Final answer:
Heap sort is a comparison-based sorting algorithm that organizes data into a binary heap and has a time complexity of O(n log n) for worst, average, and best cases.
Step-by-step explanation:
What is Heap Sort?
Heap sort is a comparison-based sorting technique based on a binary heap data structure. It is similar to selection sort where we first find the maximum element and place it at the end. We repeat the same process for the remaining elements. The process of creating a heap from the given set of elements is commonly referred to as 'heapifying'. A complete binary tree is used in this sorting method, which is why the heap can be stored in an array, and it does not require any extra storage.
Time Complexity of Heap Sort
The time complexity of heap sort in the average and worst case is O(n log n), where n is the number of items being sorted. This is because the process of 'heapifying' a single element takes O(log n) time and we need to heapify n elements over the course of the algorithm. In the best case, the time complexity is also O(n log n). This consistency makes heap sort particularly useful in applications that require a guaranteed upper limit on execution times.