Data Structures | Heap | Question 8

In a min-heap with n elements with the smallest element at the root, the 7th smallest element can be found in time:

(A)

theta(nlogn)

(B)

theta(n)

(C)

theta(logn)

(D)

theta(1)

Answer: (D)

Explanation:

For clarity, assume that there are no duplicates in Min-Heap and accessing heap elements below root is allowed.

The 7th smallest element must be in first 7 levels. Total number of nodes in any Binary Heap in first 7 levels is at most 1 + 2 + 4 + 8 + 16 + 32 + 64 which is a constant. Therefore we can always find 7th smallest element in time. If Min-Heap is allowed to have duplicates, then time complexity becomes Θ(Log n). Also, if Min-Heap doesn\’t allow directly accessing elements below root and supports only extract-min() operation, then also time complexity becomes Θ(Log n).

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