Notes

Outline

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