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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 (92.5k points) 964 2327 3113 | 167 views

1 Answer

+5 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 (1.1k points) 1 2 11
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

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