N Queens

Challenge

The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other

Create a program for N Queens Problem

Solution (C++)

#include<iostream>

#include<math.h>

using namespace std;

int x[200];

static int c = 0;

bool place(int k, int i) {

int j;

for (j = 1; j < k; j++) {

if ((x[j] == i) || (abs(x[j]-i) == abs(j-k))) {

return false;

}

}

return true;

}

void print(int n) {

int i, j;

for (i = 1; i <= n; i++) {

for (j = 1; j <= n; j++) {

if (x[i] == j) {

cout << "Q ";

} else {

cout << "* ";

}

}

cout << endl;

}

c++;

}

void NQueens(int k, int n) {

int i;

for (i = 1; i <= n; i++) {

if (place(k, i)) {

x[k] = i;

if (k == n) {

print(n);

cout << endl;

exit(0);

} else {

NQueens(k + 1, n);

}

}

}

}

main() {

int i, n, j;

cout << "Enter total Number of Queens" << endl;

cin >> n;

cout << endl;

NQueens(1, n);

}

Output

Enter total Number of Queens

4

* Q * *

* * * Q

Q * * *

* * Q *

Enter total Number of Queens

8

Q * * * * * * *

* * * * Q * * *

* * * * * * * Q

* * * * * Q * *

* * Q * * * * *

* * * * * * Q *

* Q * * * * * *

* * * Q * * * *

Enter total Number of Queens

16

Q * * * * * * * * * * * * * * *

* * Q * * * * * * * * * * * * *

* * * * Q * * * * * * * * * * *

* Q * * * * * * * * * * * * * *

* * * * * * * * * * * * Q * * *

* * * * * * * * Q * * * * * * *

* * * * * * * * * * * * * Q * *

* * * * * * * * * * * Q * * * *

* * * * * * * * * * * * * * Q *

* * * * * Q * * * * * * * * * *

* * * * * * * * * * * * * * * Q

* * * * * * Q * * * * * * * * *

* * * Q * * * * * * * * * * * *

* * * * * * * * * * Q * * * * *

* * * * * * * Q * * * * * * * *

* * * * * * * * * Q * * * * * *