Algorithm Design Questions
Heap sort is a comparison-based sorting algorithm that works by dividing the input into a binary heap data structure. It starts by building a max heap from the input array, where the largest element is at the root. Then, it swaps the root element with the last element in the heap and reduces the heap size by one. This process is repeated until the heap is empty. As a result, the array is sorted in ascending order. The main steps of the heap sort algorithm are:
1. Build a max heap: Starting from the first non-leaf node (n/2-1), compare each node with its children and swap if necessary to ensure that the largest element is at the root. Repeat this process for all non-leaf nodes until the entire array is a max heap.
2. Extract the maximum element: Swap the root element (largest element) with the last element in the heap. Reduce the heap size by one.
3. Heapify: After extracting the maximum element, heapify the remaining heap to maintain the max heap property. Compare the new root with its children and swap if necessary. Repeat this process until the heap is again a max heap.
4. Repeat steps 2 and 3 until the heap is empty: Continue extracting the maximum element and heapifying until the heap is empty. Each extracted element is placed at the end of the array.
5. The array is now sorted: After the heap is empty, the array is sorted in ascending order.
Heap sort has a time complexity of O(n log n) in all cases, making it an efficient sorting algorithm.