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In computer programming, a collection is an abstract data type that is a grouping of items that can be used in a polymorphic way. Often, the items are of the same data type such as int or string . Sometimes the items derive from a common type; even deriving from the most general type of a programming language such as object or variant .
Given a set of elements {1, 2, …, n} (henceforth referred to as the universe, specifying all possible elements under consideration) and a collection, referred to as S, of a given m subsets whose union equals the universe, the set cover problem is to identify a smallest sub-collection of S whose union equals the universe.
W3Schools is a freemium educational website for learning coding online. [1] [2] Initially released in 1998, it derives its name from the World Wide Web but is not affiliated with the W3 Consortium. [3] [4] [unreliable source] W3Schools offers courses covering many aspects of web development. [5] W3Schools also publishes free HTML templates.
Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of Python 2. [37] Python consistently ranks as one of the most popular programming languages, and has gained widespread use in the machine learning community. [38] [39] [40] [41]
For example, in Python, to print the string Hello, World! followed by a newline, one only needs to write print ("Hello, World!" In contrast, the equivalent code in C++ [ 7 ] requires the import of the input/output (I/O) software library , the manual declaration of an entry point , and the explicit instruction that the output string should be ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The following is a dynamic programming implementation (with Python 3) which uses a matrix to keep track of the optimal solutions to sub-problems, and returns the minimum number of coins, or "Infinity" if there is no way to make change with the coins given. A second matrix may be used to obtain the set of coins for the optimal solution.
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.