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

• 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)