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

Understanding the Problem

We are given two binary trees. The goal is to determine whether they are isomorphic. Two trees are said to be isomorphic if they have the same structure and node values, or if they can be made identical by swapping the left and right children of some nodes.

In simpler terms, two trees are isomorphic if we can transform one into the other by flipping some children at various levels, without changing any of the node values.

Step-by-Step Solution with Example

Step 1: Understand What We’re Comparing

Let’s say we have two trees:


Tree 1:           Tree 2:

     1                1
   /               /     2     3          3     2

At first glance, they look different because the children are flipped. But if we allow swapping, they become structurally identical with the same values at corresponding positions. So they are isomorphic.

Step 2: Base Case - Both Trees Are Empty

If both nodes are null, they are trivially isomorphic. Nothing to compare. Return true.

Step 3: One Node Is Null, Other Is Not

If one of the nodes is null and the other isn’t, the trees cannot be isomorphic. A tree with nodes cannot be made to match an empty tree. Return false.

Step 4: Values at the Nodes Differ

If the values stored at the current nodes are different, they can never be isomorphic, regardless of child swaps. Return false.

Step 5: Check for Isomorphism Recursively

Now comes the real check. We have two possibilities:

  • No Swap: Left with left and right with right.
  • Swap: Left with right and right with left.

We recursively check both cases. If either results in all corresponding subtrees being isomorphic, the answer is true.

Step 6: Implement the Recursive Function

boolean isIsomorphic(TreeNode n1, TreeNode n2) {
    if (n1 == null && n2 == null) return true;
    if (n1 == null || n2 == null) return false;
    if (n1.val != n2.val) return false;

    boolean noSwap = isIsomorphic(n1.left, n2.left) && isIsomorphic(n1.right, n2.right);
    boolean swap = isIsomorphic(n1.left, n2.right) && isIsomorphic(n1.right, n2.left);

    return noSwap || swap;
}

Edge Cases

Case 1: Both Trees Are Empty

This is the simplest case. Return true.

Case 2: One Tree Is Empty

Not isomorphic. Return false.

Case 3: Root Values Are Different

No possible swap can make values equal. Return false.

Case 4: Trees Are Exactly the Same

All values and positions match. No swap needed. Return true.

Case 5: Children Are Swapped

Swap makes them match. Return true.

Case 6: Multiple Swaps Needed

If recursive swaps at multiple levels result in match, still return true.

Case 7: Structure Too Different

If number of children, or their arrangement is too different, no amount of flipping helps. Return false.

Finally

Tree isomorphism is all about recursive comparison and being open to flipping children when needed. For beginners, think of it like trying to align two tangled ropes — you’re allowed to twist one, but you can’t cut or change their labels. Practice with examples and draw trees to build your intuition.

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

C
C++
Python
Java
JS
Go
Rust
Kotlin
Swift
TS
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

typedef struct TreeNode {
    int val;
    struct TreeNode *left;
    struct TreeNode *right;
} TreeNode;

TreeNode* createNode(int val) {
    TreeNode* node = (TreeNode*)malloc(sizeof(TreeNode));
    node->val = val;
    node->left = node->right = NULL;
    return node;
}

bool isIsomorphic(TreeNode* root1, TreeNode* root2) {
    if (!root1 && !root2) return true;
    if (!root1 || !root2) return false;
    if (root1->val != root2->val) return false;
    return (isIsomorphic(root1->left, root2->left) && isIsomorphic(root1->right, root2->right)) ||
           (isIsomorphic(root1->left, root2->right) && isIsomorphic(root1->right, root2->left));
}

int main() {
    TreeNode* tree1 = createNode(1);
    tree1->left = createNode(2);
    tree1->right = createNode(3);
    tree1->left->left = createNode(4);
    tree1->right->right = createNode(5);

    TreeNode* tree2 = createNode(1);
    tree2->left = createNode(3);
    tree2->right = createNode(2);
    tree2->left->left = createNode(5);
    tree2->right->right = createNode(4);

    if (isIsomorphic(tree1, tree2))
        printf("Trees are isomorphic.\n");
    else
        printf("Trees are not isomorphic.\n");

    return 0;
}

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