- Write a C program to find diameter of a binary tree.
- Write a recursive function to calculate diameter of a binary tree.

Given a binary tree, we have to find the **diameter of binary tree**. The diameter of a tree is the number of nodes in the longest path between any two leaf nodes of binary tree. The longest path may not path through root node of tree. Longest path may be completely in left or right sub tree or it mat pass through root node. We will use a recursive approach to find the **diameter of a tree**.

**Algorithm to find the diameter of a binary tree**

Let, "root" be the root node of given binary tree.

- If root is NULL, return 0.
- Calculate of height of left and right sub tree. Let it be leftHeight and rightHeight.
- The longest path which passes through root is leftHeight + rightHeight + 1.
- Recursively calculate the diameter of left and right subtree. Let it be leftDiameter and rightDiameter.
- Return maximum of leftDiameter, rightDiameter and leftHeight + rightHeight + 1.

**Time Complexity**: O(n

^{2})

In this program, we will use a recursive function "getDiameter", which returns the diameter of a binary tree by implementing above mentioned algorithm.

/* Returns the diameter of a binary tree */ int getDiameter(struct node *nodePtr) { /* Empty Tree */ if (nodePtr == NULL) return 0; /* Calculate the heigh of the left and right sub-tree */ int leftHeight = getHeight(nodePtr->left); int rightHeight = getHeight(nodePtr->right); /* Recursively calculate the diameter of left and right sub-trees */ int leftDiameter = getDiameter(nodePtr->left); int rightDiameter = getDiameter(nodePtr->right); /* diameter of a tree is maximum of (left sub-tree diameter), (right sub-tree diameter), and (height of left sub-tree + height of right sub-tree + 1)*/ return getMax(leftHeight + rightHeight + 1, getMax(leftDiameter, rightDiameter)); }

## C program to find diameter of a binary tree

#include <stdio.h> struct node { int data; struct node *left; struct node *right; }; struct node* getNewNode(int data) { /* dynamically allocate memory for a new node */ struct node* newNode = (struct node*)malloc(sizeof(struct node)); /* populate data in new Node */ newNode->data = data; newNode->left = NULL; newNode->right = NULL; return newNode; } /* This function returns below 1 / \ 2 3 / \ / \ 4 5 6 7 / 8 */ struct node* generateBTree(){ // Root Node struct node* root = getNewNode(1); // Level 2 nodes root->left = getNewNode(2); root->right = getNewNode(3); // Level 3 nodes root->left->left = getNewNode(4); root->left->right = getNewNode(5); root->right->left = getNewNode(6); root->right->right = getNewNode(7); // Level 4 nodes root->left->left->left = getNewNode(8); return root; } /* Returns maximum of two given numbers */ int getMax(int a, int b){ if(a >= b) return a; else return b; } /* Returns total number of nodes(size) in a bianry tree getHeight(root) = Maximum of (getHeight(left-subTree), getHeight(right-subTree)) + 1; */ int getHeight(struct node *root){ int leftHeight, rightHeight; if(root == NULL) return 0; leftHeight = getHeight(root->left); rightHeight = getHeight(root->right); return getMax(leftHeight, rightHeight) + 1; } /* Returns the diameter of a binary tree */ int getDiameter(struct node *nodePtr) { /* Empty Tree */ if (nodePtr == NULL) return 0; /* Calculate the heigh of the left and right sub-tree */ int leftHeight = getHeight(nodePtr->left); int rightHeight = getHeight(nodePtr->right); /* Recursively calculate the diameter of left and right sub-trees */ int leftDiameter = getDiameter(nodePtr->left); int rightDiameter = getDiameter(nodePtr->right); /* diameter of a tree is maximum of (left sub-tree diameter), (right sub-tree diameter), and (height of left sub-tree + height of right sub-tree + 1)*/ return getMax(leftHeight + rightHeight + 1, getMax(leftDiameter, rightDiameter)); } int main() { struct node *root = generateBTree(); printf("Diameter of Tree = %d", getDiameter(root)); getchar(); return 0; }Output

Diameter of Tree = 6