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What is the time complexity of quick sort when

 (i) Choosing median of sorted array as pivot.
asked in DS by Veteran (54.9k points)   | 78 views

O(nlogn).

median element divides partitions into almost equall but not 1 and (n-1) [partitions]

but the array is sorted

if array is 1,2,3,4,5,6.(median =3) assume it divides into [1,2] 3  [4,5,6]

1 Answer

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Best answer

When we choose median as pivot , this means after applying partition the division into 2 subarrays is predefined that it will get divided into 2 halves..So recurrence relation for time will be :

          T(n)   =   2T(n/2) + O(n)  [ O(n) time is required for partition algorithm ]

==>    T(n)   =   θ(nlogn)  [ i.e. as division into subarrays is prespecified so worst case = best case = average case ]

Hence θ(nlogn) is the correct answer for the given scenario..

If however , we say central element is chosen as pivot..So it may go either at first or last or middle of array..So times will differ in that case and hence worst case will be O(n2)..

answered by Veteran (66.5k points)  
selected by
is there any difference between middle element and median elelment
As I said whenever we say median it means middle element of sorted array..But what is middle element for an unsorted array may not be the middle element of the sorted array..It may go elsewhere after applying partition algorithm..

Hope this lets u understand the difference..
ok tnks :)

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