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This function is very easy to compute (k % M, in Java), and is effective in dispersing the keys evenly between 0 and M-1.
If the keys are real numbers between 0 and 1, we might just multiply by M and round off to the nearest integer to get an index between 0 and M-1.
As with separate chaining, the performance of open-addressing methods is dependent on the ratio α = N/M, but we interpret it differently.
For separate chaining α is the average number of items per list and is generally larger than 1.
There are a billion different social security numbers, but suppose that our application will need to process just a few hundred keys, so that we could use a hash table of size M = 1000.
: we choose the array size M to be prime, and, for any positive integer key k, compute the remainder when dividing k by M.
In this case, we can compute the number ), but for your own type, you have to try to do it on your own.
Program Phone illustrates one way to proceed: make integers from the instance variables and use modular hashing.
This was done in the hopes of computing the hash function more quickly.
Indeed, the hash values were computed more quickly, but it became more likely that many strings hashed to the same values.31 is also a Mersenne prime (like 127 or 8191) which is a prime number that is one less than a power of 2.