Solution of N-Queen problem in C++ using Backtracking

In this tutorial, we will learn about how to solve the N-QUEEN problem in C++ by using backtracking. Here we will also look at some examples to understand the problem.

N-Queen in C++ (Backtracking)

In N-queen problem, we have N queens and N x N chess board. The objective of this problem is such that we need to place all  N queens on N x N chess board in such a manner that no two queens in under attack to each other.

Two queens will be under attack if one of the following conditions is true:-

  • firstly, if they are in the same row.
  • secondly, if they are in the same column.
  • finally, if they are in the same diagonal.

Let’s see example,

Consider we have 4 queens, so we need to place all these 4 queens on 4×4 chess board. further Possible arrangements will be,



[0,0,1,0]                [0,1,0,0]

[1,0,0,0]                [0,0,0,1]

[0,0,0,1]                [1,0,0,0]

[0,1,0,0]                [0,0,1,0]

(i)                           (ii) – N

So, arrangements are shown in the N x N binary matrix, where 1 represent the queen positions.

therefore, for N=4, only two solutions are possible.

 

Code implementation in C++ N queens problem

 

//program to solve the n queen problem 
//grid[][] is represent the 2-d array with value(0 and 1) for grid[i][j]=1 means queen i are placed at j column.
//we can take any number of queen , for this time we take the atmost 10 queen (grid[10][10]).
#include<iostream>
using namespace std;
int grid[10][10];

//print the solution
void print(int n) {
    for (int i = 0;i <= n-1; i++) {
        for (int j = 0;j <= n-1; j++) {
            
                cout <<grid[i][j]<< " ";
            
        }
        cout<<endl;
    }
    cout<<endl;
    cout<<endl;
}

//function for check the position is safe or not
//row is indicates the queen no. and col represents the possible positions
bool isSafe(int col, int row, int n) {
  //check for same column
    for (int i = 0; i < row; i++) {
        if (grid[i][col]) {
            return false;
        }
    }
    //check for upper left diagonal
    for (int i = row,j = col;i >= 0 && j >= 0; i--,j--) {
        if (grid[i][j]) {
            return false;
        }
    }
    //check for upper right diagonal
    for (int i = row, j = col; i >= 0 && j < n; j++, i--) {
        if (grid[i][j]) {
            return false;
        }
    }
    return true;
}

//function to find the position for each queen
//row is indicates the queen no. and col represents the possible positions
bool solve (int n, int row) {
    if (n == row) {
        print(n);
        return true;
    }
    //variable res is use for possible backtracking 
    bool res = false;
    for (int i = 0;i <=n-1;i++) {
        if (isSafe(i, row, n)) {
            grid[row][i] = 1;
            //recursive call solve(n, row+1) for next queen (row+1)
            res = solve(n, row+1) || res;//if res ==false then backtracking will occur 
            //by assigning the grid[row][i] = 0
            
            grid[row][i] = 0;
        }
    }
    return res;
}

int main()
{
  ios_base::sync_with_stdio(false);
    cin.tie(NULL);
        int n;
        cout<<"Enter the number of queen"<<endl;
        cin >> n;
        for (int i = 0;i < n;i++) {
            for (int j = 0;j < n;j++) {
                grid[i][j] = 0;
            }
        }
        bool res = solve(n, 0);
        if(res == false) {
            cout << -1 << endl; //if there is no possible solution
        } else {
            cout << endl;
        }
  return 0;
}

 

Output

Enter the number of queen
4
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

 

for more information,

https://en.wikipedia.org/wiki/Eight_queens_puzzle

 

You may also learn about,

Solution of Tower Of Hanoi Problem in C++

Dijkstra’s shortest path algorithm in C++

Bubble Sort in C++

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