Question

Consider a binary heap (min heap) with N elements in it. What is the worst case time complexity of the "getMin" operation?

a) O(log N)
b) O(N)
c) O(N²)
d) O(1)

Answer 1

The worst case time complexity of the "getMin" operation in a binary min heap with N elements is O(log N).

Step-by-step explanation:

The worst case time complexity of the "getMin" operation in a binary min heap with N elements is O(log N). This means that the time it takes to get the minimum element from the heap increases logarithmically with the number of elements in the heap.

In a binary min heap, the minimum element is always at the root of the tree, so retrieving it takes constant time O(1). However, after the minimum element is removed, the heap needs to be reorganized to maintain the heap property, which takes O(log N) time. This is because the reorganization process involves repeatedly comparing and swapping elements, and the height of the heap is log N.

For example, if we have a heap with 16 elements, the maximum number of comparisons and swaps required to restore the heap property is 4.