Bidirectional map

In computer science, a bidirectional map is an associative data structure in which the $(key, value)$ pairs form a one-to-one correspondence. Thus the binary relation is functional in each direction: each $value$ can also be mapped to a unique $key$ . A pair $(a, b)$ thus provides a unique coupling between $a$ and $b$ so that $b$ can be found when $a$ is used as a key and $a$ can be found when $b$ is used as a key.

Mathematically, a bidirectional map can be defined a bijection $f: X \to Y$ between two different sets of keys $X$ and $Y$ of equal cardinality, thus constituting an injective and surjective function:

$\begin{cases}
& \forall x, x' \in X, f(x) = f(x') \Rightarrow x = x' \\
& \forall y \in Y, \exists x \in X : y=f(x)
\end{cases} \Rightarrow \exists f^{-1}(x)$

External links

[http://www.boost.org/doc/libs/1_47_0/libs/bimap/doc/html/index.html Boost.org]
[https://commons.apache.org/proper/commons-collections/apidocs/org/apache/commons/collections4/BidiMap.html Commons.apache.org]
[https://web.archive.org/web/20120205111646/http://cablemodem.fibertel.com.ar/mcape/oss/projects/mc_projects/boost_projects/boost_bimap.html Cablemodem.fibertel.com.ar (archived version)]
[http://www.codeproject.com/KB/stl/bimap.aspx Codeproject.com]
[https://google.github.io/guava/releases/19.0/api/docs/com/google/common/collect/BiMap.html BiMap in the Google Guava library]
[https://bidict.readthedocs.io/ bidict (bidirectional map implementation for Python)]

Category:Associative arrays