1. MergeSort
CSC 172

2. Sorting Lists with MergeSort
Note: a list of length 1 is sorted
If two lists are sorted, how can you combine them into one sorted list?
How can you divide one list into two?

3. Recursive Mergesort Basis: A list of length 1 is sorted
Induction: for lists of >= 1 element
Split the list into two equal (as possible) parts
Recursively sort each part
Merge the result of the two recursive sorts
One at a time, select the smaller element from the two fronts of each list
Physical demo

4. Node split public static Node split(Node head){ Node secondNode;
if (head == null) return null;
else if (head.getNext() == null) return null;
else {
secondNode = head.getNext();
head.setNext(secondNode.getNext());
secondNode.setNext(split(secondNode.getNext());
return secondNode; }

5. A linked List 6 1 3 2 5 9 

6. A linked List in Split
Split
head 6 1 3 2 5 9 

7. A linked List in Split secondNode = head.getNext(); Split 0
head secondNode 6 1 3 2 5 9 

8. A linked List in Split head.setNext(secondNode.getNext()); Split 0
head secondNode 6 1 3 2 5 9 

9. First recursive call in Split
secondNode.setNext(split(secondNode.getNext());
Split 0
head secondNode 6 1 3 2 5 9 

10. New Split split(secondNode.getNext()); Split 1 head secondNode 6 1 3 25 9 

11. New Split head.setNext(secondNode.getNext()); Split 1 head secondNode6 1 3 2 5 9 

12. Second recursive Split
secondNode.setNext(split(secondNode.getNext());
Split 1
head secondNode 6 1 3 2 5 9 

13. Second recursive Split
secondNode.setNext(split(secondNode.getNext());
Split 2
head secondNode 6 1 3 2 5 9 

14. Second recursive Split
head.setNext(secondNode.getNext());
Split 2
head secondNode 6 1 3 2 5  9 
secondNode.setNext(split(secondNode.getNext()); ?
What gets returned?
return secondNode;

15. Backing up secondNode.setNext(split(secondNode.getNext()); Split 1
head secondNode 6 1 3 2 5  9 

16. Backing up secondNode.setNext(split(secondNode.getNext()); Split 1
head secondNode 6 1 3 2 5  9 
What gets returned?
return secondNode;

17. Backing up secondNode.setNext(split(secondNode.getNext()); Split 1
head secondNode 6 1 3 2 5  9 
What gets returned?
return secondNode;

18. Backing up secondNode.setNext(split(secondNode.getNext()); Split 1
head secondNode 6 1 3 2 5  9 
What gets returned?
return secondNode;

19. Node Merge public static Node merge(Node list1, Node list2){
if (list1 == null) return list2;
else if (list2 == null) return list1;
else if (list1.getData.compareTo(list2.getData()) < 0) {
list1.setNext(merge(list1.getNext(),list2);
return list1;
} else {
list2.setNext(merge(list1,list2.getNext());
return list2; }

20. Two linked Lists 1 3 7  2 8 9 

21. Two linked Lists in merge1 3 7 
list1
merge 0
list2 2 8 9 

22. Two linked Lists in merge
0th 1 3 7 
list1
merge 1
list2 2 8 9 

23. Two linked Lists in merge
0th 1 3 7 
list1
merge 2
list2 2 8 9 
1st

24. Two linked Lists in merge
0th
2nd 1 3 7 
list1
merge 3
list2 2 8 9 
1st

25. Two linked Lists in merge
0th
2nd
3rd 1 3 7  
list1
merge 4
list2 2 8 9 
1st

26. Two linked Lists in merge
0th
2nd 1 3 7
list1
merge 3
list2 2 8 9 
1st

27. Two linked Lists in merge
0th
2nd 1 3 7
list1
merge 2
list2 2 8 9 
1st

28. Two linked Lists in merge
0th
2nd 1 3 7
list1
merge 2
list2 2 8 9 
1st

29. Two linked Lists in merge
0th
2nd 1 3 7
list1
merge 0
list2 2 8 9 
1st

30. Node MergeSort public static Node mergeSort(Node list){
Node secondList;
if (list == null) return null;
else if (list.getNext() == null) return list;
else {
secondList = split(list);
return merge(mergeSort(list),mergeSort(secondList)); }

