Example: FindMissingNumberXOR in Java

// FindMissingNumberXOR
import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        int[] arr1 = {3, 1, 5, 2}; // Missing 4
        System.out.println("Array: " + Arrays.toString(arr1) + ", Missing number: " + findMissingNumberXOR(arr1));

        int[] arr2 = {1, 2, 3, 5, 6}; // Missing 4
        System.out.println("Array: " + Arrays.toString(arr2) + ", Missing number: " + findMissingNumberXOR(arr2));

        int[] arr3 = {2, 3, 4, 5}; // Missing 1
        System.out.println("Array: " + Arrays.toString(arr3) + ", Missing number: " + findMissingNumberXOR(arr3));
    }

    /**
     * Finds the missing number in an array using the XOR method.
     * Assumes numbers from 1 to n+1, with one number missing.
     *
     * @param arr The input array of distinct integers.
     * @return The missing integer.
     */
    public static int findMissingNumberXOR(int[] arr) {
        // Step 1: Initialize XOR result.
        int xorResult = 0;

        // Step 2: XOR all numbers from 1 to (n+1) (the expected range).
        // 'n' is arr.length, so the max number in the full sequence is n + 1.
        int nPlus1 = arr.length + 1;
        for (int i = 1; i <= nPlus1; i++) {
            xorResult ^= i;
        }

        // Step 3: XOR all numbers present in the array with the current xorResult.
        for (int num : arr) {
            xorResult ^= num;
        }

        // Step 4: The final xorResult is the missing number.
        // All present numbers and their counterparts from the full sequence cancel each other out (X ^ X = 0).
        // Only the missing number remains.
        return xorResult;
    }
}