Merge sort algorithm

Merge sort algorithm

• 1.
  Prepared by:- Sruti senpatra Merge sort
• 2.
  Definition:- Merge sort isone of the most efficient sorting algorithms. It works on the principle of Divide and Conquer. Merge sort repeatedly breaks down a list into several sub lists until each sub list consists of a single element and merging those sub lists in a manner that results into a sorted list. Divide and conquer rule:- A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
• 3.
  Algorithm(divide) Mergesort(A, lb ,ub,) { If(lb < ub) { Mid = lb+ub/2 Mergesort (A,lb,mid); Mergesort (A,mid+1,ub); Merge (A,lb,mid,ub) } }
• 4.
  Algorithm(Merge) Mergesort( A, lb, mid , ub) { i=lb; J=mid +1; K= lb; While ( i<=mid && j<=ub) { If(a[i]<=a[j]) { b[k]=a[i] i++;
• 5.
  Algorithm(merge) } Else b[k]=a[j] ; J++; } K++; }} If(i>mid) { while(j< =ub) B[k]=a[j]; J++; K++;
• 6.
  Algorithm(merge) } Else { While (i<=mid) B[k]=a[i]; i++; K++; } } For(k=lb; k<=ub ; k++) { a[k]= b[k]; }}
• 7.
  Time complexity:- Merge Sortis a recursive algorithm and time complexity can be expressed as following recurrence relation. T(n) = 2T(n/2) + n  Recurrence tree method:- Recursion Tree is another method for solving the recurrence relations. A recursion tree is a tree where each node represents the cost of a certain recursive sub-problem. We sum up the values in each node to get the cost of the entire algorithm.
• 10.
  The solution ofthe above recurrence is O(nLogn). The list of size N is divided into a max of Logn parts, and the merging of all sublists into a single list takes O(N) time, the worst-case run time of this algorithm is O(nLogn) Best Case Time Complexity: O(n*log n) Worst Case Time Complexity: O(n*log n) Average Time Complexity: O(n*log n) The time complexity of MergeSort is O(n*Log n) in all the 3 cases (worst, average and best) as the mergesort always divides the array into two halves and takes linear time to merge two halves.