Question

In Java:

The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other. No two queens may be on the same row, column, nor diagonal.

The following image shows one possible solution for the 8-queens problem.

https://imgur.com/spcGSfj

The following are minimum requirements:

• Get n from user (e.g. 4, 8, etc.). Input must be greater than 3 (there is no solution for n < 4).
• Use arrays.
• Use loops or recursion.
• Print the solution. The following is the same solution to the 8-queens problem shown above, but in text

#################
# # # #X# # # # #
# # # # # # #X# #
# # #X# # # # # #
# # # # # # # #X#
# #X# # # # # # #
# # # # #X# # # #
#X# # # # # # # #
# # # # # #X# # #
#################

Answer 1

import java.util.Scanner;
public class Queens {

public static boolean safe(int[] mat, int n) {
for (int i = 0; i < n; i++) {
if (mat[i] == mat[n])
return false;
if ((mat[i] - mat[n]) == (n - i))
return false;   
if ((mat[n] - mat[i]) == (n - i))
return false;
}
return true;
}

//this function prints the queens
public static void print(int[] mat) {
int n = mat.length;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (mat[i] == j)
System.out.print("X ");
  
else
System.out.print("# ");
}
System.out.println();
}
System.out.println();
}

//this function does the backtracking and all the possible permutations are tried
public static void solution(int n) {
int[] arr = new int[n];
solution(arr, 0);
}

public static void solution(int[] mat, int k) {
int n = mat.length;
if (k == n)
print(mat);
else {
for (int i = 0; i < n; i++) {
mat[k] = i;
if (safe(mat, k))
solution(mat, k+1);
}
}
}

public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.print("Enter value of N(must be greater than 3): ");

int n = sc.nextInt();
solution(n);
}
}