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

Check if Two Binary Trees are Mirror Images - Algorithm, Visualization, Examples

Problem Statement

Given two binary trees, your task is to determine whether they are mirror images of each other. Two trees are said to be mirrors if the structure of one tree is the reverse of the other and their corresponding node values are the same. This check must be done recursively for all corresponding nodes.

Examples

Tree 1 Tree 2 Are Mirror? Description
[1, 2, 3, 4, 5]
[1, 3, 2, null, null, 5, 4]
true Tree 2 is the mirror image of Tree 1: left and right children are swapped at every node.
[10, 20, 30]
[10, 30, 20]
true Left and right subtrees are perfectly mirrored.
[1, 2, 3]
[1, 2, 3]
false Both trees have the same structure, but are not mirrors (no left-right reversal).
[] [] true Two empty trees are trivially mirrors of each other.
[1]
[1]
true Single-node trees with the same value are mirrors.
[1, 2]
[1, null, 2]
true Tree 1 has a left child; Tree 2 has a right child. Structures mirror each other.

Solution

Understanding the Problem

We are given two binary trees and asked to determine whether they are mirror images of each other. This means that the structure and values of one tree must exactly reflect those of the other, but in a mirrored way. Specifically, for every node in the first tree, its left child must match the right child of the corresponding node in the second tree, and vice versa.

This problem is common in recursion-based tree problems and tests your ability to compare tree structures and values symmetrically.

Step-by-Step Solution with Example

Step 1: Understand the Mirror Concept

Two trees are mirrors if:

  • They are both empty (null)
  • Or, their root nodes have equal values, and their left and right subtrees are mirrors of each other in opposite directions

Step 2: Use a Recursive Approach

The simplest and cleanest way to solve this is using recursion. We define a function isMirror(tree1, tree2) that checks:

  • If both trees are null, return true
  • If only one is null, return false
  • If values don't match, return false
  • Recursively check isMirror(tree1.left, tree2.right) and isMirror(tree1.right, tree2.left)

Step 3: Apply the Approach to an Example

Let’s take two trees:


Tree A         Tree B
   1              1
  /             /  2   3          3   2

We compare:

  • Roots: 1 == 1 ✅
  • Left of A (2) with Right of B (2) ✅
  • Right of A (3) with Left of B (3) ✅

All checks pass recursively, so these trees are mirror images.

Step 4: Implement the Code


boolean isMirror(TreeNode t1, TreeNode t2) {
    if (t1 == null && t2 == null) return true;
    if (t1 == null || t2 == null) return false;
    if (t1.val != t2.val) return false;
    return isMirror(t1.left, t2.right) && isMirror(t1.right, t2.left);
}

Edge Cases

Case 1: Both Trees Are Empty

Two null trees are mirrors by definition. Return true.

Case 2: One Tree is Empty

One null and one non-null tree can never be mirrors. Return false.

Case 3: Different Root Values

If the roots are not equal, trees can't be mirrors. Check t1.val != t2.val.

Case 4: Matching Roots, Unmatched Subtrees

Even if roots match, if the left and right children don't mirror each other in structure and value, return false.

Case 5: Single Node Trees

If both trees are single nodes with the same value, they are mirrors. If either node has children and the other doesn’t, they’re not mirrors.

Finally

This problem teaches the power of recursion and symmetry. The key idea is to mirror the traversal — compare left of one with right of the other and continue down the tree. Always consider the base cases carefully, and remember to match both structure and value. With these principles, you can confidently identify mirror trees!

Algorithm Steps

  1. Given two binary trees, if both trees are empty, they are mirrors; if one is empty and the other is not, they are not mirrors.
  2. Compare the root nodes of both trees. If the values are not equal, the trees are not mirrors.
  3. Recursively check if the left subtree of the first tree is a mirror of the right subtree of the second tree, and if the right subtree of the first tree is a mirror of the left subtree of the second tree.
  4. If both recursive checks return true, then the two trees are mirror images of each other.

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 isMirror(t1, t2):
    if not t1 and not t2:
        return True
    if not t1 or not t2:
        return False
    return (t1.val == t2.val) and isMirror(t1.left, t2.right) and isMirror(t1.right, t2.left)

# Example usage:
if __name__ == '__main__':
    # Tree 1:
    #      1
    #     / \
    #    2   3
    #
    # Tree 2 (mirror of Tree 1):
    #      1
    #     / \
    #    3   2
    tree1 = TreeNode(1, TreeNode(2), TreeNode(3))
    tree2 = TreeNode(1, TreeNode(3), TreeNode(2))
    print(isMirror(tree1, tree2))

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