CSC297.Java, Class 27: Sorting

Admin:
* Did you do your Homework?
  * Some of it
  * Let's fix the problems with Yvonne's work
* New homework
  * Carefully write the preconditions for sort, swap, findSmallest

Overview:
* Selection sort
  * Analysis
* Insertion sort

Morals from Selection Sort
* The comparator should be a parameter of the sorting algorithm (and of the "find smallest").
* Be careful about boundary conditions
* Selection sort is typically an "in place" algorithm

Asymptotic Analysis

; Selectionsort
;   Use "N" for length
for i = 0 to length -1 do			N repetitions
  swap(i, findSmallest(starting at i))		1 for swap
						N for findSmallest
Running time is N*(N+1) is in O(N^2)

Two perspectives:
* At worst, findSmallest takes N
* Alex's findSmallest takes decresasing amounts N + N-1 + N-2 + ...
* Still gives is O(N^2)

Insertion Sort
* Divide your world into "stuff that's in order" and "stuff that's not in order"
* Repeatedly remove one item from "stuff that's not in order" and put it in the right place in "stuff that's in order".
* How do we do this with arrays?
* Choose an index that serves as the boundary between "ordered" and "not ordered".
* Repeatedly increase that index and "fix things up"

Analysis
for i = 0 to n-1	N repetition
  insert(i)		N steps
O(N^2(