Announcements

1
Announcements

• Reading for Thursday 14.3, 14.5 in 3rd Edition,
  19.3, 19.5 in 2nd Edition
• Quiz on Thursday (your last quiz!)
• Homework 10 due Friday (11/30) at 6pm
• Skeleton code is due today (11/27) at 1159pm
• There will be one more homework after this one
• Last class is next Tuesday (12/4)
• I will host a review session for the final on
  Wednesday (1240-230?)
• Your final is the last day of the semester,
  Friday 12/14 at 2pm

2
Searching Algorithms
3
The Search Problem

• Problem Statement
• Given an ordered set of data (e.g., an array) and
  a particular piece of data,
• Find the first occurrence of the particular piece
  of data in the ordered set.

4
The Search Problem

• Problem Statement, revisited
• Input
• A set of data (an array, ArrayList, LinkedList,
  )
• A single data element
• Output
• Position of the data element in the data set, or
• -1 if the element does not appear in the data set

5
An Example Search Problem

• Imagine flipping through the Yellow Pages,
  looking for a pizza place near you.
• Its pretty easy you just flip to the section
  for P, then look for Pi, then Piz, ,
  Pizza.
• Now imagine doing the reverse find the name of
  a business given just their phone number.
• What algorithm will find the number in the phone
  book?

6
Linear Search

• Input Array D, integer key
• Output first index of key in D,
• or -1 if not found
• For i 0 to end of D
• if Di equals key
• return i
• return -1

7
Linear Search for Phone Numbers

• Input Array D of Business objects,
• phone number key
• Output first index where keys phone
• number matches D, or -1 if not found

Business phone address name
For i 0 to end of D if Di.phone matches
key return i return -1
8
Exercise

• Implement a class called Business that includes a
  static method for finding the index of a
  particular business in an array of Businesses
  using linear search.
• Create fields for name, address, and phone number
• Create a linearSearch() method that finds a
  business in an array, given the phone number

9
What happens if our array is huge?

• Imagine finding a particular word on the Web
  (approximately 10,000,000,000 documents)
• Linear search would take a long time
• Two common faster search techniques are
• Indexing (used on the Web and in databases)
• Binary search
• Well discuss binary search because its simpler,
  but you can learn about indexing in later CIS
  classes

10
Binary Search Normal Phone Book Use

• Normally, when you search the phone book, you
  implicitly use the fact that its sorted.
• Binary search does the same thing, and it only
  works if your data (array) is sorted.

11
Exercise

• Modify your Business class so that the
  Arrays.sort() method will work on it
• What are the two things you need to do?
• Declare that the class implements the Comparable
  interface
• Implement the compareTo() method
• Make it sort the Businesses according to phone
  number

12
Binary Search Algorithm

• Input Sorted Array D, integer key
• Output first index of key in D, or -1 if not
  found
• left 0, right index of last element
• while left
• middle index halfway between left, right
• if Dmiddle matches key
• return middle
• else if key comes before Dmiddle // D is
  sorted
• right middle -1
• else
• left middle 1
• return -1

13
You guessed it Exercise

• Implement a binary search method in your Business
  class

14
How much faster is binary search?

• Way, way faster
• Assuming the array is already sorted
• But precisely how much?

15
Announcements

• Reading for Tuesday 8.5 in 3rd Edition, 9.5 in
  2nd Edition
• Homework 10 due Friday (11/30) at 6pm
• Homework 11 due Friday (12/7) at 6pm
• Last class is Tuesday (12/4)
• Your final is the last day of the semester,
  Friday 12/14 at 2pm
• I will host a review session for the final on
  Wednesday during lab (12/5, 1240-230) bring
  lots of questions!

16
Introduction to Computational Complexity
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How complex is a computation?

• Computational Complexity is the study of how fast
  programs are (or sometimes how much memory they
  use).
• For example
• Binary search on an array of size m takes about
  log2(m) steps.
• Linear search on an array of size m takes about m
  steps.
• Also
• BubbleSort on an array of size m takes about m2
  steps.
• MergeSort on an array of size m takes about m
  log2(m) steps.

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What do you mean, about?

• Comp. Scientists study how fast things are
  approximately.
• For example,
• Algorithm 1 takes 2 m steps
• Algorithm 2 takes 3 m 40 steps
• (for any array of size m)
• Then we say Algorithm 1 and 2 are both about the
  same!

19
Moores Law

• Manufacturers double the speed of computers
  roughly every 1.5 years.
• This has held true since the first computers
  (1950)
• So a factor of 2 difference in an algorithm
  doesnt really matter so much just wait a year!

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Defining approximately

• We say f(m) O(g(m)) if
• There are constants a and M such that
• This is called Big-O notation
• e.g., 3m 40 O(m)
• (read Big-O of m or O of m)
• Likewise, 2m O(m)
• So, 3m 40 and 2m are basically the same

22
Complexity Classes

• The Big-O notation helps us group algorithms into
  classes with similar speed
• For example, MergeSort and QuickSort both belong
  to the class with speed O(m log2(m))
• Common classes of algorithms