Solution {
 public:
     /**
      * Get all distinct N-Queen solutions
      * @param n: The number of queens
      * @return: All distinct solutions
      * For example, A string '...Q' shows a queen on forth position
      */
     bool isOK(vector<string> &v, int n, int x, int y) {
         for (int i = ; i < x; ++i)
             if (v[i][y] == 'Q') return false;
         for (int i = ; x - i >=  && y - i >= ; ++i)
             if (v[x-i][y-i] == 'Q') return false;
         for (int i = ; x - i >=  && y + i < n; ++i)
             if (v[x-i][y+i] == 'Q') return false;
         return true;
     }
     void dfs(vector<vector<string>> &res, vector<string> &v, int n, int idx) {
         if (idx == n) {
             res.push_back(v);
             return;
         }
         for (int i = ; i < n; ++i) {
             v[idx][i] = 'Q';
             if (isOK(v, n, idx, i)) dfs(res, v, n, idx + );
             v[idx][i] = '.';
         }
     }
     vector<vector<string> > solveNQueens(int n) {
         // write your code here
         vector<vector<string>> res;
         string s;
         for (int i = ; i < n; ++i) s.push_back('.');
         vector<string> v(n, s);
         dfs(res, v, n, );
         return res;
     }
 };