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The longest alternating subsequence problem has also been studied in the setting of online algorithms, in which the elements of are presented in an online fashion, and a decision maker needs to decide whether to include or exclude each element at the time it is first presented, without any knowledge of the elements that will be presented in the future, and without the possibility of recalling ...
This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, 0, 4, 6, 9, 11, 15 0, 2, 6, 9, 13, 15 0, 4, 6, 9, 13, 15. are other increasing subsequences of equal length in the same input sequence.
This table is used to store the LCS sequence for each step of the calculation. The second column and second row have been filled in with ε, because when an empty sequence is compared with a non-empty sequence, the longest common subsequence is always an empty sequence. LCS(R 1, C 1) is determined by comparing the first elements in each sequence.
The sequence produced by other choices of c can be written as a simple function of the sequence when c=1. [1]: 11 Specifically, if Y is the prototypical sequence defined by Y 0 = 0 and Y n+1 = aY n + 1 mod m, then a general sequence X n+1 = aX n + c mod m can be written as an affine function of Y:
Longest-processing-time-first (LPT) is a greedy algorithm for job scheduling. The input to the algorithm is a set of jobs, each of which has a specific processing-time. There is also a number m specifying the number of machines that can process the jobs. The LPT algorithm works as follows:
Regular paperfolding sequence 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ... At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence.
Given a sequence of length (r − 1)(s − 1) + 1, label each number n i in the sequence with the pair (a i, b i), where a i is the length of the longest monotonically increasing subsequence ending with n i and b i is the length of the longest monotonically decreasing subsequence ending with n i.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.