CSE 326: Data Structures
Sorting by Comparison

	Zasha Weinberg in lieu of Steve Wolfman
	Winter Quarter 2000

Sorting by Comparison algorithms

	Simple: Selection Sort
		(some say Insertion Sort, or Bubble Sort)
	Quick: QuickSort
	Good worst case:  MergeSort, HeapSort
	Can we do better?

Selection Sort idea

	Find the smallest element, put it first
	Find the next smallest element, put it second
	Find the next smallest, put it next
	etc.

Selection Sort

HeapSort: sorting with a priority queue ADT (heap)

QuickSort

QuickSort Partition

QuickSort Partition (cont’d)

QuickSort
Worst case

Dealing with Slow QuickSorts

	Randomly permute input
		Bad cases more common than simple probability would suggest.  So, make it truly random.
	Pick pivot cleverly
		“Median-of-3” rule takes Median(first, middle, last element elements).
	Use MergeSort or HeapSort.

QuickSort
Average Case

	Model expected # of operations
	Manipulate the recurrences
	Get O(n log n)
	(Weiss, p. 275-279)

MergeSort

MergeSort Running Time

Could we do better?*

	For any possible correct Sorting by Comparison alg
		What is lowest best case time?
		What is lowest worst case time?

Best case time

Worst case time

	How many comparisons does it take before we can be sure of the order?
	This is the minimum # of comparisons that any algorithm could do.

Decision tree to sort list A,B,C

Max depth of the decision tree

	How many leaves does the tree have?
	What’s the shallowest tree with a given number of leaves?

Stirling’s approximation

Eine kleine Nachmath