GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
73 views
What is the time complexity of quick sort when

 (i) Choosing median of sorted array as pivot.
asked in DS by Veteran (52.4k points)   | 73 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

+4 votes
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 (65.1k 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 :)

Related questions

0 votes
0 answers
1
asked in DS by vaishali jhalani Boss (6k points)   | 30 views


Top Users Mar 2017
  1. rude

    4272 Points

  2. sh!va

    2994 Points

  3. Rahul Jain25

    2804 Points

  4. Kapil

    2608 Points

  5. Debashish Deka

    2254 Points

  6. 2018

    1514 Points

  7. Vignesh Sekar

    1344 Points

  8. Akriti sood

    1262 Points

  9. Bikram

    1258 Points

  10. Sanjay Sharma

    1016 Points

Monthly Topper: Rs. 500 gift card

21,454 questions
26,775 answers
60,982 comments
22,994 users