CSC151.01 2006S, Class 40: Binary Search

Admin:
* No reading for Friday.
* But there is homework for Friday!
  Given the following structure
  (list
    (list "Be Mean To Elementary Kids" (list 'emilyson 'richpat))
    (list "Fans of Rat-like Creatures" (list 'emilyson 'docdavis))
   )
* Thursday extra tomorrow on the GIMP.  EC for attending.
  Free pizza.

Overview:
* About common algorithms.
* Searching.
* Binary search.
* Lab.

/What is computer science?/

* The study of algorithms
* Algorithm: A way/method/process/set of instructions to solve a problem
  * Why called this?  Expect a pop quiz on it
* We write algorithms (yes, you've been writing them)
* Often: 
  * Look for problems
  * Model the problem
  * Solve the modeled problem
* Better:
  * Look for classes of problems
  * Model the class
  * Solve the class

/Searching/

* Given a collection of "keyed records" (chunks of information with a
  designated key), find ones with a matching key.
* Write good, general solutions to this problem
  * assoc
* Write efficient solutions to this problem

/Binary Searching/

* If the "keyed records" are stored in a vector and are organized by
  key from smallest to largest, we can do something more efficient.
* For the Chicago yellow pages, we certainly don't want to read each
  name in sequence.
* For the computer, one technique is to keep track of the range of the
  vector in which it falls (it must be after here and before here)
* How much does this save?
  * Consider the Chicago phone book: 700 pages, 200 per page
    140,000.  Say 2,000,000
    2,000,000
    -> 1,000,000
    -> 500,000
    -> 250,000
    -> 125,000
    -> 64,000
    -> 32,000
    -> 16,000
    -> 8,000
    -> 4,000
    -> 2,000
    -> 1,000
    -> 512
    -> 256
    -> 128
    -> 64
    -> 32
    -> 16
    -> 8
    -> 4
    -> 2
    -> 1