CSC151 2007S, Class 48: Merge Sort

Admin:
* Quiz 9 returned (finally)
* Are there questions on Exam 3?
* EC for 
  * Attending the stats poster session Thursday at 11:00 in the Science elbow.
  * Thursday's Thursday extra (the last of the semester).
  * Collaborative THING tomorrow night Flanagan at 7:00ish
  * GIMP presents Children of Eden Thursday and Friday at 7:00, Sunday at 2:00
    * Children friendly
    * Free tickets in box office
    * Herrick
  * Javanese Music Ensemble Saturday at 2:00 in Sebring-Lewis
  * G-Motion Friday at 8:00 in Harris
  * Sunday: GC Triathalon
* It's 30-something this morning.  It's supposed to dip below freezing
  tonight.  Welcome to spring in Ioway.
* I'd like to hear your thoughts on the ad on p. 3 of Friday's S&B.
  We edit for structur

Overview:
* More efficient sorting techniques.
* Divide and conquer, revisited.
* Merge sort.
* Analyzing merge sort.
* Lab!

==Exam QUestions==

Q: On Problem 10, can we find the largest element by sorting and then
  taking the last element?
A: Clever, but NO!  Since we're using largest to implement a sorting
  algorithm

==Quiz==

(cons (cons 'banana (cons 'apple null)) 'orange)

(define myproc
  (lambda (tree)
    (if (pair? tree)
        (+ (myproc (car tree))
           (myproc (cdr tree))
        (if (equal? tree 'banana) 1 0)))))

==Sorting, Reviewed==

* Goal: Put things in order (in a list or vector)
* How do we determine the order?  With a procedure that compares two
  values
  may-precede?
(sort list-or-vector may-precede?)
* Our first sorting techniques took approximately N^2 comparisons

==More Efficient Sorting Techniques==

* When confronted with an N^2 algorithm, we ask "Can we do better?"
  * Technique one: Look for other algorithms
  * Technique two: Prove that you can't do better

==Divide and Conquer==

* In the merge sort technique, we split our data, sort the two halves,
  and join them
* How do we split a vector, anyway?
  * In the middle

==Merge Sort, Revisited===

==Analyzing Merge Sort==

* N*log2N
* AND THAT'S THE BEST YOU CAN DO IN A COMPARISON-BASED ALGORITHM