Trees in Data Structures and Algorithms

In this chapter, you will learn about trees as a data structure, including definitions, types, and key concepts such as nodes, edges, levels, and heights. Trees play a crucial role in organizing data efficiently, and understanding them is essential for mastering algorithms and data structures.

• Data Structures
• Algorithms
• Trees
• Nodes
• Hierarchies

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1. Data structure and algorithm 2 Trees 1

2. Objectives After studying this chapter, the student should be able to Define trees , Learn the concepts and principles involved in Trees Binary trees 2

3. DATA STRUCRE Data structure ? A data structure is an arrangement of data in a computer's memory so as to be used effectively. There are two types of data structure . 1-Linear data structure. 2- Non linear structure . How can we decide which data structure to be used? -What needs to be stored -Cost of operation -Memory usage . -Ease of implementation . 3

4. Trees Trees:- A tree is a (possibly non-linear) data structure made up of nodes or vertices and edges without having any cycle. The tree with no nodes is called the null or empty tree. A tree that is not empty consists of a root node and potentially many levels of additional nodes that form a hierarchy . . . 4

5. Trees definitions Root The topmost node in a tree. Parent The converse notion of a child. Siblings Nodes with the same parent. . Descendant a node reachable by repeated proceeding from parent to child Ancestor a node reachable by repeated proceeding from child to parent. .. - - 5

6. Trees definitions Leaf a node with no children . . - Internal node a node with at least one child . . - External node a node with no children . . . - Degree number of sub trees of a node . - 6

7. Trees definitions Edge connection between one node to another - Path a sequence of nodes and edges connecting a node with a Descendant . Level The level of a node is defined by 1 + (the number of connections between the node and the root) ( + ) . - . 1 7

8. Trees definitions Height of tree The height of a tree is the number of edges on the longest downward path between the root and a leaf THE - . . . Height of node The height of a node is the number of edges on the longest downward path between that node and a leaf Depth The depth of a node is the number of edges from the node to the tree's root node. - THE Forest A forest is a set of n 0 disjoint trees - 0 . THE - . 8

9. Binary tree Definition: A binary tree is a finite set of nodes which is either empty or consists of a root and two disjoint binary trees called the left sub tree and the right sub tree. , : 9