A complete tree in data structure refers to a type of binary tree where all levels, except possibly the last one, are completely filled with nodes. In other words, a complete tree is a binary tree in which each level is filled from left to right.
Properties of a Complete Tree:
A complete tree has the following properties:
- Level Filling: All levels of the tree are filled except possibly the last level. If the last level is not completely filled, it is filled from left to right.
- Binary Tree Structure: Each node in the tree has at most two children.
Example of a Complete Tree:
To better understand what a complete tree looks like, let’s consider an example:
1 / \ 2 3 / \ / 4 5 6
In this example, we can see that all levels of the tree are filled except for the last level. The last level is filled from left to right.
Uses of Complete Trees:
Complete trees have various applications in data structures and algorithms. Some common uses include:
- Heap Data Structure: A heap is a complete binary tree that satisfies the heap property. Heaps are widely used in priority queues and sorting algorithms like heapsort.
- Huffman Coding: Huffman coding is a compression algorithm that uses binary trees to represent characters or symbols based on their frequency of occurrence. Complete trees can be used in constructing Huffman codes efficiently.
Determining if a Tree Is Complete:
In order to determine if a binary tree is complete, we can use various algorithms and techniques. One approach is to perform a level-order traversal of the tree and check if any node is encountered after encountering a node that has one or no children. If such a node is found, the tree is not complete.
A complete tree in data structure is a binary tree where all levels, except possibly the last one, are completely filled from left to right. Complete trees have various applications in data structures and algorithms such as heaps and Huffman coding. Understanding the properties and uses of complete trees can be beneficial in solving problems efficiently.