1. Heap Sort is one of the best sorting methods being in-place and with no quadratic worst-case running time. Heap sort takes space. We will show that in the worst case its running time is O(n2), its expected case running time is O(nlogn). Partitioning: Our next sorting algorithm is QuickSort. Heap sort involves building a Heap data structure from the given array and then utilizing the Heap to sort the array.. You must be wondering, how converting an array of numbers into a heap data structure will help in sorting the array. Heap sort runs in time, which scales well as n grows. Heap sort has the best possible worst case running time complexity of O(n Log n). Worst case for extract happens when the root node has been changed to contain the smallest value of all the nodes (we extract the root in O(1) and put the last element in the array to be a root). Heap sort and Quick Sort both are in-place sorting algorithm but heap sort has an advantage over quick sort in worst case as heap sort run in O(n*logn) even in worst case. 2. Heap sort (c) The data to be sorted is too big to fit in memory, so most of it is on disk. Unlike quicksort, there's no worst-case complexity. It doesn't need any extra storage and that makes it good for situations where array size is large. The BST is ordered, but the Heap is not. Heap vs BST. First off, (as we will present it) it is a randomized algorithm, which means that it makes use of a ran-dom number generator. 4. Heap sort O(nlogn) O(nlogn) O(nlogn) Mergesort O(nlogn) O(nlogn) O(nlogn) Quicksort O(nlogn) O(n^2) O(nlogn) Bucket ... You need an O(n log n) sort even in the worst case and you cannot use any extra space except for a few local variables. So, if order matters, then it is better to use BST. Space efficient. The main difference is that Binary Search Tree doesn’t allow duplicates, however, the Heap does. Heap Sort is not a stable sort, it does not retrieve the same order of equal elements in the sorted array. Although Heap Sort has O(n log n) time complexity even for the worst case, it doesn't have more applications ( compared to other sorting algorithms like Quick Sort, Merge Sort ). However, its underlying data structure, heap, can be efficiently used if we want to extract the smallest (or largest) from the list of items without the overhead of keeping the remaining items in the sorted order. QuickSort is interesting in a number of respects. Before looking into Heap Sort, let's understand what is Heap and how it helps in sorting. Let's say we have a max heap. That's way better than merge sort's … I will illustrate for n = 7, but logic is the same heaps of bigger size. 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