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Maximum subarray problems arise in many fields, such as genomic sequence analysis and computer vision.. Genomic sequence analysis employs maximum subarray algorithms to identify important biological segments of protein sequences that have unusual properties, by assigning scores to points within the sequence that are positive when a motif to be recognized is present, and negative when it is not ...
The Karmarkar–Karp (KK) bin packing algorithms are several related approximation algorithm for the bin packing problem. [1] The bin packing problem is a problem of packing items of different sizes into bins of identical capacity, such that the total number of bins is as small as possible.
For data in which the maximum key size is significantly smaller than the number of data items, counting sort may be parallelized by splitting the input into subarrays of approximately equal size, processing each subarray in parallel to generate a separate count array for each subarray, and then merging the count arrays.
In this variant of the problem, which allows for interesting applications in several contexts, it is possible to devise an optimal selection procedure that, given a random sample of size as input, will generate an increasing sequence with maximal expected length of size approximately . [11] The length of the increasing subsequence selected by ...
However, some contest problems may allow for partial scoring, depending on the number of test cases passed, the quality of the results, or some other specified criteria. Some other contests only require that the contestant submit the output corresponding to given input data, in which case the judge only has to analyze the submitted output data.
Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …
The k-way merge problem consists of merging k sorted arrays to produce a single sorted array with the same elements. Denote by n the total number of elements. n is equal to the size of the output array and the sum of the sizes of the k input arrays. For simplicity, we assume that none of the input arrays is empty.
The objective is to achieve the minimum perturbation to the item size vector so that all the items can be packed into the prescribed number of bins. In the maximum resource bin packing problem, [51] the goal is to maximize the number of bins used, such that, for some ordering of the bins, no item in a later bin fits in an earlier bin. In a dual ...