The presentation outlines the merge sort algorithm, developed by John von Neumann in 1945, which sorts data by recursively dividing lists and merging them. It describes the merging process, its implementation options, and highlights that while merge sort has a time complexity of O(n log n), its memory requirements can be impractical for large datasets. Different variants of merge sorts exist, but the double memory version is commonly discussed, though it can be less efficient due to memory consumption.

1. Merge Sort
Presentation By: Soumen Santra
TINT

2. In the Beginning…
John von Neumann
(1903-1957)
 Stored program
 Developed merge
sort for EDVAC in
1945
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3. Merging
 The key to Merge Sort is merging two
sorted lists into one, such that if you
have two lists X (x1x2…xm) and
Y(y1y2…yn) the resulting list is
Z(z1z2…zm+n)
 Example:
L1 = { 3 8 9 } L2 = { 1 5 7 }
merge(L1, L2) = { 1 3 5 7 8 9 }
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4. Merging (cont.)
 The merge
Algorithm:
From The Art of
Computer
Programming
vol2: Sorting and
Searching
by Donald E.
Knuth
(page 160).
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5. Merging (cont.)
3 10 23 54 1 5 25 75
X: Y:
Result:
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6. Merging (cont.)
3 10 23 54 5 25 75
1
X: Y:
Result:
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7. Merging (cont.)
10 23 54 5 25 75
1 3
X: Y:
Result:
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8. Merging (cont.)
10 23 54 25 75
1 3 5
X: Y:
Result:
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9. Merging (cont.)
23 54 25 75
1 3 5 10
X: Y:
Result:
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10. Merging (cont.)
54 25 75
1 3 5 10 23
X: Y:
Result:
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11. Merging (cont.)
54 75
1 3 5 10 23 25
X: Y:
Result:
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12. Merging (cont.)
75
1 3 5 10 23 25 54
X: Y:
Result:
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13. Merging (cont.)
1 3 5 10 23 25 54 75
X: Y:
Result:
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14. Divide And Conquer
 Merging a two lists of one element each is
the same as sorting them.
 Merge sort divides up an unsorted list until
the above condition is met and then sorts the
divided parts back together in pairs.
 Specifically this can be done by recursively
dividing the unsorted list in half, merge
sorting the right side then the left side and
then merging the right and left back
together.
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15. Merge Sort Algorithm
Given a list L with a length k:
 If k == 1  the list is sorted
 Else:
◦ Merge Sort the left side (0 thru k/2)
◦ Merge Sort the right side (k/2+1 thru k)
◦ Merge the right side with the left side
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16. Merge Sort Example
99 6 86 15 58 35 86 4 0
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17. Merge Sort Example
99 6 86 15 58 35 86 4 0
99 6 86 15 58 35 86 4 0
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18. Merge Sort Example
99 6 86 15 58 35 86 4 0
99 6 86 15 58 35 86 4 0
86 15
99 6 58 35 86 4 0
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19. Merge Sort Example
99 6 86 15 58 35 86 4 0
99 6 86 15 58 35 86 4 0
86 15
99 6 58 35 86 4 0
99 6 86 15 58 35 86 4 0
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20. Merge Sort Example
99 6 86 15 58 35 86 4 0
99 6 86 15 58 35 86 4 0
86 15
99 6 58 35 86 4 0
99 6 86 15 58 35 86 4 0
4 0
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21. Merge Sort Example
99 6 86 15 58 35 86 0 4
4 0
Merge 11/3/2021 21
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22. Merge Sort Example
15 86
6 99 58 35 0 4 86
99 6 86 15 58 35 86 0 4
Merge 11/3/2021 22
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23. Merge Sort Example
6 15 86 99 0 4 35 58 86
15 86
6 99 58 35 0 4 86
Merge 11/3/2021 23
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24. Merge Sort Example
0 4 6 15 35 58 86 86 99
6 15 86 99 0 4 35 58 86
Merge 11/3/2021 24
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25. Merge Sort Example
0 4 6 15 35 58 86 86 99
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26. Implementing Merge Sort
 There are two basic ways to implement
merge sort:
◦ In Place: Merging is done with only the input array
 Pro: Requires only the space needed to hold the array
 Con: Takes longer to merge because if the next element
is in the right side then all of the elements must be
moved down.
◦ Double Storage: Merging is done with a temporary
array of the same size as the input array.
 Pro: Faster than In Place since the temp array holds the
resulting array until both left and right sides are merged
into the temp array, then the temp array is appended
over the input array.
 Con: The memory requirement is doubled.
 The merge sort in the text (ch7.6:p238-239) is an
example of a double array implementation with
Comparable objects.
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27. Merge Sort Analysis
The Double Memory Merge Sort runs O (N log N) for
all cases, because of its Divide and Conquer approach.
T(N) = 2T(N/2) + N = O(N logN)
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28. Finally…
There are other variants of Merge Sorts including k-
way merge sorting, but the common variant is the Double
Memory Merge Sort. Though the running time is O(N logN)
and runs much faster than insertion sort and bubble sort,
merge sort’s large memory demands makes it not very
practical for main memory sorting.
Important things to remember for the Midterm:
• Best Case, Average Case, and Worst Case = O(N logN)
• Storage Requirement: Double that needed to hold the array
to be sorted.
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29. MergeSort (Example) - 1
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30. MergeSort (Example) - 2
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31. MergeSort (Example) - 3
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32. MergeSort (Example) - 4
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33. MergeSort (Example) - 5
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34. MergeSort (Example) - 6
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35. MergeSort (Example) - 7
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36. MergeSort (Example) - 8
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37. MergeSort (Example) - 9
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38. MergeSort (Example) - 10
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39. MergeSort (Example) - 11
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40. MergeSort (Example) - 12
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41. MergeSort (Example) - 13
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42. MergeSort (Example) - 14
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43. MergeSort (Example) - 15
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44. MergeSort (Example) - 16
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45. MergeSort (Example) - 17
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46. MergeSort (Example) - 18
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47. MergeSort (Example) - 19
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48. MergeSort (Example) - 20
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49. MergeSort (Example) - 21
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50. MergeSort (Example) - 22
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51. 14 23 45 98 6 33 42 67
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52. Merge
23 45 98 33 42 67
14 6
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53. Merge
23 45 98 6 42 67
6
14 33
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54. Merge
14 45 98 6 42 67
6 14
23 33
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55. Merge
14 23 98 6 42 67
6 14 23
45 33
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56. Merge
14 23 98 6 33 67
6 14 23 33
45 42
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57. Merge
14 23 98 6 33 42
6 14 23 33 42
45 67
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58. Merge
14 23 45 6 33 42
6 14 23 33 42 45
98 67
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59. Merge
14 23 45 98 6 33 42 67
6 14 23 33 42 45 67
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60. Merge
14 23 45 98 6 33 42 67
6 14 23 33 42 45 67 98
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61. THANK YOU
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