Bottom up heap construction

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A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. Williams in , as a data structure for heapsort. A binary heap is defined as a binary tree with two additional constraints: [3].
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Bottom up Construction heaps - Stack Overflow

I have to implement a heap as part of a Java assignment, and I'm trying to get bottom-up construction working. I have only ever seen heap construction algorithms which make full binary trees. No matter what horrible sort of tree you start with, using a good algorithm will give you the same runtimes, but there will be a bigger constant term I think. Bottom-up construction gives you O n , whereas top-down gives you O nlogn. I was hoping to be able to insert dummy nodes or something in order to fill out the tree. I'm not sure how to handle that, though. I think if you keep the bottom nodes all aligned to the left, then the heap still works with the expected runtimes, i.
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Time Complexity of building a heap

A quick look over the above algorithm suggests that the running time is , since each call to Heapify costs and Build-Heap makes such calls. This upper bound, though correct, is not asymptotically tight. Hence, Heapify takes different time for each node, which is. For finding the Time Complexity of building a heap, we must know the number of nodes having height h.
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Many applications require that we process records with keys in order, but not necessarily in full sorted order and not necessarily all at once. Often, we collect a set of records, then process the one with the largest key, then perhaps collect more records, then process the one with the current largest key, and so forth. An appropriate data structure in such an environment supports the operations of inserting a new element and deleting the largest element. Such a data structure is called a priority queue.
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