GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
120 views

An array of $n$ distinct elements is said to be un-sorted if for every index $i$ such that $ 2 \leq i \leq n-1$, either $A[i] > max \{A [i-1], A[i+1]\}$, or $A[i] < min \{A[i-1], A[i+1]\}$. What is the time-complexity of the fastest algorithm that takes as input a sorted array $A$ with $n$ distinct elements, and un-sorts $A$?

  1. $O(n \: \log \: n)$ but not $O(n)$
  2. $O(n)$ but not $O(\sqrt{n})$
  3. $O(\sqrt{n})$ but not $O(\log n)$
  4. $O(\log n)$ but not $O(1)$
  5. $O(1)$
asked in Algorithms by Veteran (76k points)   | 120 views

1 Answer

+2 votes
A pairwise swap will make the sorted array unsorted. Hence, the option (b) is correct.

For eg - if an array is 1 2 3 4 5 6 7 8

The array will become after a pair wise swap to 2 1 4 3 6 5 8 7. For all i between 2 and n-1, a[i] is either lower, or either greater than their adjacent elements.

Since, each element is being swapped exactly once. The operation has O(n) time complexity.
answered by Active (1k points)  
edited by
So you mean only one pass of bubble sort is enough??
Hi,

I have just edited the answer to make my point more clear. By pairwise swap, i mean here the pairwise disjoint swapping of elements. Hope, I would have made my point more clear.
I think you have got the best case

Here is my exmple-- 15 10 20 13 17...I think here we need more swap..Please check once.Let me know If i m doing any mistake
Hi

Question asks that Input is sorted. You may be missing that point..
ohh..yes..i read just the opposite..sorry

btw thanks for correction


Top Users Mar 2017
  1. rude

    4018 Points

  2. sh!va

    2994 Points

  3. Rahul Jain25

    2804 Points

  4. Kapil

    2606 Points

  5. Debashish Deka

    2092 Points

  6. 2018

    1414 Points

  7. Vignesh Sekar

    1318 Points

  8. Bikram

    1218 Points

  9. Akriti sood

    1166 Points

  10. Sanjay Sharma

    1004 Points

Monthly Topper: Rs. 500 gift card

21,439 questions
26,753 answers
60,919 comments
22,929 users