Grokking Data Structures & Algorithms for Coding Interviews
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Types of Tree
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Types of Tree

Binary Trees

Binary trees are a type of tree where each node can have at most two children, commonly referred to as the left child and the right child. The structure of a binary tree makes it a fundamental and widely used data structure in computer science.

Example

Binary Tree
Binary Tree

In this example, "A" is the root node with two children, "B" ( the left child) and "C" ( the right child). "B" also has two children, "D" (left child) and "E" (right child). "C" also has two children, "F" (left child) and "G" (right child). Nodes "D," "E," "F," and "G" are leaf nodes as they do not have any children.

Full Tree

In a full tree, every node has either zero children (leaf node) or two children. There are no nodes with only one child. Full trees are also known as proper binary trees.

Example

Full Tree
Full Tree

In this example, every node in the binary tree "A," "B," "C," "D," and "E" has either zero children (leaf nodes) or two children. It is a full tree.

Complete Tree

A complete tree is a binary tree in which all levels are filled, except possibly the last level. The last level must strictly be filled from left to right. Data structures like Heap uses complete binary trees for efficient operations.

Example

Complete Tree
Complete Tree

In this example, the binary tree is complete because all levels, except the last level, are filled. The last level is filled from left to right with nodes "D," "E," and "F."

Balanced Tree

Balanced trees are binary trees where the difference in height between the left and right subtrees of any node in the tree is not more than 1. This ensures the tree remains reasonably balanced, preventing skewed structures and maintaining optimal search and insertion times.

Example

Balanced Tree
Balanced Tree

In this example, the binary tree is balanced. The height difference between the left and right subtrees of any node is not more than 1.

Multi-way Tree

Unlike binary trees, multi-way trees allow nodes to have more than two children. Each node can have multiple branches, making multi-way trees more flexible in representing hierarchical data.

Example

Multi-way Tree
Multi-way Tree

In this example, "A" is the root node, and it has three children, "B," "C," and "D." Node "C" has one child, "E." Node "D" has three children, "F," "G," and "H." Node "F" also has one child, "I." This is an example of a multi-way tree with different numbers of children for each node.

Understanding the different types of trees and their respective examples is essential for choosing the most suitable tree structure for specific applications in computer science and data management.

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