31. Mergesort 3 1 4 1 5 9 2 6

32. Mergesort: Split 6 3 1 4 1 5 9 2

33. Mergesort: Split 6 3 1 4 1 5 9 2

34. Mergesort: Split 9 6 3 1 4 1 5 2

35. Mergesort: Split 9 6 3 1 4 1 5 2

36. Mergesort: Split 1 9 6 3 1 4 5 2

37. Mergesort: Split 1 9 6 3 1 4 5 2

38. Mergesort: Split 1 1 9 6 3 4 5 2

39. Mergesort: Split 1 1 9 6 3 4 5 2

40. Mergesort: Split 6 1 1 9 3 4 5 2

41. Mergesort: Split 6 1 1 9 3 4 5 2

42. Mergesort: Split 1 6 1 9 3 4 5 2

43. Mergesort: Split 1 6 1 9 3 4 5 2

44. Mergesort: Split 6 1 1 9 3 4 5 2

45. Mergesort: Split 6 1 1 9 3 4 5 2

46. Mergesort: Merge 6 1 1 9 3 4 5 2

47. Mergesort: Merge 6 1 1 9 3 4 5 2

48. Mergesort: Merge 1 6 1 9 3 4 5 2

49. Mergesort: Split 1 6 1 9 3 4 5 2

50. Mergesort: Split 1 6 9 1 3 4 5 2

51. Mergesort: Split 1 6 9 1 3 4 5 2

52. Mergesort: Merge 1 6 9 1 3 4 5 2

53. Mergesort: Merge 1 6 9 1 3 4 5 2

54. Mergesort: Merge 1 6 1 9 3 4 5 2

55. Mergesort: Merge 6 1 1 9 3 4 5 2

56. Mergesort: Merge 6 1 1 9 3 4 5 2

57. Mergesort: Merge 1 1 6 9 3 4 5 2

58. Mergesort: Merge 1 1 6 9 3 4 5 2

59. Mergesort: Split 1 1 6 9 3 4 5 2

60. Mergesort: Split 1 1 6 9 2 3 4 5

61. Mergesort: Split 1 1 6 9 2 3 4 5

62. Mergesort: Split 1 1 6 9 4 2 3 5

63. Mergesort: Split 1 1 6 9 4 2 3 5

64. Mergesort: Split 1 1 6 9 2 4 3 5

65. Mergesort: Split 1 1 6 9 2 4 3 5

66. Mergesort: Merge 1 1 6 9 2 4 3 5

67. Mergesort: Merge 1 1 6 9 2 4 3 5

68. Mergesort: Merge 1 1 6 9 2 4 3 5

69. Mergesort: Split 1 1 6 9 2 4 3 5

70. Mergesort: Split 1 1 6 9 2 4 5 3

71. Mergesort: Split 1 1 6 9 2 4 5 3

72. Mergesort: Merge 1 1 6 9 2 4 5 3

73. Mergesort: Merge 1 1 6 9 2 4 5 3

74. Mergesort: Merge 1 1 6 9 2 4 3 5

75. Mergesort: Merge 1 1 6 9 4 2 3 5

76. Mergesort: Merge 1 1 6 9 4 2 3 5

77. Mergesort: Merge 1 1 6 9 2 3 4 5

78. Mergesort: Merge 1 1 6 9 2 3 4 5

79. Mergesort: Merge 1 6 9 1 2 3 4 5

80. Mergesort: Merge 6 9 1 1 2 3 4 5

81. Mergesort: Merge 6 9 1 1 2 3 4 5

82. Mergesort: Merge 6 9 1 1 2 3 4 5

83. Mergesort: Merge 6 9 1 1 2 3 4 5

84. Mergesort: Merge 6 9 1 1 2 3 4 5

85. Mergesort: Merge 1 1 2 3 4 5 6 9