Binary TreesBinary Trees36
❯
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
❯
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Union of Two Arrays using Set - Optimal Approach

Arrays

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace

Problem Statement❯

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.

Examples❯

Array 1 Array 2 Union Result Description
[10, 20, 30] [30, 40, 50] [10, 20, 30, 40, 50] All unique elements from both arraysVisualization
[1, 1, 1] [1, 1, 1] [1] All elements are the same, so only one unique value in resultVisualization
[] [1, 2] [1, 2] One array is empty, return all elements of the non-empty arrayVisualization
[10, 20] [] [10, 20] One array is empty, return all elements of the non-empty arrayVisualization
[] [] [] Both arrays are empty, so result is also emptyVisualization
[5, 7, 9] [7, 5, 11] [5, 7, 9, 11] Duplicates across arrays removed in unionVisualization

Visualization Player

Solution❯

To find the union of two arrays means to combine all values that are present in either of the arrays, but without repeating any value. This is especially important when the arrays have duplicate values — we want each element to appear only once in the result.

The most efficient way to do this is by using a Set data structure. Sets automatically discard duplicate values, so you can insert all elements from both arrays into the set, and it will ensure that only unique values are kept.

What if both arrays are normal (non-empty)?

If both arr1 and arr2 contain values — whether overlapping or not — adding all elements to a set will result in a list of all distinct elements. For example, if arr1 = [1, 2, 3] and arr2 = [3, 4, 5], the union will be [1, 2, 3, 4, 5]. The duplicate 3 is included only once.

What if one array is empty?

If either arr1 or arr2 is empty, then the union is simply the unique values from the non-empty array. For example, if arr1 = [] and arr2 = [7, 8], the union will be [7, 8].

What if both arrays are empty?

If both arrays are empty, then there are no values to include in the union. So the result will also be an empty array: [].

What if arrays have only repeated values?

If both arrays contain only repeated values — even if they are the same — the union result will include just that one value. For instance, arr1 = [1, 1, 1] and arr2 = [1, 1] → union is [1].

Why is this method optimal?

Using a Set helps us achieve optimal performance because inserting into a set has an average time complexity of O(1) per element. So the overall time complexity becomes O(n + m), where n and m are the lengths of the two arrays.

This makes the solution both simple to implement and highly efficient, even for large input sizes.

Algorithm Steps❯

  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.

Code

Python
JavaScript
Java
C++
C
def union_of_arrays(arr1, arr2):
    result = set()
    for num in arr1:
        result.add(num)
    for num in arr2:
        result.add(num)
    return list(result)

# Sample Input
arr1 = [1, 2, 4, 5, 6]
arr2 = [2, 3, 5, 7]
print("Union:", union_of_arrays(arr1, arr2))

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n + m)Each element from both arrays is inserted into a set, which takes constant time per insertion on average. Best and worst case remain the same as all elements need to be processed.
Average CaseO(n + m)On average, inserting n elements from the first array and m elements from the second into a set results in linear time complexity.
Worst CaseO(n + m)Even in the worst case (e.g., hash collisions), we must iterate through all elements of both arrays once, so the time remains linear.

Space Complexity❯

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.