Analysis of Sequential and Binary Search Algorithms, Study notes of Computer Science

Download Analysis of Sequential and Binary Search Algorithms and more Study notes Computer Science in PDF only on Docsity!

CMSC 150: Introduction to Computing

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

Search for a Name

Sequential Search

public int search( String[] array, String nameToFind )

for ( int i = 0; i < array.length; i++ )

if ( array[i].equals( nameToFind ) )

return i;

return -1; // not found

Solves the problem, but…

 Is it a "good" algorithm?

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5 Bea O. Problem

Solves the problem, but…

 Is it a "good" algorithm?

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Tabooger, Ollie 999999

Ollie Tabooger Found in 1,000,000 steps…

(Worst Case)

Solves the problem, but…

 Is it a "good" algorithm?

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Tabooger, Ollie

n - 1

Ollie Tabooger Found in n steps…

(Worst Case)

On Average…

 About n /2 steps required

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Tabooger, Ollie

Maya Buttreeks Found in ~ n/2 steps…

(Average Case)

n - 1

Big-Oh: Algorithm Complexity

 We group algorithms into classes of similar

complexity (i.e., how many steps required)

 Sequential search is a O( n ) algorithm (linear)

O(1) O(log n) O(n) O(n^2 ) O(2n) constant-time logarithmic linear quadratic exponential Sequential search Traveling Salesman (brute force) Modifying a 2D image

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

A Better Algorithm

Buttreeks, Maya 6 Maya Buttreeks

Not equal, but whaddaya know?

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

A Better Algorithm

Buttreeks, Maya 6 Maya Buttreeks

"Half" of the list is eliminated!

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

A Better Algorithm

Buttreeks, Maya 6 Maya Buttreeks

Not equal, but whaddaya know?

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

A Better Algorithm

Buttreeks, Maya 6 Maya Buttreeks

"Half" of the front "half"

is eliminated!

Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

But Wait…

Buttreeks, Maya 6 Ollie Tabooger 0 1 2 3 Problem, Bea O. Hugginkiss, Amanda Jass, Hugh Rotch, Mike Strappe, Jacques Tabooger, Ollie 4 5

But Wait…

Buttreeks, Maya 6 Ollie Tabooger

 Sequential search: 7 steps

 Binary search: 3 steps

Analyzing binary search

 Consider worst case for an array of size 32:

32 elements 16 elements 8 elements 4 elements 2 elements 1 element

Analyzing binary search

 Consider worst case for an array of size 32:

32 elements 16 elements 8 elements 4 elements 2 elements 1 element

 Ignore the last (1-element array) comparison

 Start with 32 elements

 5 comparisons total until found

 Note 2^5 = 32  log 2 32 = 5

 Log 2 of input size gives ~ number of comparisons

Sequential vs. Binary Search

 Sequential

 O(n): linear

 Easy to implement

 Inefficient for large input size

 Binary: O(log n)

 O(log n): logarithmic

 Reasonably efficient for large input size

 Requires the list to be sorted