Heap is a kind of #Queue that prioritise short tasks over long tasks. Its implementation could be based on tree# or list#.
Heap can be used for:
There are several implementations of heap:
Priority Queue/Heap
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d-Heap
d-Heap is a #202202062259 where the nodes have \(d\) children. The most common d-Heaps other than 2-heap#, are 3-heap and 4-heap.
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Rust Box
Box<T>is a kind of #202111301656 implemented by Rust standard library which is actually a single element Tuple with 202206221604# and Drop 202204061235#. It doesn’t have performance overhead. It stores data on the 202202062259# rather than on the 202112031157#. We can directly print the value (if it is of simple type) just like other primitive types without dereferencing it. Comparing to normal references, box is pointing to a copied value. -
Replacement Selection
It needs at least two structures: a 202202062259 which is used to compare the items in the tape or drive and an array which is used to store any items that is smaller than the latest inserted item.
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List Implementation of Heap
#202202062259 could be implemented in #202110191729.
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Kruskal’s Algorithm
It is advised to build a 202202062259 for it. To further optimise it, use an array of pointers instead of edges.
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K-way Merge
Unlike 202203102127, it could use more than two, \(k\), drives or tapes as input or output. \(k\) parts will then be grouped into a run which will be stored into \(k\) drives or tapes. It is ill-advised to use comparison to obtain the smallest element among the parts since it could result in \(O(N^2)\) which is bad. We could take advantage of some #data-structure peculiarly 202202062259 or 202112102110. We will then obtain a sorted run by repeating the process recursively. The same steps will be performed for the next run.
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Dijkstra’s Algorithm
For sparse graph, we could use 202202062259 to increase the runtime to \(O(\vert E \vert \log \vert V \vert)\) by using its DeleteMin after the smallest vertex has been found and DecreaseKey to decrease the distance of W to the distance of V + \(c_{v,w}\) if the latter is smaller. This could be implemented in Paring Heap.
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Binomial Queue
Binomial Queue is a #Priority Queue/Heap that seeks to improve Leftist Heap’s and Skew Heap’s Insert. Unlike those, it is a collection of Linked List Tree.
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Binary Heap
Binary Heap is a #Priority Queue/Heap that use #Binary Search Tree as its chassis. It can be represented in the form of simple array.