Class 48: Merge Sort

Held: Wednesday, 25 November 2009

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:

• EBoard.
• Lab: Merge Sort.
• Reading: Merge Sort.

Notes:

• No reading for Monday. (I may distribute links to the project images so that we can better discuss project code on Monday.)
• I hope you have a wonderful Thanksgiving!

Overview:

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

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 N*log₂N 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.