Bidirectional map explained

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

and

so that

can be found when

is used as a key and

can be found when

is used as a key.

f:X\toY

between two different sets of keys

and

of equal cardinality, thus constituting an injective and surjective function:

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

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