What is Heap Sort?
The knowledge of Heap Data Structure
Max-Heap and Min-Heap
What is a Heap Sort Algorithm?
Heap Sort in C++
Time complexity, Space complexity
Cons and Pros
Real-World Applications
So, let us get down to it.
What is Heap Sort?
Heap Sortirement-based sorting algorithm that finds its application in sorting elements using a binary healing structure. J. W. J. Williams invented it in 1964 and it is an instance of an in-place sorting algorithm: it does not take any additional memory space (except a few variables).
The gist of the matter is:
1. Construct (in the case of ascending order) a Max Heap over the unordered array.
2. Continually find the largest item (i.e. the root of the heap), put it after the end of the array and then the smaller heap.
This goes on until the elements are sorted.
What is Heap Data Structure?
A pile or heap is an important concept that a student should know before being introduced to Heap Sort.
A heap is a specific data structure based on a tree which the main condition is the heap property:
Max Heap In a Max Heap, the value of any node `i` is either equal to, or larger than, its children.
((In a Min Heap), at any node `i` the value of `i` will be at most as large as its children node).
A heap will always be a complete binary tree i.e. all the levels are filled to capacity except possibly the last, which is filled left to right.
Heap: Array Representation:
Binary heap is usually expressed as an array. For node at index `i`:
Left child = ` 2i + 1` `
Right child = 2i + 2 Parent = (i-1)/2 ( integer division )
This ensures that children and parent nodes are accessed very effectively.
Max-heap Vs. Min-heap
Heap Sort is the sorting algorithm that normally uses Max Heap to sort the elements in the ascending order. The two are different in the following way:
Feature | Max Heap | Min Heap |
------------ | ------------------------- | ---------------------------------- |
Root Node | Greatest value | least value |
Sorting type | i Ascending | d Descending
Use Case Heap Sort, Priority Queue Heap Sort (descending), Dijkstra s
A Min Heap can be utilized to sort an array in reverse order as opposed to a Max Heap.
An Explanation of Heap Sort Algorithm
So as to disintegrate the Heap Sort algorithm into several steps, the following is given:
Step 1: Construct Max Heap
Make the array into a Max Heap.
This action guarantees that the greatest thing is at the base.
Step 2: Draw the Elements One after Another
Interchange the root (numeral greatest in value) with the final element in the heap.
And shrink the heap size by one.
Perform on the root so that heap property would remain.
Repeat to repeat the size of heap 1.
And this guarantees the biggest leftover element will be at the right spot after each iteration.
Time and Space Complexity
Time Complexity:
Operation | Complexity |
---------- | ------------ | specifically | in Particular
| Heap Building | O(n) |
| Heapify (per element) | O(log n) |
| Total Heap Sort | O (n log n) |
Stack sort and Heap Sort has an O(n log n) complexity due to the following reason:
The construction of heap takes O(n)
Separation of the elements and creating a heap is O(log n) but it is n times.
Space Complexity:
Heap Sort is an in-place algorithm and thus its space complexity is O 1 (disregarding recursion stack in the ).
The Heap Sort merits mentioned above are:
Time Complexity: It always works on O (n log n) time.
In-Place sorting: Does not need extra memory.
Not Recursive (Can Be Made Iterative): Appropriate in limited memory space.
Does not need pre-sorted input: Studies random data well.
Demerits of Heap Sort
Not Stable: the elements that are equal in relation to each other may not preserve original positioning.
Cache performance: The algorithm has a performance that is anti-cache compared to other algorithms such as Quick Sort or Merge Sort.
Slow with small datasets: When presented with small lists it may be an overkill compared with more basic algorithms such as Insertion Sort.
Real-World Applications
Heap Sort applies in such cases where there is a very strict constraint on the memory consumption and when the worst case behaviour is highly important:
Embedded systems
Scheduling (priority queues) of the operating system
Top- k problems (data streaming)
In an algorithm such as Dijkstra shortest path heaps are used
Comparison to Other Sorting Algorithm
Algorithm | Time Complexity | Space complexity | Stable | in-place |
-------------- | --------------- | ---------------- | ------ | -------- | energies
| Quick Sort | log n avg | lg n | No | Yes |
Merge Sort | O (n log n) | O (n) | Yes | No |
| Heap Sort | n log n | 1 | No | Yes |
Insertion Sort | O(n 2 ) | O(1 ) | Yes | Yes |
Conclusion
A Heap Sort is a solid and powerful sorting algorithm whose time complexity is reliable O(n log n) in all scenarios; best case, average case, and worst case. When there is a need to utilize memory and behave in the same way, it will be an excellent option due to the in-place and predictable behavior.
Although it has no stability of its own and might not merely be better than Quick Sort in real life scenarios, Heap Sort does retain its space in the domain of sorting algorithms as one of the stable and academically prolific algorithms.
Being ready to attend coding interviews or designing optimal systems, you should learn more about Heap Sort as you can utilize such an algorithm in many cases.
