# What Is a Complete Binary Tree in Data Structure?

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Scott Campbell

A complete binary tree is an important concept in data structures that plays a significant role in various algorithms and applications. In this article, we will explore what a complete binary tree is, its properties, and how it differs from other types of binary trees.

What is a Binary Tree?
A binary tree is a hierarchical data structure composed of nodes, where each node has at most two children, referred to as the left child and the right child. The topmost node in the tree is called the root node. The children of a node are known as its descendants.

Understanding Complete Binary Trees
A complete binary tree is a special type of binary tree in which all levels, except possibly the last one, are completely filled with nodes. In other words, all nodes are as far left as possible on each level.

• The last level of a complete binary tree may not be fully filled.
• If any nodes are missing on the last level, they will be left-aligned.

This unique property of complete binary trees makes them useful for efficient storage and retrieval operations.

Complete Binary Tree Example:

### Full Binary Tree

A full binary tree is another type of binary tree that has every level completely filled with nodes. Each node either has two children or no children at all.

### Perfect Binary Tree

A perfect binary tree is a special case of both full and complete binary trees. It has all levels completely filled with nodes, including the last level.

Differences between Complete, Full, and Perfect Binary Trees

• A complete binary tree may not be full or perfect.
• A full tree may not be complete or perfect.
• A perfect tree is both full and complete.

Properties of Complete Binary Trees
Complete binary trees have some interesting properties:

• The maximum number of nodes at level ‘i’ is 2^(i-1), where i is the level number.
• The maximum number of nodes in a complete binary tree with height ‘h’ is 2^h – 1.

These properties can be useful when analyzing or implementing algorithms that involve complete binary trees.

Applications of Complete Binary Trees
Complete binary trees find applications in various domains, including:

• Heap data structure: Heaps are often implemented using complete binary trees, as their properties align well with heap operations.
• Binary heaps: A special kind of heap that is used to efficiently extract the minimum or maximum element.
• Huffman coding: A compression algorithm that utilizes a complete binary tree to represent characters with variable-length codes.

In conclusion, a complete binary tree is a type of binary tree where all levels, except possibly the last one, are completely filled. It has various applications and unique properties that make it an essential concept in data structures. Understanding complete binary trees can greatly enhance your problem-solving skills and algorithmic knowledge.

Now that you have a solid understanding of what a complete binary tree is, you can apply this knowledge to solve problems and design efficient algorithms. Happy coding!