Author: Takdir, S.ST. ([email protected]) © Sekolah Tinggi Ilmu Statistik

Data StructuresLesson10

Author: Takdir, S.ST. ([email protected]) © Sekolah Tinggi Ilmu Statistik

Binary Trees &

Search Trees


INTRODUCTION • Ordered Tree: The sequence of

node is important • Unordered Tree: The sequence of

node is not important • Equal Tree: if two unordered trees

have the same subsets, then they are equal; but as ordered trees, they won’t be equal unless their equal subtrees are in the same order.


INTRODUCTION (2)• A binary tree is an ordered tree in

which every internal node has degree 2 (left sub tree and right sub tree)

• An empty left sub tree is different from an empty right sub tree.

• Complete Binary Tree: Either a full binary tree or one that is full except for a segment of missing leaves on the right side of the bottom level.

• Forest: Sequence of disjoint ordered trees.


EXAMPLEUnequal Ordered Tree:

Unequal Binary Tree:


EXAMPLE (2)Complete binary trees:


MAPPINGA COMPLETE BINARY TREE

INTO AN ARRAY


MAPPINGA COMPLETE BINARY TREE

INTO AN ARRAY (2)


EXPRESSION TREE


SEARCH TREE

mlow = smallest key in the M (middle) subtreerlow = smallest key in the R (right) subtree


SEARCH TREE EXAMPLE

Five-Way Search Tree


INSERTING INTOFIVE-WAY SEARCH TREE


INSERTING INTOFIVE-WAY SEARCH TREE (2)


INSERTING INTOFIVE-WAY SEARCH TREE (3)


B-TREE


EXAMPLE OF B-TREE ORDER 5


INSERTING INTO B-TREE


BINARY SEARCH TREES (BST)


BUILDING BST


AVL TREE


NON-AVL TREE


BUILDING AVL TREE


BUILDING AVL TREE EXAMPLE


AVL TREE ROTATION


THANK YOU

Documents

Author: Takdir, S.ST. ([email protected]) © Sekolah Tinggi Ilmu Statistik