# 1. Introduction

The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root. It’s an important measure to understand the “width” of a tree and has applications in various tree-based algorithms.

# 2. Program Steps

1. Create a class for the binary tree with a nested class for nodes. Each node will have a value and left and right child references.

2. Define a recursive function that calculates the height of a tree. During this calculation, also compute the diameter considering the current node as the root.

3. The diameter is the maximum value of:

a. Diameter of left subtree

b. Diameter of right subtree

c. Height of left subtree + height of right subtree + 1

4. Return the maximum diameter obtained from the above recursive calculations.

# 3. Code Program

```
public class BinaryTree {
static class Node {
int data;
Node left, right;
Node(int item) {
data = item;
left = right = null;
}
}
Node root;
int diameter = 0;
public int diameter() {
calculateHeight(root);
return diameter;
}
private int calculateHeight(Node node) {
if (node == null) {
return 0;
}
// Calculate height of left and right subtrees
int leftHeight = calculateHeight(node.left);
int rightHeight = calculateHeight(node.right);
// Update diameter
diameter = Math.max(diameter, leftHeight + rightHeight + 1);
// Return height of current node
return Math.max(leftHeight, rightHeight) + 1;
}
public static void main(String[] args) {
BinaryTree tree = new BinaryTree();
tree.root = new Node(1);
tree.root.left = new Node(2);
tree.root.right = new Node(3);
tree.root.left.left = new Node(4);
tree.root.left.right = new Node(5);
System.out.println("The diameter of the binary tree is: " + tree.diameter());
}
}
```

### Output:

The diameter of the binary tree is: 4

# 4. Step By Step Explanation

1. The nested *Node* class represents individual nodes in our binary tree.

2. The *calculateHeight* function is responsible for computing the height of the tree. During this computation, we also keep track of the diameter using the logic described in the program steps.

3. The diameter is the maximum length path that can be obtained between any two nodes in the tree.

4. The final result gives the length of the longest such path in the tree, which is the diameter of the binary tree.