Held: Tuesday, 8 December 2015

Back to Outline 53 - Insertion Sort. On to Outline 55 - Recap.

Summary

We continue our exploration of sorting by considering the applicability of divide-and-conquer to the problem of sorting. We look at one particular divide-and-conquer algorithm, merge sort. We explore how the running time for that algorithm varies based on the number of values we are sorting.

Related Pages

• Reading: Merge Sort
• Lab: Merge Sort
• EBoard 54 (Source 54)

Overview

• More efficient sorting techniques.
• Divide and conquer, revisited.
• Merge sort.
• Analyzing merge sort.

Administrivia

• Continue partners.
• Please make sure to attend class on Wednesday and Friday this week.
  I consider those days particularly important.
• Review sessions Wednesday at 8 p.m., Thursday at 10 a.m., Thursday at 8 p.m. A chance to ask about the sample final (except for nest).

Upcoming Work

• No more readings!
• No more lab writeups!
• Exam 4 cover sheet due Tuesday, Dec. 8. NOW
• Exam 4 epilogue due Tuesday, Dec. 8. TONIGHT

Extra Credit Opportunities

Academic

• CS Table, Today, 3821. Bring your own lunch. Discuss cartoons with fun people.
• Any visit to the current show in the Faulconer gallery.
• "Summer Opportunities in CS", Thursday at 4:15 p.m.

Peer Support

• Women's Basketball vs. Carroll, Saturday, Dec. 12 at 3:00 p.m.

Key Ideas of Merge Sort

• Divide and conquer is often a useful design strategy.
• For sorting, natural division is "first half" / "second half".
• What do we do after sorting the two halves? Merge 'em.

An Alternate Implementation

• We can do something very much like merge sort while avoiding the splitting step.
• We start with a list of sorted lists, and repeatedly merge neighboring pairs.
• This technique is slightly easier to implement.
• This technique is much easier to analyze.

The Costs of Merge Sort

• What's the running time? We do approximately Nlog₂N* comparisons.
• The analysis:
  • N steps to merge 2 sorted lists of length N/2
  • N steps to merge 4 sorted lists of length N/4 into those two sorted lists.
  • N steps to merge 8 sorted lists of length N/8 into those four sorted lists.
  • And so on and so forth.
• Can we do better? Not if our sorting is based on comparing values to each other.

Lab

• Do the lab
• Pause to reflect.