Lecture 04 - Jan 12

Introduction to Algorithms

ADT (Abstract Data Type):

• Specifies what data values it can hold
• Specifies what operations can be performed on it

Data Structure: How we organize data in memory

Array Operations: Inserting, deleting, searching, traversing

Basic Operations

Unified Computational Model: Each basic operation takes constant time (1 unit)

Linear Search

Given an array of elements, check if is present by examining each element.

Best Case: (element found at first position)

Worst Case: (element at end or not present)

Average Case:

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Asymptotic Analysis of Algorithms

Asymptotic analysis describes how an algorithm behaves as input size increases.

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Time Complexity Notations

Example:

Big-O Notation

Definition: if there exist positive constants and such that:

Example:

Given , we want to show

Choosing and :

Therefore,