Heap Sort: A Powerful Sorting Algorithm

In case of sorting algorithms, Heap Sort stands out as a robust and efficient method used to arrange data elements in ascending or descending order. Employing the concept of a heap data structure, Heap Sort offers a reliable solution for sorting arrays efficiently. Let's dive deeper into this sorting algorithm and understand its working process.

Heap Sort

Heap Sort is a comparison-based sorting algorithm that transforms an array into a binary heap, a specialized tree-based data structure. It then repeatedly extracts the maximum (for a max heap) or minimum (for a min heap) element from the heap and places it at the end of the sorted array.

Heap is a special tree-based data structure, that satisfies special heap properties, like -

• Shape Property - Heap data structure is always a Complete Binary Tree, which means all levels of the tree are fully filled.
• Heap Property - All nodes are either greater than or less than or equal to each of its children. Greater parent nodes heap is called a Max-Heap and small parent nodes heap is called Min-Heap.

Working Process

2. Sorting

Once the heap is constructed, the algorithm repeatedly extracts the root element (the maximum for a max heap or minimum for a min heap) and places it at the end of the array. After each extraction, the heap is adjusted to maintain its properties.

3. Heap Rebuilding

The extracted element leaves a gap at the root of the heap. To maintain the heap structure, the algorithm restructures the heap by moving the last element of the heap to the root position. This process is known as heapify-down, where the heap property is restored by comparing and swapping elements with their children until the heap property is satisfied.

4. Repeat

Steps 2 and 3 continue until the entire array is sorted. The result is an array arranged in ascending or descending order, depending on the sorting criteria.

Key Characteristics of Heap Sort

• Time Complexity: Heap Sort exhibits a time complexity of O(n log n) for average and worst-case scenarios.
• Space Complexity: The algorithm has a space complexity of O(1) as it operates in place, requiring minimal additional memory.

Logic of Heap Sort

# heapify
for i = n/2:1, sink(a,i,n)
    invariant: a[1,n] in heap order

# sortdown
for i = 1:n,
   swap a[1,n-i+1]
   sink(a,1,n-i)
       invariant: a[n-i+1,n] in final position
end

# sink from i in a[1..n]
function sink(a,i,n):
   # {lc,rc,mc} = {left,right,max} child index
   lc = 2*i
   if lc > n, return # no children
   rc = lc + 1
   mc = (rc > n) ? lc : (a[lc] > a[rc]) ? lc : rc
   if a[i] >= a[mc], return # heap ordered
   swap a[i,mc]
   sink(a,mc,n)
   return result

Heap Sort Implementation in Different Programming Languages

Sort your data using Heap Sort in Python

Sort your data using Heap Sort in Java

Sort your data using Heap Sort in C

Sort your data using Heap Sort in C++