CSC153 2004S, Class 26: "Fast" Sorting Algorithms

Admin:
* Cool convo today.  Go.  Enjoy.  Think.
* Questions on exam 2?
* Exam 1 graded!
  * Problem 1: Ratio of longest/shortest: 4
  * Problem 2: 4.5
  * Problem 3: 5.5
  * Problem 4: 10
* We'll return to continuations on Friday (our last Scheme day).
* Did you hear the lastest SCO news?

Overview:
* Consider how to apply the "divide and conquer" technique to sorting
* Key ideas in merge sort.
* Key ideas in Quicksort
* Lab 

/Notes on Exam 1/
* Don't use multi-line end-of-line comments!!!!!!!!!
        ; This is a procedure that does some really
        ; cool stuff
	(define my-silly-proc    ; This is a procedure
	  (lambda (whatever)     ;   that does some really
            (display "xxx")
	    (if (test whatever whatever)  ;   wonderful stuff

	if (test)	/* test for
	  foo;           * an important condition */
	bar;
* Work on those 6 P's, particularly the postconditions.
	;;; Procedure:
	;;;   A DESCRIPTION OF THE PROCEDURE
	;;; 
  * Deal with it!
* Document your strategies!
  (letrec kernel ((stuff (reverse lst))
                  (base 1))
     (if (null? stuff)
         0
         (+ (* base (car stuff)) (kernel (cdr stuff) (* base 10)))))
* Style (see problem 4 in exam1.scm)
	(if (= (length (car collection)) 3)
    	    #t
            #f)
is the same as
	(= (length (car collection)) 3)
Similarly
	(if (test1)
            (test2)
            #f)
is the same as
	(and (test1) (test2))
Fixing code
	(letrec ((verify? (lambda (collection)
	                    (and (list? collection)
                                 (list? (car collection))
                                 (= (length (car collection)) 3)
                                 (or (null? (cdr collection))
                                     (verify? (cdr collection)))))))

	Running time of verify? in big-O
		time-verify(n) = time-listp(n)
                               + time-listp(element)
                               + time-length(element)
                               + time-verify(n-1)
		time-verify(n) = cn
                               + 3
                               + 3
                               + time-verify(n-1)

		f(n) = n + k + f(n-1)
		f(n) = n + k + n-1 + k + f(n-2)
		f(n) = n + n-1 + 2k + f(n-2)
		f(n) = n + n-1 + n-2 + 3k + f(n-3)
		f(n) = (n + n-1 + n-2 + ... n-m+1) + mk + f(n-m)
	When m=n
		f(n) = (n + n-1 + n-2 + ... 1) + nk + f(0)
	Assume f(0) = 0
		f(n) = (n + n-1 + n-2 + ... 1) + nk 
		f(n) = n(n+1)/2 + nk
		f(n) in O(n^2)
	Fix it by not asking whether it's a list at every step!
* Consider efficiency
* Remember built-in procedures
	string-ci<?
	caar cadr cdar