Lesson plan

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)

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Article summary

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)

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  1. Summarise the article in your own words. Which single claim would you verify first, and why?
  2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
  3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

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