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

Find the Distance Between Two Nodes in a Binary Tree - Algorithm & Examples

Binary Trees

Contents

ProblemExamplesSolutionAlgorithmCode

Problem Statement❯

Given a binary tree and two node values n1 and n2, find the number of edges in the shortest path between them. The distance between two nodes in a binary tree is defined as the number of edges in the path from one node to another.

If either node does not exist in the tree, return -1.

Examples❯

Input Tree Node 1 Node 2 Distance Description
[1, 2, 3, 4, 5, 6, 7]
4 5 2 LCA is 2. Distance = depth(4) + depth(5) - 2 × depth(2) = 2 + 2 - 2 = 2
[1, 2, 3, null, 4, null, 5]
4 5 4 LCA is 1. Path: 4 → 2 → 1 → 3 → 5 (4 steps)
[10, 5, 15, 3, 7, null, 18]
3 7 2 LCA is 5. Path: 3 → 5 → 7 = 2 steps
[1, 2, 3, 4, null, null, 5]
4 5 4 LCA is 1. Path: 4 → 2 → 1 → 3 → 5 = 4 steps
[1, 2, null, 3, null, 4]
3 4 2 LCA is 3. Distance from 3 to 4 is 1, from 3 to 3 is 0 → total = 1 + 1 = 2
[7]
7 7 0 Both nodes are the same → distance is 0

Solution❯

Case 1: Normal Case — Both Nodes Exist and Are Different

To find the distance between two distinct nodes in a binary tree, we first need to locate their Lowest Common Ancestor (LCA). The LCA is the deepest node that is an ancestor of both target nodes. Once we have the LCA, we compute the distance from the LCA to each of the two nodes separately, then sum them up.

For example, in the tree:

      1
     / \
    2   3
   / \
  4   5

The distance between 4 and 5 is 2 (Path: 4 → 2 → 5). LCA is 2, and each node is one edge away from it.

Case 2: One Node is Ancestor of the Other

When one of the nodes is an ancestor of the other, the LCA is the ancestor node itself. In that case, the distance is simply the depth difference between the two nodes. For instance, in the same tree, the distance between 2 and 5 is 1 because 2 is the parent of 5.

Case 3: Same Node

If the two input node values are the same, then the distance is obviously 0, since we are at the same position in the tree. No traversal is needed.

Case 4: Empty Tree

If the tree is empty (null root), then there is no node to compare. In such cases, we return -1 as both nodes are non-existent by default.

Case 5: One or Both Nodes Not Present

If one or both of the nodes are missing from the tree, we should not proceed with distance calculation. Instead, we return -1 indicating the operation is not valid because required data is missing. Always verify presence before processing.

Algorithm Steps❯

  1. Given a binary tree and two target node values.
  2. Find the lowest common ancestor (LCA) of the two nodes.
  3. Compute the distance from the LCA to the first node.
  4. Compute the distance from the LCA to the second node.
  5. The distance between the two nodes is the sum of these two distances.

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 lowestCommonAncestor(root, n1, n2):
    if not root or root.val == n1 or root.val == n2:
        return root
    left = lowestCommonAncestor(root.left, n1, n2)
    right = lowestCommonAncestor(root.right, n1, n2)
    if left and right:
        return root
    return left if left else right

def distanceFromRoot(root, target, distance):
    if not root:
        return -1
    if root.val == target:
        return distance
    left = distanceFromRoot(root.left, target, distance + 1)
    if left != -1:
        return left
    return distanceFromRoot(root.right, target, distance + 1)

def distanceBetweenNodes(root, n1, n2):
    lca = lowestCommonAncestor(root, n1, n2)
    d1 = distanceFromRoot(lca, n1, 0)
    d2 = distanceFromRoot(lca, n2, 0)
    return d1 + d2

if __name__ == '__main__':
    # Construct binary tree:
    #         1
    #        / \
    #       2   3
    #      / \   
    #     4   5  
    root = TreeNode(1)
    root.left = TreeNode(2, TreeNode(4), TreeNode(5))
    root.right = TreeNode(3)
    print(distanceBetweenNodes(root, 4, 5))  # Expected output: 2