Bidirectional map

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In computer science, a bidirectional map, or hash bag[citation needed], 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:

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