n_queen_problem.cpp

#include <iostream>
#include <vector>

using namespace std;

bool isSafe(vector<vector<int>>& board, int row, int col, int n) {
    // Check if there is a queen in the same column
    for (int i = 0; i < row; ++i) {
        if (board[i][col] == 1) {
            return false;
        }
    }

    // Check upper-left diagonal
    for (int i = row, j = col; i >= 0 && j >= 0; --i, --j) {
        if (board[i][j] == 1) {
            return false;
        }
    }

    // Check upper-right diagonal
    for (int i = row, j = col; i >= 0 && j < n; --i, ++j) {
        if (board[i][j] == 1) {
            return false;
        }
    }

    return true;
}

bool solveNQueens(vector<vector<int>>& board, int row, int n) {
    if (row == n) {
        // All queens have been placed successfully
        return true;
    }

    for (int col = 0; col < n; ++col) {
        if (isSafe(board, row, col, n)) {
            board[row][col] = 1;  // Place the queen

            if (solveNQueens(board, row + 1, n)) {
                return true;
            }

            board[row][col] = 0;  // Backtrack if no solution found
        }
    }

    return false;  // No safe placement in this row
}

void printBoard(vector<vector<int>>& board, int n) {
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            if (board[i][j] == 1) {
                cout << "Q ";
            } else {
                cout << ". ";
            }
        }
        cout << endl;
    }
}

int main() {
    int n;
    cout << "Enter the value of N for N-Queens: ";
    cin >> n;

    vector<vector<int>> board(n, vector<int>(n, 0));

    if (solveNQueens(board, 0, n)) {
        cout << "Solution exists. Here is the board:\n";
        printBoard(board, n);
    } else {
        cout << "No solution exists for N = " << n << endl;
    }

    return 0;
}