Heap Sort: A Powerful Sorting Algorithm

 

Heap Sort: A Powerful Sorting Algorithm 🔥

Heap Sort is an efficient comparison-based sorting algorithm that uses a binary heap data structure to organize elements. It’s known for its O(n log n) time complexity, making it faster than many quadratic sorting methods like Bubble Sort or Insertion Sort.

How Heap Sort Works? 🛠️

1️⃣ Build a Max Heap – Convert the array into a max heap (a complete binary tree where the parent node is always larger than its children).
2️⃣ Extract the Maximum – Swap the root (largest value) with the last element and reduce the heap size.
3️⃣ Heapify the Remaining Elements – Restore the heap structure and repeat until the array is sorted.

Time Complexity ⏳

• Best Case: O(n log n)
• Average Case: O(n log n)
• Worst Case: O(n log n)
• Space Complexity: O(1) (In-place sorting)

Why Use Heap Sort?

✅ Efficient: Performs well with large datasets.
✅ In-Place: Requires minimal extra memory.
✅ Consistent Performance: Always O(n log n) regardless of input order.

Use Cases

📌 Priority Queues
📌 Scheduling Systems
📌 Graph Algorithms (like Dijkstra’s Shortest Path)

Heap Sort vs. Other Sorting Algorithms

Sorting Algorithm	Time Complexity	Space Complexity	Stable?
Heap Sort	O(n log n)	O(1)	❌ No
Quick Sort	O(n log n)	O(log n)	❌ No
Merge Sort	O(n log n)	O(n)	✅ Yes
Bubble Sort	O(n²)	O(1)	✅ Yes

🔹 Though Heap Sort is not stable (doesn’t preserve the order of equal elements), it’s still widely used in systems requiring reliable, in-place sorting.