GATE CS 2015 Set 2 — Question 16
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Algorithms → Searching → Selection (Order Statistics)
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Question
An unordered list contains distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is
Correct answer
(D) Θ(1)
Solution
To find an element that is neither maximum nor minimum in an unordered list of distinct elements (assuming , as for such an element does not exist):
1.Find the maximum element: This requires comparisons.
2.Find the minimum element: This requires comparisons.
Alternatively, both the maximum and minimum can be found in approximately comparisons by comparing elements in pairs.Once the maximum () and minimum () elements are identified, any other element in the list (if ) is guaranteed to be neither the maximum nor the minimum. We can then iterate through the list to find the first element such that and . This iteration takes at most comparisons.Combining these steps, the total number of comparisons will be proportional to . Therefore, the complexity is .For example, if the list is :- Find max (10) and min (1). This takes comparisons.
- Iterate: 5 is not 10 and not 1. So 5 is an element that is neither max nor min. This takes comparisons in the worst case to find such an element after max/min are known.
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