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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.
The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. The main steps of the algorithm are: Order the numbers from large to small. Replace the largest and second-largest numbers by their difference.
Time bounds for integer sorting algorithms typically depend on three parameters: the number n of data values to be sorted, the magnitude K of the largest possible key to be sorted, and the number w of bits that can be represented in a single machine word of the computer on which the algorithm is to be performed.
The natural generalization of the greedy number partitioning algorithm is the envy-graph algorithm. It guarantees that the allocation is envy-free up to at most one item (EF1). Moreover, if the instance is ordered (- all agents rank the items in the same order), then the outcome is EFX, and guarantees to each agent at least 2 n 3 n − 1 ...
A general-purpose factoring algorithm, also known as a Category 2, Second Category, or Kraitchik family algorithm, [10] has a running time which depends solely on the size of the integer to be factored. This is the type of algorithm used to factor RSA numbers. Most general-purpose factoring algorithms are based on the congruence of squares method.
On the right Nicomachus's example with numbers 49 and 21 resulting in their GCD of 7 (derived from Heath 1908:300). In mathematics, the Euclidean algorithm, [note 1] or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder.
The Complete Greedy Algorithm (CGA) considers all partitions by constructing a k-ary tree. Each level in the tree corresponds to an input number, where the root corresponds to the largest number, the level below to the next-largest number, etc. Each of the k branches corresponds to a different set in which the current number can be put.
When there are no unchecked numbers left in the set, consider the current largest number to be the largest in the set. (Quasi-)formal description: Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in pseudocode or pidgin code :