Introduction

Heap Sort Technique: Heap Sort is an efficient sorting algorithm that uses a binary heap data structure to sort elements. The algorithm ensures that the heap property is maintained, and repeatedly extracts the maximum or minimum element to build the sorted array.
This technique gets its name because it utilizes the heap structure for sorting.

How can we sort an array?

• In Heap Sort, we first build a Max Heap or Min Heap from the unsorted array.
• The root of the heap (largest or smallest element) is extracted and placed in the sorted array.
• The heap property is restored for the remaining unsorted portion of the array.
• This process continues until all elements are extracted and sorted.

Important Observations

• After building the initial heap, the largest or smallest element is placed at the root.
• The array is sorted by repeatedly restoring the heap and extracting elements.
• The algorithm works well for in-place sorting.
• The array will be sorted in ascending or descending order based on the heap type used.

Key Characteristics:

• Comparison-based sorting technique.
• In-place sorting algorithm; does not require additional memory.
• Efficient for large datasets.

Advantages:

• Efficient for in-place sorting.
• Time complexity is (O(n log n)) in all cases.
• Does not require additional memory space.

Disadvantages:

• Not a stable sorting algorithm (does not preserve the order of equal elements).
• Heap creation may involve overhead for large datasets.

Time Complexity:

• Best Case: (O(n log n)).
• Average Case: (O(n log n)).
• Worst Case: (O(n log n)).