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In computer science, the maximum sum subarray problem, also known as the maximum segment sum problem, is the task of finding a contiguous subarray with the largest sum, within a given one-dimensional array A[1...n] of numbers. It can be solved in () time and () space.
The maximum sum is 1, attained by giving one agent the item with value 1 and the other agent nothing. But the max-min allocation gives each agent value at least e, so the sum must be at most 3e. Therefore the POF is 1/(3e), which is unbounded. Alice has two items with values 1 and e, for some small e>0. George has two items with value e. The ...
(i+1, s+ +), implying that + is included in the subset. Starting from the initial state (0, 0), it is possible to use any graph search algorithm (e.g. BFS) to search the state (N, T). If the state is found, then by backtracking we can find a subset with a sum of exactly T.
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
This algorithm is an improvement over previously known quadratic time algorithms. [1] The maximum scoring subsequence from the set produced by the algorithm is also a solution to the maximum subarray problem. The Ruzzo–Tompa algorithm has applications in bioinformatics, [4] web scraping, [5] and information retrieval. [6]
Comparison of two revisions of an example file, based on their longest common subsequence (black) A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences).
The longest increasing subsequence problem is closely related to the longest common subsequence problem, which has a quadratic time dynamic programming solution: the longest increasing subsequence of a sequence is the longest common subsequence of and , where is the result of sorting.
Sum of sets The Minkowski sum of two sets A {\displaystyle A} and B {\displaystyle B} of real numbers is the set A + B := { a + b : a ∈ A , b ∈ B } {\displaystyle A+B~:=~\{a+b:a\in A,b\in B\}} consisting of all possible arithmetic sums of pairs of numbers, one from each set.