nqueen.cpp

// N - QUEENS | LEETCODE | RECURSION 

// TC : O(N! * N)
// SC : O(N ^ 2)

#include <bits/stdc++.h>

using namespace std;
class Solution {
  public:
    void solve(int col, vector < string > & board, vector <vector<string>> & ans, vector<int> & leftrow, vector<int> & upperDiagonal, vector<int> & lowerDiagonal, int n) {
      if (col == n) {
        ans.push_back(board);
        return;
      }
      for (int row = 0; row < n; row++) {
        if (leftrow[row] == 0 && lowerDiagonal[row + col] == 0 && upperDiagonal[n - 1 + col - row] == 0) {
          board[row][col] = 'Q';
          leftrow[row] = 1;
          lowerDiagonal[row + col] = 1;
          upperDiagonal[n - 1 + col - row] = 1;
          solve(col + 1, board, ans, leftrow, upperDiagonal, lowerDiagonal, n);
          board[row][col] = '.';
          leftrow[row] = 0;
          lowerDiagonal[row + col] = 0;
          upperDiagonal[n - 1 + col - row] = 0;
        }
      }
    }

  public:
    vector<vector<string>> solveNQueens(int n) {
      vector<vector<string >> ans;
      vector<string> board(n);
      string s(n, '.');
      for (int i = 0; i < n; i++) {
        board[i] = s;
      }
      vector<int> leftrow(n, 0), upperDiagonal(2 * n - 1, 0), lowerDiagonal(2 * n - 1, 0);
      solve(0, board, ans, leftrow, upperDiagonal, lowerDiagonal, n);
      return ans;
    }
};
int main() {
  int n = 4; // we are taking 4*4 grid and 4 queens
  Solution obj;
  vector < vector < string >> ans = obj.solveNQueens(n);
  for (int i = 0; i < ans.size(); i++) {
    cout << "Arrangement " << i + 1 << "\n";
    for (int j = 0; j < ans[0].size(); j++) {
      cout << ans[i][j];
      cout << endl;
    }
    cout << endl;
  }
  return 0;
}