1. Merge Sort

2. Divide And Conquer
Merging 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 left side then the right side and then merging the left and right back together.

3. Mergesort Example 8 2 9 4 5 3 1 6 Divide 8 2 9 4 5 3 1 6 Divide 8 2
Divide
8 2
9 4
5 3
1 6
Divide
1 element
Merge
Merge
Merge

4. Merge Sort – Example
Original Sequence
Sorted Sequence 18 26 32 6 43 15 9 1 18 26 32 6 43 15 9 1 1 6 9 15 18 26 32 43 18 26 32 6 18 26 32 6 43 15 9 1 43 15 9 1 6 6 18 18 26 26 32 32 1 1 9 9 15 15 43 43 18 26 18 26 32 6 32 6 43 15 43 15 9 1 9 1 18 18 26 26 6 6 32 32 15 15 43 43 1 1 9 9 18 26 32 6 43 15 9 1 18 26 32 6 43 15 9 1 18 18 26 26 32 32 6 6 43 43 15 15 9 9 1 1 18 26 32 6 43 15 9 1 18 26 32 6 43 15 9 1

5. Divide-and-conquer Technique
a problem of size n
subproblem 1
of size n/2
subproblem 2
of size n/2
a solution to
subproblem 1
a solution to
subproblem 2
a solution to
the original problem

6. Using Divide and Conquer: Mergesort strategy
first
last
(first  last)2
Sorted
Sort recursively by Mergesort
Sorted
Merge

7. Merge Sort Algorithm
Divide: Partition ‘n’ elements array into two sub lists with n/2 elements each
Conquer: Sort sub list1 and sub list2
Combine: Merge sub list1 and sub list2

8. Merge Sort Example 99 6 86 15 58 35 4

9. Merge Sort Example 99 6 86 15 58 35 4 99 6 86 15 58 35 86 4

10. Merge Sort Example 99 6 86 15 58 35 4 99 6 86 15 58 35 86 4 99 6 86 15 58 35 86 4

11. Merge Sort Example 99 6 86 15 58 35 4 99 6 86 15 58 35 86 4 99 6 86 15 58 35 86 4 99 6 86 15 58 35 86 4

12. Merge Sort Example 99 6 86 15 58 35 4 99 6 86 15 58 35 86 4 99 6 86 15 58 35 86 4 99 6 86 15 58 35 86 4 4

13. Merge Sort Example 99 6 86 15 58 35 86 4
Merge 4

14. Merge Sort Example 6 99 15 86 35 58 4 86 99 6 86 15 58 35 86 4
Merge

15. Merge Sort Example 6 15 86 99 4 35 58 86 6 99 15 86 35 58 4 86
Merge

16. Merge Sort Example 4 6 15 35 58 86 99 6 15 86 99 4 35 58 86
Merge

17. Merge Sort Example 4 6 15 35 58 86 99

18. Program
void MS::get_data() { cout<<"\n Enter the length of the list"; cin>>n; cout<<"\n Enter the list elements: \n"; for(int i = 0; i<n; i++) cin>>A[i]; } void MS::Mergesort(int low, int high) int mid; if(low<high) mid = (low+high)/2; //split the list at mid Mergesort(low, mid); //first sublist Mergesort(mid+1, high); //second sublist Combine(low, mid, high); //merging two sublists
#include<iostream.h> #include<conio.h> class MS { private: int A[10]; public: int n; int low, high; void get_data(); void Mergesort(int low, int high); void Combine(int low, int mid, int high); void Display(); };

19. Program
void MS::Combine(int low, int mid, int high) { int i,j,k; int temp[10]; i = low; j = mid+1; k = low; while(i <= mid && j <= high) if(A[i] <= A[j]) temp[k] = A[i]; i++; k++; } else temp[k] = A[j]; j++;
while(i<=mid) { temp[k] = A[i]; i++; k++; } while(j<=high) temp[k] = A[j]; j++; for(k = low; k <= high; k++) A[k] = temp[k];

20. Program
int main() { MS obj; obj.get_data(); obj.low=0; obj.high=(obj.n)-1; obj.Mergesort(obj.low, obj.high); obj.Display(); getch(); return 0; }
void MS::Display() { cout<<"\n The sorted array is:\n"; for(int i = 0; i<n; i++) cout<<" "<<A[i]; }

21. Time Complexity Analysis
Worst case: O(nlog2n)
Average case: O(nlog2n​​)
Best case: O(nlog2n​​)