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Algorithm Efficiency: Search, Analysis & Big O Notation

Explore Selection Sort & Binary Search algorithms, complexity analysis, Big O Notation, and coding examples in this informative lecture recap. Learn to analyze algorithm efficiency and compare linear vs. binary search techniques. Unlock the power of binary search for optimized data searching! Enjoy the journey of algorithm complexity analysis and time efficiency considerations.

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Algorithm Efficiency: Search, Analysis & Big O Notation

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  1. CMPT 120 Lecture 32 – Unit 5 – Internet and Big Data Algorithm – Searching and Complexity Analysis

  2. Review - Selection Sort Algorithm How it works: • Repeatedly selects the next smallest (or largest) element from the unsorted section of the list and swaps it into the correct position in the already sorted sectionof the list: for index = 0 to len(data) – 2 do select: let x = location of element with smallest value in data from index to len(data) – 1 if index != x swap: tempVar = data[index] data[index] = data[x] data [x] = tempVar

  3. Review - Selection Sort Function • https://repl.it/repls/ParallelMindlessPresses

  4. Last Lecture – Little Activity • The story of Jean-Dominique Bauby • locked-in syndrome(due to a stroke) which almost completely paralyzed him … he could only blink one eye • Yet, Bauby, with the help of a speech therapist, “wrote” the book The Diving Bell and the Butterfly

  5. One possible solution • Bauby wants to “write” the word elephant • Question 1: does the word start with a letter < M? • Answer 1: 1 blink -> Yes - So we can ignore ½ of the alphabet: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z • Question 2: does the word start with a letter < F? • Answer 2:1 blink -> Yes - So we can ignore ½ of ½ of the alphabet: A B C D E F G H I J K L • Question 3: does the word start with a letter < C? • Answer 3: 2 blinks -> No - So we can ignore ½ of ½ of ½ of the alphabet: A B C DE • Question 4: does the word start with a letter < D? • Answer 4: 2 blinks -> No -So we can ignore ½ of ½ of ½ of ½ of the alphabet:CD E • Question 5: does the word start with the letter D? • Answer 5: 2 blinks -> No • Question 6: does the word start with the letter E? • Answer 6: 1 blink -> Yes - Bingo!

  6. This solution has a name … … Binary search algorithm

  7. Another example • Suppose we have a sorted list • Using Binary Search algorithm, we can search for target = 7 without having to look at every element 1 3 4 7 9 11 12 14 21

  8. How binary search works – In a nutshell • Binary search uses the fact that the datais sorted! • Find element in the middle -> 9 • Since we are looking for 7 and 7 != 9 and 7 < 9, then there is no need to search the second half of the list • We can ignore half of the list right away! • Then we repeat the above steps • Bottom line: using binary search, we do not need to look at every element to search a list • So binary search is moretime efficient than linear search

  9. Visualising Binary Search • http://www.cs.armstrong.edu/liang/animation/web/BinarySearch.html

  10. Let’s look at some code! • https://repl.it/repls/GlaringRemoteBookmarks

  11. Algorithm Complexity The amount of resources (time and space) required to execute an algorithm

  12. So, which is fastest? • In order to answer this question, we need to analyze the complexity of these two algorithms (or code) • Once we have done so, we express it using something called the Big O Notation • In this course, we shall focus on the time required to run an algorithm Linear search or binary search?

  13. How to do Complexity Analysis? Actually, we are interested in 1 particular operation that is common to both algorithms: • We analyze thetime an algorithm requires to execute • by counting the number of operations it executes • when the algorithm executesthe worst-case scenario What on earth is that?

  14. Worst-Case Scenario • Remember this slide in Lecture 29

  15. Let’s give this a go! How many comparison operations are performed in linear search?

  16. Let’s give this a go! How many comparison operations are performed in binary search?

  17. Log2 n Pattern Binary Search Algorithm At each iteration: • We compare the middle element with target and if target not found • We partition the list in half, ignoring one half and searching the other Size of data in 1st iteration: n Size of data in 2nd iteration : n/2 D Size of data in 3rd iteration : n/4 Size of data in Tth iteration : 1

  18. Log2 n Pattern (cont’d) Note, on this slide, N is used instead of n. D

  19. Big O Notation Expresses time complexity of algorithms (also called algorithm “efficicency”)as they execute worst-case scenarios

  20. Big O Notation O(n) - Linear search O(log n) - Binary search https://en.wikipedia.org/wiki/Big_O_notation

  21. A smart music app Let’s have some fun! https://repl.it/repls/ShortEducatedSearchengine

  22. End-of-Semester Party The end-of-semester party is coming up! To prep this party, we need to build our playlist -> most “danceable” songs. Problem Statement: Let’s say we want to build an application that searches for most danceable songs from our favourite musical artist.https://repl.it/repls/ShortEducatedSearchengine Download the dataset: https://goo.gl/KAYTuf (sourced from https://www.kaggle.com/nadintamer/top-tracks-of-2017/data)

  23. Spotify Music Data

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