Merge Sort

1
Merge Sort
2
Outline

• Prerequisites
• Insertion Sort
• Merge
• Objectives
• Understand Merge Sort
• Reference

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Background

• Sorting takes an unordered collection and makes
  it an ordered one.
• Insertion Sort can be terribly slow for large
  data sets.

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Divide and Conquer

• Divide and Conquer cuts the problem in half each
  time, but uses the result of both halves
• cut the problem in half until the problem is
  trivial
• solve for both halves
• combine the solutions

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Merge Sort

• A divide-and-conquer algorithm
• Divide the unsorted list into 2 halves until the
  sub-lists are empty
• Merge the sub-problem solutions
• Compare the sub-lists first elements
• Remove the smallest element and put it into the
  result list
• Continue the process until all elements have been
  put into the result list

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How to Remember Merge Sort?
7
How To Remember Merge Sort?
(q,t)
Just as Mariah recursively moves her hands into
smaller circles, so too does merge sort
recursively split an array into smaller segments.

We need two such recursions, one for each half of
the split array.
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Algorithm

• Merge-sort(Passed list of numbers)
• if array size 1
• Divide list in half
• Call merge-sort on first half.
• Call merge-sort on second half.
• Merge two halves.
• Merge(Passed two lists)
• Compare leading element in each list
• Select lower and place in new list.
• (If one input list is empty then place
• remainder of other list in output list)

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50
Summary

• Divide the unsorted collection into two
• Until the sub-lists only contain one element
• Then merge the sub-problem solutions together

51
Merge-sort.scm
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Questions?
53
Summary

• You should now know
• Merge Sort

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