Tree Traversals: A Comprehensive Guide with Examples and Applications, Exams of Data Structures and Algorithms

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A. Sam Silva

J. Jeya Praise

TREE TRAVERSALS

Synopsis

Introduction

Tree Terminologies

Binary Tree

Tree Traversal

Application

Conclusion

Tree Collection of nodes  (^) The collection can be empty  (^) Consists of finite set of elements, called nodes, and a finite set of directed lines called branches, that connect the nodes.

Structure of Tree H

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Level 0 Level 1 Level 2 Level 3

ROOT

LEAF

NODE

Basic Tree Concepts  (^) Root

• (^) Top most element of the tree Root = A  (^) Node
• (^) Each data item in the tree Node = {A,B,C,D,E,F,G,H,I,J} H

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Basic Tree Concepts  (^) Degree of node

• (^) Maximum number of sub-tree of a node Deg {A,B,C,G} = 2 Deg {E} = 1 Deg {D,F,H,I,J} = 0 H

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Basic Tree Concepts

Terminal Node

• (^) The node which is not having any sub-tree.
• (^) It is also called as Leaf {D,H,F,I,J} H

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Basic Tree Concepts

Non-Terminal Node

• (^) The node which are having sub-trees {A,B,C,E,G} H

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Basic Tree Concepts

Level

• (^) The entire tree structure is leveled in such a way that the root node is always at level 0 {A} - Level 0 {B,C} - Level 1 {D,E,F,G} - Level 2 {H,I,J} - Level 3 H

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Basic Tree Concepts

Edge

• (^) The line drawn from one node to another node is called edge B

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EDGE

Basic Tree Concepts

Depth

• (^) The maximum level of any node is called depth
• (^) i.e. The longest path in the tree  (^) LEVEL 3 H

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Basic Tree Concepts

Forest

• (^) It is a set of disjoint trees
• (^) If the root is removed, then any tree becomes a forest H

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Binary Search Tree

• (^) A binary search tree is a special binary tree, which may be empty or not
• (^) It should have the following characteristics  (^) Every node will have a value  (^) No node can have same value  (^) Value (left) < value (parent)  (^) Value (right) > value (parent)

Operations

1. Node Insertion
2. Node Deletion
3. Searching a Node
4. Traversing