# 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).
#include<iostream>
using namespace std;
int grid;

//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```