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

Tree Isomorphism Problem - Algorithm, Visualization, and Code Examples

Problem Statement

Given two binary trees, determine whether they are isomorphic. Two trees are isomorphic if one can be transformed into the other by swapping the left and right children of some nodes. This is not just about structure — the node values must also match. Your task is to check if the trees can become identical by any number of such flips.

Examples

Tree 1 (Level Order) Tree 2 (Level Order) Isomorphic? Description
[1, 2, 3, 4, 5, 6, 7]
[1, 3, 2, 7, 6, 5, 4]
true Trees are isomorphic by swapping left and right children at nodes 1 and 2.
[1, 2, 3]
[1, 2, 4]
false Tree 2 has a different node (4 instead of 3), making them not isomorphic.
[1]
[1]
true Both trees have only a single identical node, hence are trivially isomorphic.
[] [] true Both trees are empty; empty trees are considered isomorphic.
[1, 2, null, 3]
[1, null, 2, null, 3]
true Structures differ but by flipping child nodes they become structurally identical with same values.

Solution

Case 1: Both Trees Are Empty

If both trees are empty (i.e., both root nodes are null), then they are trivially isomorphic. This is the base case and the simplest scenario. There’s nothing to compare, so the answer is Yes.

Case 2: One Tree Is Empty, the Other Is Not

If only one of the trees is empty, they can't be isomorphic. A non-empty structure can't match an empty one — regardless of how you flip the children. Hence, the answer is No.

Case 3: Node Values Are Different

Even if the structure matches exactly, differing node values break the isomorphism. For instance, if the left child of one root is 2 and the left child of the other is 5, there's no flipping that can resolve the mismatch. Thus, the answer is No.

Case 4: Trees Are Identical

If both trees have the same structure and the same node values, then they are naturally isomorphic. No flipping is needed. The answer is Yes.

Case 5: Trees Become Identical After Swapping

In many cases, the trees may not look the same initially, but a swap of children at certain nodes makes them identical. For example, if tree1 has left = 2 and right = 3, and tree2 has left = 3 and right = 2, a flip at the root node makes them identical. Recursion is used to check both ‘no swap’ and ‘with swap’ conditions at every node.

Case 6: Trees Require Multiple Swaps

Sometimes, the trees need multiple swaps at different levels to become isomorphic. This involves checking all combinations recursively. As long as you can match all corresponding subtrees via a series of such swaps, the trees are considered isomorphic. The answer is Yes.

Case 7: Deep Structural Differences

If the trees differ significantly in depth or structure in a way that no sequence of child swaps can fix, then they are not isomorphic. Even if the values are the same, the arrangement of nodes matters. The answer is No.

Algorithm Steps

  1. If both trees are empty, they are isomorphic.
  2. If one tree is empty and the other is not, they are not isomorphic.
  3. If the values of the current nodes differ, return false.
  4. Recursively check two possibilities: (a) the left subtree of tree1 is isomorphic to the left subtree of tree2 and the right subtree of tree1 is isomorphic to the right subtree of tree2, OR (b) the left subtree of tree1 is isomorphic to the right subtree of tree2 and the right subtree of tree1 is isomorphic to the left subtree of tree2.
  5. If either condition holds, the trees are isomorphic.

Code

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


def isIsomorphic(root1, root2):
    if not root1 and not root2:
        return True
    if not root1 or not root2:
        return False
    if root1.val != root2.val:
        return False
    return (isIsomorphic(root1.left, root2.left) and isIsomorphic(root1.right, root2.right)) or \
           (isIsomorphic(root1.left, root2.right) and isIsomorphic(root1.right, root2.left))

# Example usage:
if __name__ == '__main__':
    # Construct two example trees
    # Tree 1:       1
    #             /   \
    #            2     3
    #           /       \
    #          4         5
    
    # Tree 2:       1
    #             /   \
    #            3     2
    #           /       \
    #          5         4
    
    tree1 = TreeNode(1, TreeNode(2, TreeNode(4)), TreeNode(3, None, TreeNode(5)))
    tree2 = TreeNode(1, TreeNode(3, TreeNode(5)), TreeNode(2, None, TreeNode(4)))
    print(isIsomorphic(tree1, tree2))