# Find the Distance between Two Nodes of a Binary Tree.

Objective: Given nodes in a binary tree, find the distance between them.

Example : Approach:

• Distance(X, Y) = Distance(root, X) +Distance(root, Y) – 2*(Distance(root to LCA(X,Y)
• where LCA(X,Y) = Lowest Common Ancestor of X,Y
• In the above example if Distance(20,45) = 3
• Distance(root, 20) = 2
• Distance(root, 45) = 3
• LCA(20, 45) = 10
• Distance(root, 10) = 1
• Distance(20,45) = 2+3 – 2*1 = 3

Now problem is reduced to How to find distance from root to any given node and How to find Lowest Common Ancestor of two given nodes.

Complete Code:

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 public class PrintDistance { public int findDistance(Node root, int n1, int n2) { int x = Pathlength(root, n1) – 1; int y = Pathlength(root, n2) – 1; int lcaData = findLCA(root, n1, n2).data; int lcaDistance = Pathlength(root, lcaData) – 1; return (x + y) – 2 * lcaDistance; } public int Pathlength(Node root, int n1) { if (root != null) { int x = 0; if ((root.data == n1) || (x = Pathlength(root.left, n1)) > 0 || (x = Pathlength(root.right, n1)) > 0) { // System.out.println(root.data); return x + 1; } return 0; } return 0; } public Node findLCA(Node root, int n1, int n2) { if (root != null) { if (root.data == n1 || root.data == n2) { return root; } Node left = findLCA(root.left, n1, n2); Node right = findLCA(root.right, n1, n2); if (left != null && right != null) { return root; } if (left != null) { return left; } if (right != null) { return right; } } return null; } public static void main(String[] args) throws java.lang.Exception { Node root = new Node(5); root.left = new Node(10); root.right = new Node(15); root.left.left = new Node(20); root.left.right = new Node(25); root.right.left = new Node(30); root.right.right = new Node(35); root.left.right.right = new Node(45); PrintDistance i = new PrintDistance(); System.out.println("Distance between 45 and 20 is : " + i.findDistance(root, 45, 20)); } } class Node { int data; Node left; Node right; public Node(int data) { this.data = data; this.left = null; this.right = null; } }

Output:

```Distance between 45 and 20 is : 3
```

### 1 thought on “Find the Distance between Two Nodes of a Binary Tree.”

1. Hi,
Thanks for the program., its cool ..
There is 1 thing I would like to suggest is to have a better readable piece of code to get the node count ..

You should get -1 for the node which is not in the tree.
private static int findNodeCount(Node head, int n, int count) {