- External links
In computer science, a bidirectional map, or hash bag, is an associative data structure in which the 
pairs form a one-to-one correspondence. Thus the binary relation is functional in each direction: each 
can also be mapped to a unique 
. A pair 
thus provides a unique coupling between 
and 
so that can be found when is used as a key and can be found when is used as a key.
Mathematically, a bidirectional map can be defined a bijection 
between two different sets of keys 
and 
of equal cardinality, thus constituting a injective and surjective function:
External links
- 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)]
- 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)]
1 : Associative arrays