# Compute Height of a Binary Tree

“** Compute Height of a Binary Tree**” is a very basic problem of Tree data structure. Here, we are given a Binary Tree and our task is to compute height of given binary tree. The height of the tree is defined as total number of nodes in a longest path from root node to any leaf node.

We can compute height of a binary tree using recursion. The steps/algorithm to compute height of a binary tree is as follows:

- If Tree is empty, then return 0 as height of tree.
- Else:
- Compute Maximum depth of left subtree recursively.
- Compute Maximum depth of right subtree recursively.
- Compute max of max depths of left and right subtrees and add 1 to it for the current node.
- Return max_depth.

#### C++ Program to compute height of a binary tree is as follows:

```
/* C++ Program to Compute Height of a Binary Tree */
#include<bits/stdc++.h>
using namespace std;
typedef struct Node
{
int data;
struct Node *left;
struct Node *right;
Node(int ele)
{
data = ele;
left = NULL;
right = NULL;
}
} Node;
/* Function to Compute height of a Binary Tree */
int height(Node *root)
{
/* If tree is empty, height will be 0 */
if(root == NULL)
{
return 0;
}
else
{
/* Compute Height of Left Subtree */
int leftHeight = height(root -> left);
/* Compute Height of Right Subtree */
int rightHeight = height(root -> right);
/* Return max of height of subtree and right subtree + 1 */
return max(leftHeight,rightHeight) + 1;
}
}
int main()
{
/* Creating a Binary tree and inserting some nodes in it */
Node *root = NULL;
root = new Node(1);
root -> left = new Node(2);
root -> right = new Node(3);
root -> left -> left = new Node(4);
root -> left -> right = new Node(5);
root -> right -> left = new Node(6);
root -> right -> right = new Node (7);
root -> left -> right -> left = new Node(8);
root -> right -> left -> right = new Node(9);
/* Calling and Printing Height of Binary Tree */
cout<<"The Height of Given Binary Tree is "<<height(root);
}
```

**OUTPUT**:

The Height of Given Binary Tree is 4

**Related Posts:**

**Introduction to Tree Data Structure****Binary Tree Traversals****Print All Leaf Nodes of a Binary Tree****Count Number of Nodes in a Binary Tree****Print Alternate Levels of Binary Tree****Maximum Width of Binary Tree****Level Order Tree Traversal****Left View of Binary Tree****Right View of Binary Tree****Inorder Tree Traversal Using Stack****Preorder Tree Trasversal Using Stack****Postorder Tree Traversal Using Stack****Vertical Order Tree Traversal****Top View of Binary Tree****Bottom View of Binary Tree****Delete Complete Binary Tree****Check if two trees are mirror Trees of Each Other****Convert Binary Tree to its Mirror Tree****Check if Binary Tree is Symmetric or Not****Print All Root to Leaf Paths in a Binary Tree**