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In this case, the array from which samples are taken is [2, 3, -1, -20, 5, 10]. 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 subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1] The problem is known to be NP-complete. Moreover, some restricted variants of it are NP-complete too ...
In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5 6 = 1 2 + 1 3 .
The 3-partition problem is similar to the partition problem, in which the goal is to partition S into two subsets with equal sum, and the multiway number partitioning, in which the goal is to partition S into k subsets with equal sum, where k is a fixed parameter. In 3-Partition the goal is to partition S into m = n /3 subsets, not just a fixed ...
This can be proven by a reduction from the partition problem: given an instance of Partition where the sum of all input numbers is , construct an instance of bin-packing in which the bin size is T. If there exists an equal partition of the inputs, then the optimal packing needs 2 bins; therefore, every algorithm with an approximation ratio ...
Activity selection problem. The activity selection problem is a combinatorial optimization problem concerning the selection of non-conflicting activities to perform within a given time frame, given a set of activities each marked by a start time (s i) and finish time (f i ). The problem is to select the maximum number of activities that can be ...
In computational complexity theory, the 3SUM problem asks if a given set of real numbers contains three elements that sum to zero. A generalized version, k-SUM, asks the same question on k elements, rather than simply 3. 3SUM can be easily solved in () time, and matching (⌈ / ⌉) lower bounds are known in some specialized models of computation (Erickson 1999).
Rabin–Karp algorithm. In computer science, the Rabin–Karp algorithm or Karp–Rabin algorithm is a string-searching algorithm created by Richard M. Karp and Michael O. Rabin ( 1987) that uses hashing to find an exact match of a pattern string in a text. It uses a rolling hash to quickly filter out positions of the text that cannot match the ...