Merge SortIt closely follows the divide & Conquers paradigm. Conceptually, it works as follows:
The Main purpose is to sort the unsorted list in nondecreasing order. ALGORITHMMERGE SORT 1. If p<r 2. Then q ← ( p+ r)/2 3. MERGESORT (A, p, q) 4. MERGESORT ( A, q+1,r) 5. MERGE ( A, p, q ,r) The following figure illustrates the dividing (splitting) procedure. FUNCTIONS: MERGE (A, p, q, r) 1. n 1 = qp+1 2. n 2= rq 3. create arrays [1.....n 1 + 1] and R [ 1.....n 2 +1 ] 4. for i ← 1 to n 1 5. do [i] ← A [ p+ i1] 6. for j ← 1 to n2 7. do R[j] ← A[ q + j] 8. L [n 1+ 1] ← ∞ 9. R[n 2+ 1] ← ∞ 10. I ← 1 11. J ← 1 12. For k ← p to r 13. Do if L [i] ≤ R[j] 14. then A[k] ← L[ i] 15. i ← i +1 16. else A[k] ← R[j] 17. j ← j+1 In this method, we split the given list into two halves. Then recursively analyzing merge sort and dividing. We get many sorted lists. At last, we combine the sorted lists. Analysis of Merge Sort:Let T (n) be the total time taken in Merge Sort
So, the relational formula becomes But we ignore '1' because the element will take some time to be copied in merge lists. So T (n) = 2T + n.........equation 1 Note: Stopping Condition T (1) =0 because at last there will be only 1 element left which need to be copied and there will be no comparison.Put 2 equation in 1 equation Putting 4 equation in 3 equation From Stopping Condition: Apply log both sides: log n=log_{2}i From 6 equation
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