N-Queens_backtracking.cpp

#include <bits/stdc++.h>
#define N 4
using namespace std;

void printSolution(int board[N][N])
{
    cout << "\n";
    for (int i = 0; i < N; i++)
    {
        for (int j = 0; j < N; j++)
            cout << "" << board[i][j];
        cout << "\n";
    }
}

bool isSafe(int board[N][N], int row, int col)
{
    int i, j;

    /* Check this row on left side */
    for (i = 0; i < col; i++)
        if (board[row][i])
            return false;

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

    /* Check lower diagonal on left side */
    for (i = row, j = col; j >= 0 && i < N; i++, j--)
        if (board[i][j])
            return false;

    return true;
}

void solveNQ(int board[N][N], int col)
{

    if (col >= N)
    {
        printSolution(board);
        return;
    }

    /* Consider this column and try placing
       this queen in all rows one by one */
    for (int i = 0; i < N; i++)
    {
        /* Check if queen can be placed on
          board[i][col] */
        if (isSafe(board, i, col))
        {
            /* Place this queen in board[i][col] */
            //            cout<<"\n"<<col<<"can place"<<i;
            board[i][col] = 1;

            /* recur to place rest of the queens */
            solveNQ(board, col + 1);

            board[i][col] = 0; // BACKTRACK
        }
    }
}

int main()
{

    int board[N][N] = {{0, 0, 0, 0},
                       {0, 0, 0, 0},
                       {0, 0, 0, 0},
                       {0, 0, 0, 0}};

    solveNQ(board, 0);
    return 0;
}