Can you explain how heap sort works?

Can you explain how heap sort works?

Sure! Heap sort is a comparison-based sorting algorithm that uses a binary heap data structure. It first builds a max heap from the input data, then repeatedly extracts the maximum element from the heap and rebuilds the heap until all elements are sorted.

What is a binary heap?

A binary heap is a complete binary tree that satisfies the heap property. In a max heap, for any given node, the value of the node is greater than or equal to the values of its children. This property allows for efficient retrieval of the maximum element.

How does the heap sort algorithm compare to quicksort?

Heap sort has a worst-case time complexity of O(n log n), similar to quicksort. However, quicksort is often faster in practice due to better cache performance, while heap sort has a more predictable performance.

Can you give me a step-by-step example of heap sort?

Absolutely! Let's say we have an array: [4, 10, 3, 5, 1]. First, we build a max heap, which results in [10, 5, 3, 4, 1]. Then we swap the root with the last element, reduce the heap size, and heapify again. We repeat this process until the array is sorted.