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Hash Tables for Integer Keys in Data Structure
Here we will discuss about the Hash tables with the integer keys. Here the key values ? comes from universe ? such that ? = {0, 1, … , ? – 2, ? – 1}. A hash function is ?. The domain of this hash function is ?. The range is in the set {0, 1, … , ? – 1}, and ? ≤ ?.
A hash function h is said to be a perfect hash function for a set ? ⊆ ? if for every ? ∈ ?, ?(?) is unique. A perfect hash function ? for ? is minimal if ? = |?|. So ? is bijection between S and {0, 1, … , ? – 1}. Obviously a minimal perfect hash function is desirable since this allows us to store all the elements of S in a single array of length n.
Unfortunately, perfect hash functions are very rare, even if m is much larger than n. If each element in S is uniformly and independently mapped to a random element in {0, 1, … , ? – 1}, then according to birthday paradox if m is much less than n2 then there will almost surely exists two elements of S, that have the same hash value.
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