nqueens.cpp

#include <iostream>
#include <vector>

using namespace std;

class Solution {
public:
    bool isSafe(vector<vector<int>>& board, int row, int col, int n) {
        for (int i = 0; i < row; i++)
            if (board[i][col] == 1)
                return false;
        
        for (int i = row, j = col; i >= 0 && j >= 0; i--, j--)
            if (board[i][j] == 1)
                return false;
        
        for (int i = row, j = col; i >= 0 && j < n; i--, j++)
            if (board[i][j] == 1)
                return false;
        
        return true;
    }

    bool solveNQueensUtil(vector<vector<int>>& board, int row, int n) {
        if (row >= n)
            return true;
        
        for (int col = 0; col < n; col++) {
            if (isSafe(board, row, col, n)) {
                board[row][col] = 1;
                if (solveNQueensUtil(board, row + 1, n))
                    return true;
                board[row][col] = 0;
            }
        }
        return false;
    }

    void solveNQueens(int n) {
        vector<vector<int>> board(n, vector<int>(n, 0));
        if (solveNQueensUtil(board, 0, n)) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    cout << (board[i][j] == 1 ? "Q " : ". ");
                }
                cout << endl;
            }
        } else {
            cout << "No solution exists for " << n << " queens." << endl;
        }
    }
};

int main() {
    Solution solution;
    int n = 4;  // 4 queens
    solution.solveNQueens(n);
    return 0;
}