programming-examples/c++/Computational_Geometry/C++ Program to Solve N-Queen Problem.cpp

/*
 * C++ Program to Solve N-Queen Problem
 */
#include <iostream>
#include <cstdio>
#include <cstdlib>
#define N 8
using namespace std;

/* print solution */
void printSolution(int board[N][N])
{
    for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < N; j++)
                cout<<board[i][j]<<"  ";
            cout<<endl;
        }
}

/* check if a queen can be placed on board[row][col]*/
bool isSafe(int board[N][N], int row, int col)
{
    int i, j;
    for (i = 0; i < col; i++)
        {
            if (board[row][i])
                return false;
        }
    for (i = row, j = col; i >= 0 && j >= 0; i--, j--)
        {
            if (board[i][j])
                return false;
        }
    for (i = row, j = col; j >= 0 && i < N; i++, j--)
        {
            if (board[i][j])
                return false;
        }
    return true;
}

/*solve N Queen problem */
bool solveNQUtil(int board[N][N], int col)
{
    if (col >= N)
        return true;
    for (int i = 0; i < N; i++)
        {
            if ( isSafe(board, i, col) )
                {
                    board[i][col] = 1;
                    if (solveNQUtil(board, col + 1) == true)
                        return true;
                    board[i][col] = 0;
                }
        }
    return false;
}

/* solves the N Queen problem using Backtracking.*/
bool solveNQ()
{
    int board[N][N] = {0};
    if (solveNQUtil(board, 0) == false)
        {
            cout<<"Solution does not exist"<<endl;
            return false;
        }
    printSolution(board);
    return true;
}

// Main
int main()
{
    solveNQ();
    return 0;
}

/*
1  0  0  0  0  0  0  0
0  0  0  0  0  0  1  0
0  0  0  0  1  0  0  0
0  0  0  0  0  0  0  1
0  1  0  0  0  0  0  0
0  0  0  1  0  0  0  0
0  0  0  0  0  1  0  0
0  0  1  0  0  0  0  0