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A multimap generalizes an associative array by allowing multiple values to be associated with a single key. [9] A bidirectional map is a related abstract data type in which the mappings operate in both directions: each value must be associated with a unique key, and a second lookup operation takes a value as an argument and looks up the key ...
the Add method, which adds a key and value and throws an exception if the key already exists in the dictionary; assigning to the indexer, which overwrites any existing value, if present; and assigning to the backing property of the indexer, for which the indexer is syntactic sugar (not applicable to C#, see F# or VB.NET examples).
An associative array stores a set of (key, value) pairs and allows insertion, deletion, and lookup (search), with the constraint of unique keys. In the hash table implementation of associative arrays, an array A {\displaystyle A} of length m {\displaystyle m} is partially filled with n {\displaystyle n} elements, where m ≥ n {\displaystyle m ...
Linear probing is a component of open addressing schemes for using a hash table to solve the dictionary problem.In the dictionary problem, a data structure should maintain a collection of key–value pairs subject to operations that insert or delete pairs from the collection or that search for the value associated with a given key.
In a student enrollment system, where students may be enrolled in multiple classes simultaneously, there might be an association for each enrollment of a student in a course, where the key is the student ID and the value is the course ID. If a student is enrolled in three courses, there will be three associations containing the same key.
The keys in a dictionary must be of an immutable Python type, such as an integer or a string, because under the hood they are implemented via a hash function. This makes for much faster lookup times, but requires keys not change.
Python dictionaries (a form of associative array) can also be directly iterated over, when the dictionary keys are returned; or the items() method of a dictionary can be iterated over where it yields corresponding key,value pairs as a tuple:
In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.