Aug 27, 2012 · Look at the Wikipedia implementation notes for binary heaps. If the heap's root is placed at index 0, then the formulas for parent, left-child and right-child of the node at index n are respectively (n-1)/2, 2n+1 and 2n+2. If you use a 1-based array then the formulas become the simpler n/2, 2n and 2n + 1.

Nov 8, 2015 · In the worst case, the time complexity for finding elements in heap is still O(n). You should use a binary search tree for O(logn) time complexity if you have to find a particular element. Heap is better at finding/find max (O(1)), while BST is good at all finds (O(logN)).

Nov 1, 2013 · A binary heap is a complete binary tree obeying the heap property. That's all. The fact that it can be stored using an array, is just nice and convenient. But sure, you can implement it using a linked structure. It's a fun exercise!

Oct 8, 2010 · The binary heap is a data structure that can be used to quickly find the maximum (or minimum) value in a set of values. It's used in Dijkstra's algorithm (shortest path), Prim's algorithm (minimum spanning tree) and Huffman encoding (data compression).

Mar 18, 2012 · Building a binary heap will take O(n) time with Heapify(). When we add the elements in a heap one by one and keep satisfying the heap property (max heap or min heap) at every step, then the total time complexity will be O(nlogn). Because the general structure of a binary heap is of a complete binary tree. Hence the height of heap is h = O(logn ...

In a binary heap, the heap is a single tree, which is a complete binary tree. In a binomial heap, the heap is a collection of smaller trees (that is, a forest of trees), each of which is a binomial tree. A complete binary tree can be built to hold any number of elements, but the number of elements in a binomial tree of some order n is always 2 ...

Feb 18, 2016 · Since the heap is an (almost) complete binary tree, its height is in O(log n). Both heapify functions have to visit all tree levels, in the worst case, thus the removal by index is in O(log n). Note that finding the element with a certain key in a heap is in O(n). Thus, removal by key value is in O(n) because of the find complexity, in general.

Oct 29, 2017 · If this is too inefficient, a minimum heap may not a a good fit. A binary-tree might be better (red-black tree for example), where removal and insertion scale better. However I'm not sure about an rb-trees ability to re-order in-place, as a min-heap can do.

Jun 23, 2015 · I've read that binary heaps are faster at delete minimum operations and d-ary heaps are faster at at decrease priority operations (although I don't get why), but then I've also read that a 4-heap is

Jan 10, 2013 · >>Actually, the time-analysis is wrong. I found this out a few days later and haven't been back. It actually ends up being a total of O(log^2(n)), because the bubble-up function also uses the O(log(n)) search to update the index in the …