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Given a composite integer, and in particular one which is the product of two large primes =, the integer factorization problem is to find and (more generally, find primes , …, such that =). It is a major open problem to find an algorithm for integer factorization that runs in time polynomial in the size of representation ( log n ...
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. [33] Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional ...
R is a programming language for statistical computing and data visualization. It has been adopted in the fields of data mining, bioinformatics and data analysis. [9] The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data. R software is open-source and free software.
A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. A problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do.
These range from "Algorithmica", where P = NP and problems like SAT can be solved efficiently in all instances, to "Cryptomania", where P ≠ NP and generating hard instances of problems outside P is easy, with three intermediate possibilities reflecting different possible distributions of difficulty over instances of NP-hard problems.
Image credits: anon #2. We have the world's stupidest dachshund. One time he sneezed next to a kitchen cabinet and hit his head on the door. He barked at the cabinet for hitting him.
As budget airlines struggle with profitability and major airlines cater increasingly to high-end customers, inexpensive airfare could be harder to come by, experts say. Airlines are going premium ...
Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete. Despite its worst-case hardness, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many approximation algorithms exist.