52. N-Queens II | LeetCode Solution

Raunit Verma June 06, 2022

52. N-Queens II | 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 the number of distinct solutions to the n-queens puzzle.

Example 1:

Input: n = 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown.

Example 2:

Input: n = 1
Output: 1

Constraints:

1 <= n <= 9

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