math - function mapping set of integers

I need function that maps any m integers between a and b (where b-a > m) into integers between 0 to m-1. Th开发者_高级运维e m integers between a and b may not be in any order. The mapping could be in any order as long as it is one-to-one mapping.

For example I have a set of integers between 10 and 50 and I pick any 10 integers randomly and map them into 0-9. The function could take one, two or three inputs that may different for each set of those 10 integers. And one more thing, it has to be reversible, i.e using those inputs I can get back the original number.

does it exist of such function and is it possible ?

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It's fairly easy. Map the smallest number to 0, the second smallest to 1, etc. The map is invertible if and only if you know the set of numbers you began with.

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It sounds like you're asking for a minimal perfect hash. Such functions do exist, there are algorithms for finding them, and even preexisting libraries to do the work.