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.."]
]

 
class Solution {
public:
    bool isValid(vector<int> placement, int row)
    {
        for(int i = 0; i< row; i++)
           if (placement[i] == placement[row] || row - i == abs(placement[i] - placement[row]))
                return false;
        return true;
    }
   
    vector<string> getBoard(const vector<int> &placed)
    {
        vector<string> output;
        for(int i = 0; i < placed.size(); i++)
        { 
           string temp;
           for(int j = 0; j < placed.size(); j++)
              temp.push_back(j==placed[i]?'Q':'.');
             
            output.push_back(temp);
        }
       
        return output;
    }
   
    void helper(int n, int row, vector<int>& placement, vector<vector<string>> &ans){
        if (row == n) {
            ans.push_back(getBoard(placement));
            return;
        }
        for(int i = 0;i < n; i++) {
            placement[row] = i;
            if (isValid(placement, row))
                helper(n, row+1, placement, ans);
        }
    }
   
    vector<vector<string> > solveNQueens(int n) {
       vector<vector<string>> ans;
       vector<int> placement(n);
       helper(n, 0, placement, ans);
       return ans;
    }   
};

 vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> output;
        vector<int> placed(n, 0);
        
        int row = 0, col = 0;
        while(true) {
            if (col == n) {
                if(row == 0) return output;
                else {
                    row--;
                    col = placed[row]+1;
                    continue;
                }
            }
            
            if (canPlace(placed, row, col)) {
                placed[row] = col;
                if (row == n-1) {
                    output.push_back(getBoard(placed));
                    col++;
                }
                else {
                    row++;
                    col = 0;
                }
            }
            else
              col++;
        }
        
        return output;
    }