CSC151 2007S, Class 45: Binary Search

Admin:
* EC for ...
  * Tonight's talk on mental health.
  * Some Pride Week activity, particularly the Saturday parade.
  * Thursday's convo.
  * Thursday's Thursday Extra (Dr. Davis).
* Are there questions on the project?
  * Do we have to squish our squares and circles?
    * I'd prefer that you do, unless you have good artistic reasons for 
      keeping aspect ratio
  * What is a nice size for images?
    * Well, we'll be putting them in digital frames, so 640x480 will
      probably work or 480x640
* There is no reading for Wednesday.

Overview:
* The problem of searching.
* Analyzing algorithmic efficiency.
* Making searching more efficient using divide-and-conquer.
* Lab.

==Searching==

* Given a collection of values, find one that meets some criterion
* How?  assoc gives a good model, at least for lists
  * Either (a) find the value or (b) run off the end
* If there are N values in the list, how many values do we expect
  to look at?
  * If we only look for things in the list, on average, we look at 
    N/2 values
  * If we only look for things not in the list, on average, we look at 
    N values

==Improving the Search==

* Can we do better than c*N?
* Yes, if we organize the data.
* Consider phone books, which are organized by name
  * Jump to "appropriate section"  
  * And then search there
* THe computer scientist's favorite technique: Divide-and-conquer
  * Break in half
  * SOlve for one or both halves

For binary search:
* Look in the middle, figure out if the thing you're looking for is 
  in the left half or the right half
* Throw away other half, and recurse
* Eventually, you find the thing in the middle, or run out of stuff

How long does it take to find something in a vector of 1000 values
* 1000
=> 500
=> 250
=> 125
=> 63
=> 32
=> 16
=> 8
=> 4
=> 2
=> 1

Ten steps to search through a list of 1000 people.
Eleven steps to search through a list of 2000 people.
Twelve steps to search through a list of 4000 people.
Twenty steps to search through a list of 1000000 people.

Name: Binary Search
Technique: Divide and conquer