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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