Joseph Lindo

Trees

Sir Joseph LindoUniversity of the Cordilleras

Joseph Lindo

BST

Cases

Traversals

Binary Tree

Trees

Course TitleTree

In computer science, a tree is an abstract model of a hierarchical structure

Trees

Joseph Lindo

BST

Cases

Traversals

Binary Tree

Trees

Course TitleBinary Tree

A binary tree is a finite set of elements that is either empty or is partitioned into three disjoint subsets.

The other two subsets are themselves binary trees called the left and right subtrees.

Binary Trees

Joseph Lindo

BST

Cases

Traversals

Binary Tree

Trees

Course TitleBinary Tree

The other two subsets are themselves binary trees called the left and right subtrees.

• Ordered Tree• Full binary tree• Skewed binary tree

Binary Trees

Joseph Lindo

BST

Cases

Traversals

Binary Tree

Trees

Course TitleBinary SearchTree• All identifiers in the left

subtree are less than the identifier in the root node

• All identifiers in the right subtree are greater than the identifier in the root node

BST

Joseph Lindo

BST

Cases

Traversals

Binary Tree

Trees

Course TitleTraversing• It is the process of visiting

each node in a tree exactly one.

Common traversals:Traversals

Joseph Lindo

BST

Cases

Traversals

Binary Tree

Trees

Course TitleTraversals• Preorder

Node - Left - Right • InorderLeft - Node -Right

• PostorderLeft - Right - Node• Level - order

Traversals

Want an easy way to do INORDER

Traversal?

SQUISHING

Joseph Lindo

Trees

-- end --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

Trees

-- end na --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

Applications

Tree

Organization charts

File systems Programming

environments

Joseph Lindo

Terminologies

Tree

Node Root Node Parent Node Siblings Internal Node External

Node/Leaf/ Terminal

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Terminologies

Tree

Ancestors Descendants Subtree Level Depth Height Degree Weigth

Joseph Lindo

Properties

Binary Tree

• 2i-1: maximum number of nodes on level I of a binary tree

• 2k-1: maximum number of nodes in a binary tree of height k

Joseph Lindo

Examples

Traversals

Joseph Lindo

Squishing

INORDER Traversal

Joseph Lindo

Level - Order

Traversal

Joseph Lindo

Trees

-- end --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

Trees

-- end na --Sir Joseph Lindo

University of the Cordilleras

Joseph Lindo

Examples