Union of Two Arrays using Set - Optimal Approach

You are given two arrays arr1 and arr2. Your task is to return their union — a collection of all distinct elements that appear in either of the arrays.

The union should not contain any duplicate elements. The result can be returned in any order.

If both arrays are empty, return an empty array.

Understanding the Problem: Union of Two Arrays

The goal is to compute the union of two arrays. That means we need to gather all the elements from both arrays, but include each element only once, even if it appears multiple times in either array.

For example, if the two arrays are:

arr1 = [1, 2, 3]
arr2 = [3, 4, 5]

The result should be [1, 2, 3, 4, 5] — note that 3 is not repeated.

Step-by-Step Approach

Step 1: Use a Set to Handle Uniqueness

A Set in most programming languages (like JavaScript, Python, Java) automatically keeps only unique values. This makes it perfect for solving union problems.

Step 2: Add All Elements from Both Arrays

Loop through each array, and add every element to the set. The set will automatically ignore duplicates.

Step 3: Convert the Set to a List (if needed)

Once all elements are added to the set, you can convert it back to an array or list to return the result.

Detailed Example for Beginners

Let’s consider:

arr1 = [1, 2, 3, 2]
arr2 = [2, 3, 4, 5]

1. Add from arr1:

• Add 1 → set is {1}
• Add 2 → set is {1, 2}
• Add 3 → set is {1, 2, 3}
• Add 2 again → set remains {1, 2, 3}

2. Add from arr2:

• Add 2 → already in set
• Add 3 → already in set
• Add 4 → set is {1, 2, 3, 4}
• Add 5 → set is {1, 2, 3, 4, 5}

Final result: [1, 2, 3, 4, 5]

Handling Edge Cases Intuitively

Case 1: One array is empty

arr1 = []
arr2 = [7, 8]

The result is just the unique values of the second array: [7, 8]

Case 2: Both arrays are empty

arr1 = []
arr2 = []

The result is an empty array: []

Case 3: Arrays contain only repeated values

arr1 = [1, 1, 1]
arr2 = [1, 1]

Set will store only one 1, so the result is: [1]

Case 4: Arrays with completely distinct values

arr1 = [10, 20]
arr2 = [30, 40]

No overlap — the result is just a merge of all elements: [10, 20, 30, 40]

Why is This Method Efficient?

Using a set allows for average O(1) time for insertions. So processing both arrays of lengths n and m takes O(n + m) time.

This method is fast, intuitive, and works well even with large arrays.

1. Given two arrays arr1 and arr2.
2. Create a set to store unique elements.
3. Insert all elements of arr1 into the set.
4. Insert all elements of arr2 into the set.
5. The set now contains the union of both arrays with no duplicates.
6. Convert the set to a list (or array) if needed and return it.

O(n + m)

Explanation: A set is used to store up to all unique elements from both arrays. In the worst case, none of the elements are duplicates, resulting in a total of n + m unique entries.