Marge Sort

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Merge sort in Detail

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Marge Sort

  1. 1. ANKIT S. CHITNAVIS
  2. 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. 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
  4. 4. 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.
  5. 5. 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
  6. 6. 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
  7. 7. 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
  8. 8. 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
  9. 9. 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
  10. 10. 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.
  11. 11. Example :- Run :- A sorted segment of a file, which is termed as an ascending run or simply run.
  12. 12. 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.
  13. 13. 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
  14. 14. 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
  15. 15. THANK YOU

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