Heapsort

1. Detailed Elaboration

Definition: Heapsort is a comparison-based sorting algorithm utilizing a binary heap data structure. It is an efficient way to sort a collection of items.
Complexity:
- Time Complexity:
  - Worst-case: O(n log n)
  - Average-case: O(n log n)
  - Best-case: O(n log n)
- Space Complexity: O(1) (in-place sorting)
Process:
1. Heap Construction: Transform the list into a max-heap (or min-heap).
2. Sorting:
  - Remove the maximum (or minimum) element from the heap, placing it in the sorted output.
  - Re-establish the heap property (heapify).
  - Repeat until the heap is empty.
Stability: Heapsort is not a stable sorting algorithm because it can change the relative order of equal elements.
Use Cases:
- Best suited for situations where memory space is limited.
- Effective for large datasets and when the complete data is not available at once.