What is the overall time complexity for building a min-heap with n elements and performing n extract-min operations?

• A. O(n)
• B. O(n log n)
• C. O(n^2)
• D. O(n log log n)

Answer: (B)

The total time is governed by two parts: building the heap and then repeatedly removing the minimum. Building a binary min-heap from n elements can be done in O(n) time using the bottom-up heapify approach. Each extract-min operation costs O(log n) because you remove the root and may need to move the new root down the height of the heap, which is about log n levels. Doing this n times gives O(n log n). Adding the initial O(n) build time, the sum is O(n) + O(n log n) = O(n log n). So the overall time complexity is O(n log n).