Complete Binary Trees

University
University of California San Diego
Course
CSE 100/101 | Data Structures and Algorithms
Pages

2

Academic year

2023
Author

anon
Views

23

Complete Binary Trees: An Overview and Benefits A binary tree is complete when all levels—possibly with the exception of the top level—are completely packed. In other words, every node at the toplevel is as far to the left as it can be. It is a frequently employed data structure incomputer science and differs from other binary trees in a number of ways. A Complete Binary Tree's Height Complete binary trees' height is one of its key benefits. A full binary tree with n nodes has a height of O. (log n). Accordingly, the height of the treeincreases logarithmically as the number of nodes increases. This is because, in acomplete binary tree, every level—aside from the final one, perhaps—iscompletely packed. Simple Formulas for Parent and Child Node Calculation Complete binary trees also have the benefit of making it easy to calculate the parent and child nodes of any given node. We can utilize the followingformulas by numbering each node from top to bottom and left to right: ● Node i's parent node is node i/2 rounded down. ● Node i's two offspring are 2i and 2i + 1. These algorithms eliminate the need to manually search through each node ofthe tree in order to efficiently navigate it. Uses for Complete Binary Trees There are several real-world uses for complete binary trees in computer science. They are frequently used as heaps, which are data structures for priorityqueue implementation. They are also utilized in algorithms like Huffman codingand Dijkstra's shortest path algorithm.

In conclusion, complete binary trees are a practical data structure that provide a number of benefits over other binary trees. They make it possible tonavigate the tree effectively and their height increases logarithmically with thenumber of nodes. Both novices and experts in computer science shouldunderstand entire binary trees.