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

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

👁 {\displaystyle {\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)}

• Boost.org
• Commons.apache.org
• Cablemodem.fibertel.com.ar (archived version)
• Codeproject.com
• BiMap in the Google Guava library
• bidict (bidirectional map implementation for Python)
• BidirectionalDictionary (bidirectional map implementation for C#)