Determine if a function is bijective

Concise Problem Specification

Given an integer \$n\$ and a function \$f : X \to X \$ where \$X = \{1,2,3,..,n\}\$ Determine whether the given function is a bijective function or not.

Definition:

According to Wikipedia:


In mathematics, a bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

Constraints

\$1\le n \le 20 \$

Input format

There are lines in the input.
The first line contains a single positive integer \$n\$.

The second line contains space separated integers, the values of \$f(1)\$ , \$f(2)\$ ... , \$f(n)\$, respectively.

Output Format

On a single line, output "YES" if is bijective. Otherwise, output "NO".

Solution

import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Solution {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);

        int n = in.nextInt();

        Set codomain = new HashSet();

        for (int i = 0; i < n; i++) {
            int y = in.nextInt();
            codomain.add(y);
        }

        System.out.println(codomain.size() == n ? "YES" : "NO");

        in.close();

    }

}

Comments

I am still relatively new to Java and would appreciate any comments on the above regarding improvements to my code.

Your code looks nice. The only suggestion I have is to separate the bijection check out of the main, and make it, say, a static method. All in all, I had this in mind:

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

public class FunctionUtils {

    public static boolean isBijection(final Map function) {
        final Set domain = new HashSet<>(function.keySet());
        final Set range  = new HashSet<>(function.values());
        return range.equals(domain);
    }

    public static void main(String[] args) {
        final Map function = new HashMap<>();

        try (final Scanner in = new Scanner(System.in)) {
            final int n = in.nextInt();

            for (int i = 1; i <= n; i++) {
                function.put(i, in.nextInt());
            }

            System.out.println("Bijection: " + isBijection(function));
        }
    }
}

Hope that helps.

Edit

Validating general bijections \$f \colon X \to Y\$ is not any harder:

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;

public class FunctionUtils {

    public static  boolean isBijection(final Map function) {
        return function.size() == new HashSet<>(function.values()).size();
    }

    public static void main(String[] args) {
        final Map function = new HashMap<>();

        try (final Scanner in = new Scanner(System.in)) {
            final int n = in.nextInt();

            for (int i = 1; i <= n; i++) {
                function.put(i, in.nextInt());
            }

            System.out.println("Function:  " + function);
            System.out.println("Bijection: " + isBijection(function));
        }
    }
}

StackExchange Code Review Q#132544, answer score: 4