Question

There is probably an efficient solution for this, but I’m not seeing it.
I’m not sure how to explain my problem but here goes…

Lets say we have one array with n integers, for example {3,2,0,5,0,4,1,9,7,3}.
What we want to do is to find the range of 5 consecutive elements with the “maximal minimum”…
The solution in this example, would be this part {3,2,0,5,0,4,1,9,7,3} with 1 as the maximal minimum.

It’s easy to do with O(n^2), but there must be a better way of doing this. What is it?

Answer 1

If you mean literally five consecutive elements, then you just need to keep a sorted window of the source array.
Say you have:
{3,2,0,5,0,1,0,4,1,9,7,3}

First, you get five elements and sort’em:

{3,2,0,5,0, 1,0,1,9,7,3}
{0,0,2,3,5} – sorted.

Here the minimum is the first element of the sorted sequence.

Then you need do advance it one step to the right, you see the new element 1 and the old one 3, you need to find and replace 3 with 1 and then return the array to the sorted state. You actually don’t need to run a sorting algorithm on it, but you can as there is just one element that is in the wrong place (1 in this example). But even bubble sort will do it in linear time here.

{3,2,0,5,0,1, 0,4,1,9,7,3}
{0,0,1,2,5}

Then the new minimum is again the first element.

Then again and again you advance and compare first elements of the sorted sequence to the minimum and remember it and the subsequence.

Time complexity is O(n).