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Algorithms: Introduction, Peak Finding, Complexity, Lecture notes of Data Structures and Algorithms

University of Bradford Data Structures and Algorithms

It is a lecture note for Design of algorithms

Typology: Lecture notes

2018/2019

Uploaded on 01/04/2019

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Introduction to the Course

Setting Targets

Peak Finding Problem

Complexity

Peak Finding Problem - Again

Computational Complexity - Again

Characterizing an Algorithm

Design and Analysis of Algorithms

(Week-1)

Malik Jahan Khan

Namal College Mianwali

Malik Jahan Khan Namal College Mianwali Design and Analysis of Algorithms (Week-1)

Partial preview of the text

Download Algorithms: Introduction, Peak Finding, Complexity and more Lecture notes Data Structures and Algorithms in PDF only on Docsity!

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Design and Analysis of Algorithms

(Week-1)

Malik Jahan Khan

Namal College Mianwali

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Introduction

Course outline

Classic data structures

Efficient procedures to solve large-scale problems

What is large-scale?

History of hardware progress vs algorithms

Exercise

Peak-Finder

Benchmarking and setting targets

Disclaimer: Content provided in slides of this course has been

borrowed from different sources including Cormen’s book on

Introduction to Algorithms, Khan Academy and MIT OCW.

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Exercise - Sort given n numbers

Input

n = 10 million numbers

Compute exact physical time for both of the following scenarios

Computer A - Insertion Sort

Speed: 1 billion instructions per second

Number of instructions to execute: 2n

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Exercise - Sort given n numbers

Input

n = 10 million numbers

Compute exact physical time for both of the following scenarios

Computer A - Insertion Sort

Speed: 1 billion instructions per second

Number of instructions to execute: 2n

Computer B - Merge Sort

Speed: 10 million instructions per second

Number of instructions to execute: 50nlog (n)

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Peak Finding Problem

Given a set of numbers stored in a one-dimensional array, find one

of the peaks. We are not interested in highest peak.

This is your HW of lecture-

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Complexity [Source: www.bigocheatsheet.com]

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Peak Finding Problem

Given a set of numbers stored in a one-dimensional array, find one

of the peaks. We are not interested in highest peak.

This was your HW of lecture-

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Peak Finding Problem

Given a set of numbers stored in a one-dimensional array, find one

of the peaks. We are not interested in highest peak.

This was your HW of lecture-

How would your algorithm change in its working as well as

performance if it had to compute the highest peak? e.g. ECG

signals

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Exercise-

What is the smallest value of n such that an algorithm whose

running time is 100n

runs faster than an algorithm whose running

time is 2

n

on the same machine?

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Exercise-

For each function f (n) and time t in the following table, determine

the largest size of n of a problem that can be solved in time t,

assuming that the algorithm to solve the problem takes f (n)

microseconds.

1 sec 1 min 1 hr 1 day 1 mon 1 yr 1 cent

log (n)

n

nlog (n)

n

n!

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Θ− Notation

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

O− Notation

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

o− Notation

Is O asymptotically tight bound?

Setting Targets Peak Finding Problem Complexity Peak Finding Problem - Again Computational Complexity - Again Characterizing an Algorithm

Algorithms: Introduction, Peak Finding, Complexity, Lecture notes of Data Structures and Algorithms

Related documents

Partial preview of the text

Download Algorithms: Introduction, Peak Finding, Complexity and more Lecture notes Data Structures and Algorithms in PDF only on Docsity!

Design and Analysis of Algorithms

(Week-1)

Malik Jahan Khan

Namal College Mianwali

Introduction

Course outline

Classic data structures

Efficient procedures to solve large-scale problems

What is large-scale?

History of hardware progress vs algorithms

Exercise

Peak-Finder

Benchmarking and setting targets

Disclaimer: Content provided in slides of this course has been

borrowed from different sources including Cormen’s book on

Introduction to Algorithms, Khan Academy and MIT OCW.

Exercise - Sort given n numbers

Input

n = 10 million numbers

Compute exact physical time for both of the following scenarios

Computer A - Insertion Sort

Speed: 1 billion instructions per second

Number of instructions to execute: 2n

Exercise - Sort given n numbers

Input

n = 10 million numbers

Compute exact physical time for both of the following scenarios

Computer A - Insertion Sort

Speed: 1 billion instructions per second

Number of instructions to execute: 2n

Computer B - Merge Sort

Speed: 10 million instructions per second

Number of instructions to execute: 50nlog (n)

Peak Finding Problem

Given a set of numbers stored in a one-dimensional array, find one

of the peaks. We are not interested in highest peak.

This is your HW of lecture-

Complexity [Source: www.bigocheatsheet.com]

Peak Finding Problem

Given a set of numbers stored in a one-dimensional array, find one

of the peaks. We are not interested in highest peak.

This was your HW of lecture-

Peak Finding Problem

Given a set of numbers stored in a one-dimensional array, find one

of the peaks. We are not interested in highest peak.

This was your HW of lecture-

How would your algorithm change in its working as well as

performance if it had to compute the highest peak? e.g. ECG

signals

Exercise-

What is the smallest value of n such that an algorithm whose

running time is 100n

runs faster than an algorithm whose running

time is 2

n

on the same machine?

Exercise-

For each function f (n) and time t in the following table, determine

the largest size of n of a problem that can be solved in time t,

assuming that the algorithm to solve the problem takes f (n)

microseconds.

1 sec 1 min 1 hr 1 day 1 mon 1 yr 1 cent

log (n)

n

n

nlog (n)

n

n

n

n!

Θ− Notation

O− Notation

o− Notation

Is O asymptotically tight bound?

o− Notation

Is O asymptotically tight bound? may or may not!