Sorting and Order Statistics - Heap Sort - The Logic Tutorial

Sorting and Order Statistics - Heap Sort

Heap Sort is a popular sorting algorithm known for its efficiency and simplicity. It falls under the category of comparison-based sorting algorithms and is particularly useful when dealing with large datasets.

Algorithm Overview:

Heap Sort utilizes the concept of a binary heap to achieve sorting. A binary heap is a complete binary tree where every parent node is smaller (for min-heap) or larger (for max-heap) than its children. The main steps of Heap Sort are:

1. Build a heap from the input data.
2. Repeatedly remove the root (i.e., the maximum or minimum element in the case of max-heap or min-heap respectively) and place it at the end of the sorted array.
3. Heapify the remaining elements to maintain the heap property.
4. Repeat steps 2 and 3 until the heap is empty.

Key Features:

Heap Sort offers several advantages:

• Efficient: Heap Sort has a time complexity of O(n log n), making it suitable for large datasets.
• Space Complexity: Heap Sort has a space complexity of O(1) as it sorts the elements in-place.
• Stable: Unlike some other sorting algorithms, Heap Sort is stable, meaning it preserves the relative order of equal elements.

Implementation:

Implementing Heap Sort involves constructing the heap and then performing the sorting process. Here's a high-level overview of the implementation:

  // Function to heapify a subtree rooted at index i
  heapify(array, n, i):
      largest = i
      left = 2*i + 1
      right = 2*i + 2

      if left < n and array[left] > array[largest]:
          largest = left

      if right < n and array[right] > array[largest]:
          largest = right

      if largest != i:
          swap(array[i], array[largest])
          heapify(array, n, largest)

  // Function to perform Heap Sort
  heapSort(array):
      n = array.length

      // Build a max heap
      for i from n/2 - 1 down to 0:
          heapify(array, n, i)

      // Extract elements one by one
      for i from n-1 down to 0:
          swap(array[0], array[i])
          heapify(array, i, 0)
  

Heap Sort is widely used in various applications where efficiency is crucial, such as in operating system scheduling algorithms, priority queues, and network routing protocols.