CSC151.01 2006S, Class 45: Quicksort

Admin:
* Due: HW15.
* Assigned: HW16 (the last part of this lab).
  *** HW16 is the last homework for 151 ***
* Reading: Variable-Arity Procedures.
* Post-Preregistration hints
* Today's prospies:
  * Alex
    * Is it warmer there?  "Eeeh"
    * Where else: Pomona, UC Bezerkeley
  * TJ
    * Is it warmer there?  "Oh yeah"
    * Lewis and Clark (in Oregon) (as opposed to the many other
      Lewis's and Clarkses)

Overview:
* The key ideas of Quicksort.
* Lab.

/Key Ideas/

* Split lists (yay "Divide and conquer")
* Split using a "random pivot"
  * A random border between left and right
  * Into things that are smaller than the pivot and larger than the pivot
  * Simulates the median
* What is the median?
  * The one in the middle of a sorted list
  * The one for which half the numbers are smaller and half are larger
  * Whoops, hard to compute

/Lab/

Observation: When we insertion-sort a list of 50 values, it does about
666 calls to the may-precede? procedure. Why?

* Why is it so large?
* Why does it vary?

* BG: How does insertion sort work?
* We have a sorted list and an unsorted list and repeatedly
  insert into the sorted list.

  * Suppose there are k elements in the sorted list.  How many times
    do we call may-precede? to insert.
    * On average, k/2
    * But it varies depending on where in the list the value gets inserted.
    * For a list of length 50 ...
      0 + 1/2 + 2/2 + 3/2 + 4/2 + ... + 49/2

      (50*49/2)/2  approximately 2500/4 approximately 625