Heapsort-Know More

The heapsort algorithm is divided into two parts: creating a maximum heap and sorting it. The heapsort then sorts the array by repeatedly inserting the largest element of the heap into the array. Each time something is removed, the heap is updated. let us know more about that the Heapsort-Know More.

Heapsort-Know More

Heapsort is a sorting approach that uses a comparison-based data structure based on the Binary Heap data structure.

It’s comparable to how we discover the smallest element first and put it first in a selection sort. 

What exactly is a Binary Heap, and how does it function?

Let’s start with a complete binary tree definition. Every level except the last is full, and all nodes in a complete binary tree are as far left as possible.

A Binary Heap is a Complete Binary Tree where the value of the parent node is bigger (or smaller) than the values of its two progeny nodes. The max heap is the first, while the min-heap is the second.

A binary tree or an array can be used to represent a heap.

Why does Binary Heap use an array-based representation?

Because it is a Complete Binary Tree, a Binary Heap can be stored as an array.

If the parent node is stored at index I, the left child is 2 * I + 1, and the right child is 2 * I + 2. (assuming the indexing starts at 0).

How can a tree be “heapify”?

The process of transforming a binary tree into a Heap data structure is called ‘Heapify.’ A binary tree is a data structure in which each child node has just two descendants.

If the children nodes of a node have been ‘heapified,’ then only the ‘heapify’ procedure can be applied to that node. At all times, a heap must be a full binary tree.

We can turn a complete binary tree into a Max-Heap by calling a function called ‘heapify’ on all of the heap’s non-leaf items. ‘heapify,’ for example, employs recursion.

The “heapify” algorithm is as follows

heapify(array)

Root = array[0]

Largest = largest( array[0] , array [2 * 0 + 1]. array[2 * 0 + 2])

if(Root != Largest)

Swap(Root, Largest)

For sorting in ascending order, use the Heap Sort Algorithm

  • Create a maximum heap based on the provided data.
  • At this point, the biggest object is placed on top of the heap. Replace it with the heap’s last item, then reduce the heap’s size by one. Finally, heapify the tree’s trunk.
  • Step 2 should be repeated as long as the heap size is more than 1.

How do you make the heap?

Only if a node’s descendant nodes are piled may the heapify technique be done to it. As a result, the beatification must be done from the bottom up.

Heapsort’s advantages

  • Efficiency – As the number of objects to sort rises, the time required to conduct Heap sort climbs logarithmically, whereas alternative methods may become exponentially slower. This algorithm for sorting is extremely efficient.
  • Memory Usage – Memory usage is modest since, aside from what is required to store the initial list of objects to be sorted, it does not require any further memory to operate.
  • Because it does not involve difficult computer science concepts such as recursion, it is easier to comprehend than other equally efficient sorting algorithms.

In comparison to other kinds

Heapsort’s major opponent is Quicksort, another highly efficient in-place comparison-based sort algorithm.

Primary Advantage

Heapsort’s main advantages are its simple, non-recursive code, low auxiliary storage requirements, and consistently good performance: its best and worst cases are within a tiny constant factor of each other, and the theoretical lower bound on comparison sorts is also within a small constant factor.

While it cannot beat O(n log n) for pre-sorted inputs, it avoids the worst-case O(n2) performance of quicksort.

(The latter can be avoided with correct implementation, but it makes quicksort much more complicated, and one of the most common alternatives, intro sort, uses heapsort for this purpose.)

Main drawback

Its main drawbacks are its lack of locality of reference and intrinsically serial character; accesses to the implicit tree are dispersed and mostly random, and there’s no easy method to convert it to a parallel process.

As a result, embedded systems, real-time computers, and systems that deal with maliciously selected inputs, such as the Linux kernel, use it frequently. It’s also a fantastic choice for any application that won’t be slowed down by sorting.

Well-implemented Quicksort 

Quicksorts are often 2–3 times faster than heapsorts when implemented properly. Even though quicksort necessitates fewer comparisons, it is a minor consideration. 

(Top-down heapsort results claim twice as many comparisons; see Bottom-up heapsort.) The main advantage of Quicksort is its superior reference locality: partitioning is a linear scan with good spatial locality, and recursive subdivision has good temporal locality.

Quicksort can be done in mostly branch-free code with a little more effort, and several CPUs can be used to sort subpartitions in parallel with a little more effort. When the improved performance justifies the implementation effort, quicksort is chosen.

Merge sort is another important O(n log n) sorting algorithm; however, because it is not implemented, it rarely competes directly with heapsort.

The requirement for (n) extra space (about half the size of the input) in merge sort is usually prohibitive, except in the following cases

  • When a consistent sort is needed
  • When using input that has been (partially) pre-sorted
  • Lists that are linked Sorting out (in which case merge sort requires minimal extra space)
  • Merge sort has a lot of reference locality.

Conclusion

Heapsort works similarly to selection sort in that it divides its input into a sorted and an unsorted region, then reduces the unsorted part by picking the largest piece from it and putting it into the sorted region.

Heapsort, unlike selection sort, saves the unsorted region in a heap data structure, allowing the largest element in each stage to be located more quickly.

FAQS

What is the reason for the instability of heap sort?

Because heap operations might affect the relative order of equivalent keys, heapsort isn’t very stable.

Is there any additional memory used by heap sort?

Heapsort is a no-extra-space algorithm.

Heapsort-Know More

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