Sorting Algorithms Questions Medium
The heap sort algorithm is a comparison-based sorting algorithm that uses a binary heap data structure to sort elements. It works by first building a max heap from the given array, where the largest element is at the root. Then, it repeatedly swaps the root element with the last element of the heap, reducing the size of the heap by one, and ensuring that the largest element is at its correct position. This process is repeated until the heap is empty and all elements are sorted in ascending order.
The steps involved in the heap sort algorithm are as follows:
1. Build a max heap: Starting from the middle element of the array and moving towards the first element, heapify each subtree to create a max heap. Heapify is the process of arranging the elements in a binary heap such that the parent node is greater than its children.
2. Swap and heapify: Swap the root element (largest element) with the last element of the heap and reduce the heap size by one. Heapify the new root to maintain the max heap property.
3. Repeat step 2: Repeat the swap and heapify process until the heap is empty. This will result in the array being sorted in ascending order.
The time complexity of heap sort is O(n log n) in all cases, where n is the number of elements in the array. The space complexity is O(1) as it sorts the array in-place without requiring any additional space.
Heap sort is considered an efficient sorting algorithm, especially for large datasets, as it has a consistent time complexity and does not require additional space. However, it is not a stable sorting algorithm, meaning that the relative order of equal elements may change during the sorting process.