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Input: a multiset S containing n positive integer elements. Conditions: S must be partitionable into m triplets, S 1, S 2, …, S m, where n = 3m. These triplets partition S in the sense that they are disjoint and they cover S. The target value T is computed by taking the sum of all elements in S, then divided by m.
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
The function q(n) gives the number of these strict partitions of the given sum n. For example, q(3) = 2 because the partitions 3 and 1 + 2 are strict, while the third partition 1 + 1 + 1 of 3 has repeated parts. The number q(n) is also equal to the number of partitions of n in which only odd summands are permitted. [20]
In Python 2 (and most other programming languages), unless explicitly requested, x / y performed integer division, returning a float only if either input was a float. However, because Python is a dynamically-typed language, it was not always possible to tell which operation was being performed, which often led to subtle bugs, thus prompting the ...
Each input integer can be represented by 3nL bits, divided into 3n zones of L bits. Each zone corresponds to a vertex. Each zone corresponds to a vertex. For each edge (w,x,y) in the 3DM instance, there is an integer in the SSP instance, in which exactly three bits are "1": the least-significant bits in the zones of the vertices w, x, and y.
The New Zealand Customs Service said that the seized drugs would have been worth up to NZ$3.8 million (about $2.2 million USD) in street value and had a potential social harm cost of approximately ...
Both algorithms involve only simple loops over the input data (taking time O(n)) and over the set of possible keys (taking time O(K)), giving their O(n + K) overall time bound. Radix sort is a sorting algorithm that works for larger keys than pigeonhole sort or counting sort by performing multiple passes over the data. Each pass sorts the input ...
Arrays take linear (O(n)) space in the number of elements n that they hold. In an array with element size k and on a machine with a cache line size of B bytes, iterating through an array of n elements requires the minimum of ceiling( nk /B) cache misses, because its elements occupy contiguous memory locations.