# How to Find the Height of Tree in Data Structure?

//

Larry Thompson

In data structures, finding the height of a tree is a common problem. The height of a tree refers to the length of the longest path from the root node to any leaf node in the tree. It is an important metric as it helps in understanding the overall structure and complexity of the tree.

To find the height of a tree, we can use several approaches. In this tutorial, we will explore two popular methods:

## Method 1: Recursion

One way to find the height of a tree is by using recursion. Recursion involves breaking down a problem into smaller subproblems. Here’s how we can implement this method:

1. Step 1: Define a recursive function to find the height.
2. Step 2: Base case: If the current node is null, return -1.
3. Step 3: Recursive case: Calculate the height of the left subtree recursively and store it in a variable.
4. Step 4: Calculate the height of the right subtree recursively and store it in another variable.
5. Step 5: Return the maximum between the heights of the left and right subtrees, plus one (to account for the current level).

This method can be implemented using HTML code as follows:

``````<p>One way to find
the <b>height</b>
of a <u>tree</u>
is by using recursion.</p>

<ol>
<li><b>Step 1:</b>
Define a recursive
function to find the
height.</li>
<li><b>Step 2:</b>
Base case: If the current
node is null, return -1.</li>
<li><b>Step 3:</b>
Recursive case: Calculate
the height of the left
subtree recursively and
store it in a variable.</li>
<li><b>Step 4:</b> Calculate
the height of the right
subtree recursively and
store it in another variable.</li>
<li><b>Step 5:</b>
Return the maximum between
the heights of the left and
right subtrees, plus one
(to account for the current level).</li>
</ol>```
```

## Method 2: Iteration using Level Order Traversal

Another method to find the height of a tree is by using iteration and level order traversal. This method involves traversing the tree level by level and counting the number of levels. Here’s how we can implement this method:

1. Step 1: Define a queue data structure to store nodes.
2. Step 2: Enqueue the root node.
3. Step 3: Initialize a variable to keep track of levels (starting from -1).
4. Step 4: Start a loop while the queue is not empty.
• a) Get the current level size by getting the queue size.
• b) Increment the level variable.
• c) Dequeue all nodes at the current level and enqueue their children.
5. Step 5: Return the level variable as the height of the tree.

To implement this method using HTML code, follow these steps:

``````<h3>Method 2:
Iteration using Level
Order Traversal</h3>

<p>Another method to find
the height of a tree is by
using iteration and level
order traversal. This method
involves traversing the tree
level by level and counting
the number of levels. Here's
how we can implement this method:</p>

<ol>
<li><b>Step 1:</b> Define a queue data structure to store nodes.</li>
<li><b>Step 2:</b> Enqueue the root node.</li>
<li><b>Step 3:</b> Initialize a variable to keep track of levels (starting from -1).</li>
<li><b>Step 4:</b> Start a loop while the queue is not empty.
<ul>
<li><b&a;)gt;>``````

By incorporating these HTML styling elements, we have created an engaging and structured tutorial on how to find the height of a tree in data structures. The use of bold and underlined text highlights important concepts and instructions.

The

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1. tags are used to present the steps in an organized manner, making it easy for readers to follow along. Additionally, the use of