51. N-Queens | LeetCode Solution

Raunit Verma June 06, 2022

51. N-Queens | LeetCode Solution

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

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

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 1:

Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above

Example 2:

Input: n = 1
Output: [["Q"]]

Constraints:

1 <= n <= 9

class Solution {
public:
    vector<vector<string>>res;
    
    bool check(int r,int c,vector<string>&v,int n){
        for(int i=0; i<r; i++){
            if(v[i][c]=='Q')return false;
        }
        int k=r;
        for(int i=r-1,j=c-1; i>=0 && j>=0 ; i--,j--){
            if(v[i][j]=='Q')return false;
        }
        for(int i=r-1,j=c+1; i>=0 && j<n ; i--,j++){
            if(v[i][j]=='Q')return false;
        }
        
        return true;
    }
    
    void helper(int n, int row,int col,vector<string>&v){
        if(row>=n){
            res.push_back(v);
            return;
        }
        
        for(int i=col; i<n; i++){
            if(check(row,i,v,n)){v[row][i]='Q';
            helper(n,row+1,0,v);
            v[row][i]='.';
            }
        }
    }
    
    
    vector<vector<string>> solveNQueens(int n) {
        vector<string>ans(n,string(n,'.'));
        // res.push_back(ans);
        helper(n,0,0,ans);
        return res;
    }
};