Union and Intersection of Two Unsorted Arrays - Complete Tutorial
Last Updated :
23 Jul, 2025
Union of two arrays is an array having all distinct elements that are present in either array whereas Intersection of two arrays is an array containing distinct common elements between the two arrays. In this post, we will discuss about Union and Intersection of unsorted arrays.
To know about union and intersection of sorted input arrays, please refer to Union and Intersection of Two Sorted Arrays – Complete Tutorial.
Union of Two Arrays
Union of two unsorted arrays combines all unique elements from both arrays into a single array. The resultant array can be in any order. There are several methods to find the Union of two unsorted arrays based on whether the input arrays contain duplicate elements or not:
- Union with Duplicates: When the input arrays may contain duplicate elements.
- Union with Distinct Elements: When the input arrays consist of distinct elements only.
1. Union with Duplicates
We are given two arrays a[] and b[] and the task is to find the union of both the arrays. Union of two arrays is an array having all distinct elements that are present in either array. The input arrays may contain duplicates.
Examples:
Input : a[] = {1, 2, 3, 2, 1}, b[] = {3, 2, 2, 3, 3, 2}
Output : {3, 2, 1}
Explanation: Each element in the output either belongs to array a or array b, and we need to print only one occurrence of such elements.
Input : a[] = {1, 2, 3}, b[] = {4, 5, 6}
Output : {1, 2, 3, 4, 5, 6}
Explanation: Each element in the output either belongs to array a or array b, and we need to print only one occurrence of such elements.
The naive approach is to traverse both the arrays a[] and b[] and for each element, check if the element is present in the result or not. If not, then add this element to the result.
We can optimize this further in the expected approach by using a hash set and adding all the elements from both arrays. The hash set ensures that no duplicates are stored. After adding all the elements, we can create the final union array by iterating through the hash set.
To know more about the implementation, please refer to Union of Two Arrays.
2. Union with Distinct Elements
We are given two arrays a[] and b[] with distinct elements and the task is to find the union of both the arrays. Union of two arrays is an array having all distinct elements that are present in either array.
Examples:
Input: a[] = {1, 2, 3}, b[] = {5, 2, 7}
Output: {1, 2, 3, 5, 7}
Explanation: 1, 2, 3, 5 and 7 are the distinct elements present in either array.
Input: a[] = {2, 4, 5}, b[] = {1, 2, 3, 4, 5}
Output: {1, 2, 3, 4, 5}
Explanation: 1, 2, 3, 4 and 5 are the distinct elements present in either array.
The naive approach is to add all elements from the first array a[] to a result array. Then iterate through the second array b[] and add its elements to the result only if they were not present in a[].
The expected approach is to use a hash set and add all the elements from both arrays. The hash set ensures that no duplicates are stored. After adding all the elements, we can create the final union array by iterating through the hash set.
To know more about the implementation, please refer to Union of Two Arrays with Distinct Elements.
Intersection of Two Arrays
Intersection of two arrays combines all unique elements that are common to both arrays into a single array. The resultant array can be in any order. There are several methods to find the Intersection of two arrays based on whether the input arrays contain duplicate elements or not:
- Intersection with Duplicates: When the input arrays may contain duplicate elements.
- Intersection with Distinct Elements: When the input arrays consist of distinct elements only.
1. Intersection with Duplicates
We are given two arrays a[] and b[], the task is to return intersection of both the arrays in any order. Intersection of two arrays is an array having all common elements in both the arrays. The input arrays may contain duplicates.
Examples:
Input: a[] = {1, 2, 1, 3, 1}, b[] = {3, 1, 3, 4, 1}
Output: {1, 3}
Explanation: 1 and 3 are the only common elements and we need to print only one occurrence of common elements.
Input: a[] = {1, 2, 3}, b[] = {4, 5, 6}
Output: {}
Explanation: No common element in both the arrays.
The naive solution is to create an empty result array. For each element in a[], check if it exists in b[] and is not already in the result. If both conditions are met, add the element to the result.
We can optimize this further in the expected approach by using a hash set and inserting all elements of a[] into it. Then, traverse b[] and check if an element is in the hash set, add it to the result and remove it from the hash set to avoid duplicates.
To know more about the implementation, please refer to Intersection of two Arrays.
2. Intersection with Distinct Elements
Given two arrays a[] and b[] with distinct elements, the task is to find intersection (or common elements) of both the arrays. We can return the answer in any order.
Examples:
Input: a[] = { 5, 6, 2, 1, 4 }, b[] = { 7, 9, 4, 2 }
Output: { 2, 4 }
Explanation: The only common elements in both arrays are 2 and 4.
Input: a[] = { 4, 5, 2, 3 } , b[] = { 1, 7 }
Output: { }
Explanation: There are no common elements in array a[] and b[]
The naive approach is to traverse the first array a[] and for each element in a[], check whether it is present in array b[]. If present then add this element to result array.
We can optimize the approach further in the expected approach by using a hash set to store the elements of array a[]. Then, go through array b[] and check if each element is present in the hash set. If an element is found in the hash set, add it to the result array since it is common in both the arrays.
To know more about the implementation, please refer to Intersection of Two Arrays with Distinct Elements.
Conclusion
Finding the union and intersection of two arrays can be efficiently achieved using hash set as we are able to handle the duplicates and even check whether an element is present in hash set or not in constant time.
For the union of arrays, whether the input arrays contain duplicates or consist of distinct elements, maintaining a hash set allows us to efficiently combine all elements from both arrays without storing any duplicates. Similarly, for the intersection of arrays, we insert all elements of the first array into a hash set and then check the elements of second array, adding them to the result only if they exist in the hash set.
Sample Problem : Intersection of two unsorted Arrays
Visit Course
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem