First time here? Checkout the FAQ!
+1 vote
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


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 (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 :)

Related questions

0 votes
0 answers
asked in DS by vaishali jhalani Boss (6k points)   | 35 views

Top Users Jun 2017
  1. Bikram

    3912 Points

  2. Arnab Bhadra

    1526 Points

  3. Hemant Parihar

    1502 Points

  4. Niraj Singh 2

    1501 Points

  5. Debashish Deka

    1480 Points

  6. junaid ahmad

    1432 Points

  7. pawan kumarln

    1286 Points

  8. Rupendra Choudhary

    1242 Points

  9. rahul sharma 5

    1240 Points

  10. Arjun

    1232 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 Jun 26 - Jul 02
  1. pawan kumarln

    418 Points

  2. akankshadewangan24

    334 Points

  3. Arjun

    272 Points

  4. Debashish Deka

    234 Points

  5. Abhisek Das

    230 Points

23,433 questions
30,149 answers
28,486 users