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A mapping type is one that supports the membership operator (in) and the size function (len()), and is iterable Mappings are collections of key value items and provide methods for accessing items and their keys and values When iterated, unordered mapping types provide their items in an arbitrary order Python 30 provides two unordered mapping types, the built-in dict type and the standard library s collectionsdefaultdict type A new, ordered mapping type, collectionsOrderedDict, was introduced with Python 31; this is a dictionary that has the same methods and properties (ie, the same API) as the built-in dict, but stores its items in insertion order We will use the term dictionary to refer to any of these types when the difference doesn t matter

Only hashable objects may be used as dictionary keys, so immutable data types such as float, frozenset, int, str, and tuple can be used as dictionary keys, but mutable types such as dict, list, and set cannot On the other hand, each key s associated value can be an object reference referring to an object of any type, including numbers, strings, lists, sets, dictionaries, functions, and so on Dictionary types can be compared using the standard equality comparison operators (== and !=), with the comparisons being applied item by item (and recursively for nested items such as tuples or dictionaries inside dictionaries) Comparisons using the other comparison operators (<, <=, >=, >) are not supported since they don t make sense for unordered collections such as dictionaries

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Task based decompositions are extremely common in parallel computing For example, the distance geometry code DGEOM [Mat96] uses a task based decomposition, as does the parallel WESDYN molecular dynamics program [MR95]

A dict is an unordered collection of zero or more key value pairs whose keys are object references that refer to hashable objects, and whose values are object references referring to objects of any type Dictionaries are mutable, so we can easily add or remove items, but since they are unordered they have no notion of index position and so cannot be sliced or strided

API stands for Application Programming Interface, a generic term used to refer to the public methods and properties that classes provide, and to the parameters and return values of functions and methods For example, Python s documentation documents the APIs that Python provides

The dict data type can be called as a function, dict() with no arguments it returns an empty dictionary, and with a mapping argument it returns a dictionary based on the argument; for example, returning a shallow copy if the argument is a dictionary It is also possible to use a sequence argument, providing that each item in the sequence is itself a sequence of two objects, the rst of which is used as a key and the second of which is used as a value Alternatively, for dictionaries where the keys are valid Python identi ers, keyword arguments can be used, with the key as the keyword and the value as the key s value Dictionaries can also be created using braces empty braces, {}, create an empty dictionary; nonempty braces must contain one or more commaseparated items, each of which consists of a key, a literal colon, and a value Another way of creating dictionaries is to use a dictionary comprehension a topic we will cover later in this subsection Here are some examples to illustrate the various syntaxes they all produce the same dictionary:

Problem How can a problem's data be decomposed into units that can be operated on relatively independently Context The parallel algorithm designer must have a detailed understanding of the problem being solved In addition, the designer should identify the most computationally intensive parts of the problem, the key data structures required to solve the problem, and how data is used as the problem's solution unfolds After the basic problem is understood, the parallel algorithm designer should consider the tasks that make up the problem and the data decomposition implied by the tasks Both the task and data decompositions need to be addressed to create a parallel algorithm The question is not which decomposition to do The question is which one to start with A data based decomposition is a good starting point if the following is true

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