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

Merge Two Binary Search Trees - Algorithm, Visualization, Examples

Binary Search Trees

Contents

ProblemExamplesVisualizationSolutionAlgorithmCode

Problem Statement❯

Given two binary search trees (BSTs), the goal is to merge them into a single balanced binary search tree. The resulting tree should contain all elements from both BSTs and should maintain the BST property: for every node, values in the left subtree are smaller and values in the right subtree are greater.

You are not allowed to insert elements one by one into the new tree; instead, consider using optimized steps to build the tree.

Examples❯

Tree 1 Tree 2 Merged Output Description
[2, 1, 3]
[5, 4, 6]
[1, 2, 3, 4, 5, 6] In-order traversal of both BSTs: [1,2,3] and [4,5,6], merged and sorted to [1,2,3,4,5,6]
[10, 5, 15]
[20, 16, 25]
[5, 10, 15, 16, 20, 25] In-order of Tree 1: [5,10,15], Tree 2: [16,20,25]. Merged into sorted array.
[] [7, 3, 9]
[3, 7, 9] One tree is empty. Output is just the in-order traversal of Tree 2.
[8, 3, 10, 1, 6, null, 14]
[7, 4, 12]
[1, 3, 4, 6, 7, 8, 10, 12, 14] Combined in-order traversals from both BSTs merged into sorted order.

Visualization Player

Solution❯

Case 1: Normal Trees with Elements

When both binary search trees contain multiple elements, we can perform an in-order traversal on each tree. This traversal gives a sorted array of elements for each BST. Next, merge these two sorted arrays into one using the standard merging technique from merge sort.

The final step is to build a balanced BST from the merged sorted array. This is done by picking the middle element as the root and recursively building the left and right subtrees. This ensures that the tree remains balanced.

For example, Tree1 = [2, 1, 4] gives [1, 2, 4] and Tree2 = [3, 6] gives [3, 6]. Merging them: [1, 2, 3, 4, 6]. Then build a balanced BST using this array.

Case 2: One Tree is Empty

If one of the trees is empty, we can skip traversal and merging for that tree. Simply return the other tree as it is already a valid BST. There’s no need to perform any merging or reconstruction.

For example, Tree1 = [] and Tree2 = [1], the merged result is just [1], which itself is a BST.

Case 3: Both Trees are Empty

If both trees are empty, the result is also an empty tree. There are no elements to process or build into a BST.

This is the base case in recursive solutions and can be handled easily by returning null or an empty list.

Case 4: Trees with Disjoint or Overlapping Ranges

If the values in the trees are completely disjoint (e.g., all values in Tree1 are less than those in Tree2), the merged array remains sorted with no overlap. If there’s an overlap, the merge step ensures the final array maintains sorted order.

For example, Tree1 = [5, 3, 7, 2, 4, 6, 8] and Tree2 = [10, 9, 11] gives merged array [2, 3, 4, 5, 6, 7, 8, 9, 10, 11], and this is used to construct the final balanced BST.

Case 5: Skewed Trees

In cases where one or both trees are skewed (all nodes are either on the left or right), the traversal step will still generate sorted arrays. Hence, the merge and build steps work the same way.

The final BST after construction will be balanced, even if input trees were not.

Algorithm Steps❯

  1. Given two binary search trees, perform an in-order traversal on each tree to obtain two sorted arrays. Use inorder traversal on each tree.
  2. Merge the two sorted arrays into a single sorted array using a merge operation.
  3. Construct a balanced binary search tree from the merged sorted array using a recursive buildBST or sortedArrayToBST function.
  4. The resulting tree is the merged binary search tree.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def inorder(root, arr):
    if root:
        inorder(root.left, arr)
        arr.append(root.val)
        inorder(root.right, arr)


def mergeArrays(arr1, arr2):
    i = j = 0
    merged = []
    while i < len(arr1) and j < len(arr2):
        if arr1[i] < arr2[j]:
            merged.append(arr1[i])
            i += 1
        else:
            merged.append(arr2[j])
            j += 1
    merged.extend(arr1[i:])
    merged.extend(arr2[j:])
    return merged


def sortedArrayToBST(nums):
    if not nums:
        return None
    mid = len(nums) // 2
    root = TreeNode(nums[mid])
    root.left = sortedArrayToBST(nums[:mid])
    root.right = sortedArrayToBST(nums[mid+1:])
    return root


def mergeTwoBSTs(root1, root2):
    arr1, arr2 = [], []
    inorder(root1, arr1)
    inorder(root2, arr2)
    merged = mergeArrays(arr1, arr2)
    return sortedArrayToBST(merged)

# Example usage:
if __name__ == '__main__':
    # BST 1:   2
    #         / \
    #        1   3
    root1 = TreeNode(2, TreeNode(1), TreeNode(3))
    
    # BST 2:   7
    #         / \
    #        6   8
    root2 = TreeNode(7, TreeNode(6), TreeNode(8))
    
    mergedRoot = mergeTwoBSTs(root1, root2)
    result = []
    inorder(mergedRoot, result)
    print(result)

Comments

💬 Please keep your comment relevant and respectful. Avoid spamming, offensive language, or posting promotional/backlink content.
All comments are subject to moderation before being published.

Loading comments...