// Code-A5 (N-Queen)

#include <iostream>
#include <vector>
using namespace std;

// Function to print the board
void printBoard(vector<vector<int>>& board, int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++)
            cout << board[i][j] << " ";
        cout << endl;
    }
    cout << endl;
}

// Function to check if placing a queen is safe
bool isSafe(vector<vector<int>>& board, int row, int col, int n) {
    // Check column
    for (int i = 0; i < row; i++)
        if (board[i][col]) return false;

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

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

    return true;
}

// Backtracking function
bool solveNQueens(vector<vector<int>>& board, int row, int n) {
    if (row == n) {
        printBoard(board, n); // Print one valid arrangement
        return true;
    }

    for (int col = 0; col < n; col++) {
        if (isSafe(board, row, col, n)) {
            board[row][col] = 1; // Place queen
            solveNQueens(board, row + 1, n);
            board[row][col] = 0; // Backtrack
        }
    }
    return false;
}

int main() {
    int n, firstRow, firstCol;
    cout << "Enter size of board (N): ";
    cin >> n;

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

    cout << "Enter position of first queen (row and column index starting from 0): ";
    cin >> firstRow >> firstCol;

    // Place first queen
    board[firstRow][firstCol] = 1;

    cout << "\nAll possible solutions:\n";
    solveNQueens(board, 0, n); // Start solving from row 0

    return 0;
}

// SAMPLE OUTPUT
/*
* $ ./a.out 
* Enter size of board (N): 4
* Enter position of first queen (row and column index starting from 0): 0 0
* 
* All possible solutions:
* 0 1 0 0 
* 0 0 0 1 
* 1 0 0 0 
* 0 0 1 0 
* 
* 0 0 1 0 
* 1 0 0 0 
* 0 0 0 1 
* 0 1 0 0 
*/
