What is the time complexity of Heap Sort in the worst case?

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Question: What is the time complexity of Heap Sort in the worst case?

Options:

Correct Answer: O(n log n)

Solution:

The worst-case time complexity of Heap Sort is O(n log n) due to the heap construction and sorting process.

What is the time complexity of Heap Sort in the worst case?

What is the time complexity of Heap Sort in the worst case?

Step 1: Understand what time complexity means. It tells us how the time to complete an algorithm grows as the size of the input (n) increases.
Step 2: Know that Heap Sort is a sorting algorithm that uses a data structure called a heap.
Step 3: Recognize that there are two main parts to Heap Sort: building the heap and sorting the elements.
Step 4: Building the heap takes O(n) time. This is because we can create a heap from an array in linear time.
Step 5: Sorting the elements involves repeatedly removing the largest element from the heap and takes O(log n) time for each removal.
Step 6: Since we need to remove n elements, the total time for sorting is O(n log n).
Step 7: Combine the times from building the heap and sorting. The dominant term is O(n log n), which is the worst-case time complexity.

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