CSC151.01 2006S, Class 44: Merge Sort

Admin:
* Reading for Friday: Quicksort.
* Are there questions on HW15?
* EC for tomorrow's convo.
* EC and free pizza for tomorrow's Thursday Extra.
* We'll spend a few minutes going over the insert! procedure.

Overview:
* insert!
* Key Ideas.
* Lab
* Reflection.

/Insertion Sort/

* Key idea in list-based insertion sort:  You insert a value that you've
  just prepared into a list that is already sorted.
* Parameters to insert
  * The value to insert
  * The sorted list into which to insert the value
  * THe may-precede? that determines the ordering of the list.
* Vector based insertion sort in which we work "in place" (modifying
  the vector)

+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| 2| 3| 7| 8|14|18| 1|17| 5|17|17|11|10| 7| 0| 5|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

* Idea: Insert into the beginning of the vector, in increasing order
* After a few steps, we've divided the vector into things that are
  sorted and things that aren't sored.

  sorted          |   unsorted
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| 2| 3| 7| 8|14|18| 1|17| 5|17|17|11|10| 7| 0| 5|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

After inserting 1
  sorted             |   unsorted
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| 1| 2| 3| 7| 8|14|18|17| 5|17|17|11|10| 7| 0| 5|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

After inserting teh 17

After inserting 1
  sorted                |   unsorted
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
| 1| 2| 3| 7| 8|14|17|18| 5|17|17|11|10| 7| 0| 5|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

We want to write this insertion procedure, called insert!

* Length of the vector or something similar (the length of the
  sorted region)
* value to insert (as in the list)
* vec (like the sorted list)
* may-precede?, which determines the ordering

/Merge Sort: Key Ideas?/

* Divide whatever you're trying to sort in half
* Sort the halves
* Put the sorted halves back together

/Lab/

* How do you decide whether (list "Jager" "Leah") or (list "Moore" "Tom")
  comes first?
  * Take the car, which gives you the last name
  * Compare the cars using string<?
* How would you express that in Scheme?
(define name<?
  (lambda (name1 name2)
    (string<? (car name1) (car name2))))

* How do you decide whether (list "Moore" "Ed") or (list "Moore" "Tom")
  comes first?
* How would that affect your previous expression?