How Can I Find Songs Quickly in My Music Library?

Transcription

1 How Can I Find Songs Quickly in My Music Library? Searching and Sorting Algorithms

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3 Learning Objectives Learn how to formulate searching and sorting problems in a way a computer can solve them, and understand the efficiency of the solutions.

4 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

5 Algorithms A series of steps to solve a problem in a general way

6 Algorithms

7 Algorithms

8 Algorithms sidenum = 1 while sidenum <= 5: alex.forward(100) alex.left(72) sidenum = sidenum + 1

9 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

10 Battleships Demo

11 In an ideal situation, which type of searching would be the fastest? Linear searching (the first one) Binary searching (the second one) Hash searching (the third one)

12 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

13 Linear Search given: an unsorted list of data to search given: a value to find set foundanswer to no set itemnumber to 0 while (foundanswer is no) and (haven t looked at all items): if value of item at itemnumber is equal to value to find: set foundanswer to yes else: increase itemnumber by 1 if foundanswer is yes: print itemnumber

14 Linear Search Works for sorted and unsorted lists Sometimes it s the only choice Can be really fast or really slow

15 Example: Find a CD when unsorted

16 Example: White pages reverse lookup

17 Example: Find the best fruit from the bin

18 Linear Search Demo undan/dsal/lsearch.html

19 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

20 Binary Search given: a sorted list of data to search given: a value to find set foundanswer to no set left to 0, right to listsize-1 while (foundanswer is no) and (left <= right): set mid to (left + ((right left) / 2)) if (item at mid) < (value to find): left = mid + 1 otherwise if (item at mid) > (value to find): right = mid 1 otherwise: set foundanswer to yes output mid

21 Binary Search Works only for sorted lists Always relatively fast Find your answer within log 2 (size of list) tries

22 Example: Find a CD when sorted

23 Example: Use name to find number

24 Example: Using the call number to find book

25 Binary Search Demos undan/dsal/bsearch.html e5eyflfr0

26 Linear vs. Binary Search

27 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

28 Hash Search given: a list of data separated into categories to search given: a value to find given: a way to hash a value into a category set hashvalue to what is obtained when hashing the search value set categorylist to the list of data inside category obtained via hashvalue use either linear or binary search on categorylist

29 Hash Search Works only if data can be categorized Speed depends on lists in categories (size and how well sorted)

30 Example: Narrow search by genre

31 Example: Narrow search by service

32 Example: Start in right area of store

33 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

34 Divide and Conquer

35 Which of these searching techniques best uses the divide-and-conquer idea? Linear searching Binary searching Hash searching

36 Unanswered question If searching sorted data is so much faster, why don t we just sort it first?

37 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

38 How do you sort when you can only compare two things?

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40 Sort Part One: Find the lightest bottle using the scale What is the easiest way to do this?

41 Sort Part Two: Choose three bottles at random Sort them using the scale What is the fewest number of comparisons you can do?

42 Sort Part Three: Sort all the bottles from lightest to heaviest by repeatedly finding the lightest bottle remaining, and moving it into the sorted list at the top This is known as Selection Sort

43 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

44 Finding the Smallest Item given: a list of data to find the minimum in set currentsmallestitem to first item in list while we haven t looked at all items in list: set compareitem to next item in list if compareitem < currentsmallestitem: save compareitem to currentsmallestitem

45 Selection Sort given: a list of data to sort set listsorted to an empty list set listremaining to the original list to be sorted while listremaining is not empty: set smallestvalue to the min value in listremaining add smallestvalue to the end of listsorted remove smallestvalue from listremaining

46 Selection Sort Dance on

47 Selection Sort Demo

48 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

49 Insertion Sort Take the leftmost bottle from the bottom Insert it into the correct location in the sorted list Do this by comparing the new item with each of the existing items (usually starting at the end) until the correct place is found This is known as Insertion Sort

50 Insertion Sort given: a list of data to sort set listsorted to an empty list set listremaining to the original list to be sorted while listremaining is not empty: set nextvaluetosort to the first item in listremaining add nextvaluetosort to the end of listsorted while (nextvaluetosort) <= (value to its left): swap nextvaluetosort with its neighbour to the left

51 Insertion Sort Dance tion

52 Insertion Sort Demo

53 Which type of sorting would be faster when the list is almost sorted? (Why?) Selection sort Insertion sort They are about the same speed

54 Searching Algorithms Demo Linear Search Binary Search Hash Search Divide-andconquer Sorting Comparisons + Demo Selection Sort Insertion Sort Quick Sort

55 Quick Sort

56 Quick Sort Demo

57 Quicksorting a Stack of Graded Papers Syr8o8jjwM

58 Selection Sort vs. Quicksort VMKXKoGu_Y

59 What would happen to quicksort if you picked the smallest value as the pivot every time? It would be faster It would be slower Nothing would change