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I'm currently looking at perfect hash functions. One thing I miss from the texts I've read so far is, how they cope when attempting to look up with a key that is outside of the set from which the perfect hash was generated from.

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    $\begingroup$ They don't. It's an invalid input. $\endgroup$ – Yuval Filmus Oct 10 '19 at 12:25
  • $\begingroup$ @YuvalFilmus: Is there a way to determine just from the PHF itself if a key is invalid? Or somehow map any value outside the set of keys to a nil value? $\endgroup$ – datenwolf Oct 10 '19 at 14:37
  • $\begingroup$ Depends on the implementation. It may return the image of another key in the domain. If the PHF is not minimal, it may also return a value that doesn't have to a preimage in the set. Some implementations detect foreign keys with a given probability (as bloom filters do) and return a special value. $\endgroup$ – Piezoid Oct 11 '19 at 11:58
  • $\begingroup$ @Piezoid: I already had the idea of prepending a bloom filter in front of the lookup to filter out all keys that are not in the set of the PHF keys. $\endgroup$ – datenwolf Oct 11 '19 at 15:15
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Given a set of keys, a “perfect” hash function is one that gives a different hash for each key. As soon as you try to apply it to a key outside that set, it is quite likely not “perfect” anymore.

Let’s say you are writing a compiler, and you found a”perfect” hash function that maps each reserved identifier of your programming language to a different hash code. And I give you a word that is not one of the reserved words of the language. If you apply your “perfect” hash function then the hash code is either not the hash code of a reserved word (you need to check for that case), or it may be the hash code of a reserved word ( you need to check for that as well). The advantage is that at most one check is needed.

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