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A queue has two ends, the top, which is the only position at which the push operation may occur, and the bottom, which is the only position at which the pop operation may occur. A queue may be implemented as circular buffers and linked lists, or by using both the stack pointer and the base pointer.
The dynamic array approach uses a variant of a dynamic array that can grow from both ends, sometimes called array deques. These array deques have all the properties of a dynamic array, such as constant-time random access , good locality of reference , and inefficient insertion/removal in the middle, with the addition of amortized constant-time ...
One example application of the double-ended priority queue is external sorting. In an external sort, there are more elements than can be held in the computer's memory. The elements to be sorted are initially on a disk and the sorted sequence is to be left on the disk. The external quick sort is implemented using the DEPQ as follows:
A sorting algorithm can also be used to implement a priority queue. Specifically, Thorup says: [ 21 ] We present a general deterministic linear space reduction from priority queues to sorting implying that if we can sort up to n keys in S ( n ) time per key, then there is a priority queue supporting delete and insert in O ( S ( n )) time and ...
Stream processing is essentially a compromise, driven by a data-centric model that works very well for traditional DSP or GPU-type applications (such as image, video and digital signal processing) but less so for general purpose processing with more randomized data access (such as databases). By sacrificing some flexibility in the model, the ...
A standard exercise in algorithm design asks for an implementation of this algorithm that takes linear time in the input size, which is the sum of sizes of all the input sets. [19] This may be solved using a bucket queue of sets in the input family, prioritized by the number of remaining elements that they cover.
A good example that highlights the pros and cons of using dynamic arrays vs. linked lists is by implementing a program that resolves the Josephus problem. The Josephus problem is an election method that works by having a group of people stand in a circle. Starting at a predetermined person, one may count around the circle n times.
This method can be implemented in time linear in the sum of sizes of the input sets, using a bucket queue to prioritize the sets. [6] It achieves an approximation ratio of H ( s ) {\displaystyle H(s)} , where s {\displaystyle s} is the size of the set to be covered. [ 7 ]