![SIMPLE MERGE SORT : The simple merge sort (or merge sort) technique closely follows the
divide –and-conqure paradigm.
let a list of n elements to be sorted with l and r being the position
of leftmost and rightmost element in the list.
The three tasks in this divided-and-conqure technique are as
followed :-
[
]
1. Divide :- Partition the list midway ,that is ,at (l+r)/2 into two
sub lists with (n/2) elements in each, if n is even or
[n/2] and [n/2]-1 element if n is odd .
2. Conquer :- Sort the two lists recursively using the merge sort.
3. Combine :- Merge the sort sub listed to obtain the sorted output.](https://image.slidesharecdn.com/mainds-140130082205-phpapp01/85/Marge-Sort-5-320.jpg)
![Combine
Conqure
Divide
l
r
.........................................................................
.
[(l+r)/2]
.................................. ..................................
.
.
Sort this left-part by merge sort Sort this right-part by merge sort
...................................
...................................
Merge the two list
Sorted List
Fig. Divide-and-conqure strategy in the merge
sort](https://image.slidesharecdn.com/mainds-140130082205-phpapp01/85/Marge-Sort-6-320.jpg)
![Algorithm Merge sort
Input :- An array A[l…r] where l and r are the lower and upper index
of A.
Output :- Array a[l…r] with all element arranged in ascending order .
Steps:
1. if(r<=l) then
2.
Return
3. else
4.
Mid=[(l+r)/2]
5.
MergeSort(A[l…mid])
6.
MergeSort(A[mid+1…r])
7.
Merge(A,L,mid,r)
8. Endif
9. Stop](https://image.slidesharecdn.com/mainds-140130082205-phpapp01/85/Marge-Sort-8-320.jpg)
Marge Sort
- 2. MERGE SORT : All sorting method based on merging can be divided into two broad categories :1. Internal merge sort 2. External merge sort. In internal merge sort , the lists under sorting are small and assumed to be stored in the high speed primary memory. There are two type of Internal merge sort :I. Simple merge sort. II. Two-way merge sort. In external merge sort, deals with very large lists of elements such that size of primary memory is not adequate to accommodate the entire lists in it. There are two type of External merge sort :I. Balanced two-way merge sort. II. Multi-way merge sort.
- 3. MERGE SORT INTERNAL MERGE SORT SIMPLE MERGE SORT TWO -WAY MERGE SORT EXTERNAL MERGE SORT BALANCED TWO-WAY MERGE SORT MULTI -WAY MERGE SORT
- 5. SIMPLE MERGE SORT : The simple merge sort (or merge sort) technique closely follows the divide –and-conqure paradigm. let a list of n elements to be sorted with l and r being the position of leftmost and rightmost element in the list. The three tasks in this divided-and-conqure technique are as followed :- [ ] 1. Divide :- Partition the list midway ,that is ,at (l+r)/2 into two sub lists with (n/2) elements in each, if n is even or [n/2] and [n/2]-1 element if n is odd . 2. Conquer :- Sort the two lists recursively using the merge sort. 3. Combine :- Merge the sort sub listed to obtain the sorted output.
- 6. Combine Conqure Divide l r ......................................................................... . [(l+r)/2] .................................. .................................. . . Sort this left-part by merge sort Sort this right-part by merge sort ................................... ................................... Merge the two list Sorted List Fig. Divide-and-conqure strategy in the merge sort
- 7. EX :I/P -> I/P -> 6 2 4 5 1 3 Merge Sort 6 2 Divide 4 5 1 3 Merge Sort Merge Sort Divide 6 Divide 2 4 Merge Sort Divide 6 5 6 1 5 Merge 1 Merge 2 4 5 6 3 1 Merge 1 Merge O/P -> Merge Sort Merge Sort 2 2 3 Divide 4 Merge Sort 1 Merge Sort Merge Sort 2 6 5 1 2 3 4 5 6 3 5
- 8. Algorithm Merge sort Input :- An array A[l…r] where l and r are the lower and upper index of A. Output :- Array a[l…r] with all element arranged in ascending order . Steps: 1. if(r<=l) then 2. Return 3. else 4. Mid=[(l+r)/2] 5. MergeSort(A[l…mid]) 6. MergeSort(A[mid+1…r]) 7. Merge(A,L,mid,r) 8. Endif 9. Stop
- 9. Two-Way Merge Sort : The two-way merge sort is based on the principle ‘burns the candle at both ends’ in manner similar to the scanning procedure. In the two-way merge sorting, we examine the input list from both the ends: Left and Right and moving toward the middle. (a) Source list Scan is done Ascending run at left i Stored merge sequneces j P Ascending run at right k Scan is done l q (b) Destination list Stored merge sequneces
- 10. EX :- 1 2 3 3 2 1 Input List-> A 44 99 57 63 77 55 88 22 96 33 11 66 Auxiliary List -> B 44 66 99 22 55 88 96 77 63 57 33 1 2 1 A B (a) After Pass 1 1 2 11 3 44 66 99 22 55 88 96 77 63 57 33 11 11 33 44 57 63 66 77 96 99 88 55 22 1 2 (b) After Pass 2 1 1 A 11 33 44 57 63 66 77 96 99 88 55 22 B 11 22 33 44 55 57 63 66 77 88 96 99 (c) After Pass 3 1 <- output List
- 11. BALANCED TOW-WAY MERGE SORT :- The balanced two-way merge is based on combining two ascending runs into a single ascending run. The merging-procedure can be applied to more than two runs at each time. That why it is two way merging. In external balanced two-way merge all intial intial runs of equal length possibly not the last run. This why the ‘ balanced’ tag is used in this technique.
- 13. Example :- Run :- A sorted segment of a file, which is termed as an ascending run or simply run.
- 15. MULTI-WAY MEGRE SORT : In multi-way merge sort , this procedure is extended to m-way merging , where m (m>2) runs are combined into a single run. In the multi-way merge sort , m input runs are stored on m tapes. Initially all element are in ascending order on all these tapes. In multi-way merge , we merge them together , that is ,we look at the first element of each run and select the smallest element. This smallest element tranferred to an output tape. This process is repeated till all runs are fully examined.
- 16. Example :- 11 44 66 88 T2 10 20 50 90 T3 15 35 55 75 T4 22 60 65 99 T1 4 input runs on tape 11 44 66 20 50 90 T3 15 35 55 60 65 (a) Initial Status 75 T4 22 Output Tape 88 T2 10 T 99 T1 4 input runs on tape T 10 Output Tape (b) After step 1
- 17. 11 44 66 88 T2 10 20 50 90 T3 15 35 55 75 T4 22 60 65 99 T1 T 10 11 Output Tape (c) After step 2 .... . . . . . . . . . . . . . . . . . . . . . 4 input runs on tape 11 44 66 88 T2 10 20 50 90 T3 15 35 55 75 T4 22 60 65 99 T1 T 10 11 15 20 22 35 44 50 55 60 65 66 75 88 90 99 Output Tape 4 input runs on tape (b) After step 16 Fig :- illustration of the multi-way merge
- 18. THANK YOU