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

[ [".Q..",  // Solution 1  "...Q",  "Q...",  "..Q."], ["..Q.",  // Solution 2  "Q...",  "...Q",  ".Q.."]]

vector<int> nums(n);num[i]表示第i行的queen放在num[i]列，这样就转化成求0-n-1的全排列，然后看每一个排列是否符合条件。

vector<vector<string>> res;void permutationHelper(vector<int> &nums, int index, int n){if(index == n){bool flag = true;for(int i = 0; i<n && flag; i++)for(int j=i+1; j<n; j++)if((j-i) == abs(nums[j]-nums[i])){flag = false;break;}if(flag){vector<string> tmp;for(int i =0; i<n;i++){string row(n,'.');row[nums[i]]='Q';tmp.push_back(row);}res.push_back(tmp);}}for(int i = index; i < n; i++){swap(nums[index], nums[i]);permutationHelper(nums, index+1, n);swap(nums[index], nums[i]);}}void permutation(int n){vector<int> nums(n);for(int i = 0; i < n; i++)nums[i] = i;permutationHelper(nums,0,n);}vector<vector<string> > solveNQueens(int n) {        // Note: The Solution object is instantiated only once.        res.clear();permutation(n);return res;    }