如何将两个正整数映射到唯一整数？

Question

I need to find a unique integer given two integers. That is, given two integers x and y..I want to find a function f...which maps these integers uniquely to another integer z. That is, z=f(x,y)

Here x=64 bit integer and y=64 bit integer. I want to map these numbers to z such it is again a 64 bit integer.

I tried Cantors pairing function, but Cantors pairing function returns to me a 'z' which is 128 bit as there is a multiplication involved in Cantors pairing function. I do not want z to map to 128 bit as modern computers have processing limitation of only upto 64 bit.

Is there some way out. A little bit of collision is acceptable to me.

Answer 1

If you want to do that for the whole range of 64 bit integer, then this is impossible.

There are 2^64 * 2^64 = 2^128 possible inputs for your function, but you have only 2^64 different outputs, which means that there have to be at least 2^64 numbers mapped to the same integer which is far more than a little bit of collision

Answer 2

You are essentially looking for a 64bit hash function. Here is a list http://en.wikipedia.org/wiki/List_of_hash_functions

Answer 3

Perhaps this function 'boiler-plate' will help?

unsigned long long f(
      unsigned long long x,
      unsigned long long y
      )
   {
   /** many options here, including those in link provided by @xosp7tom's answer... **/
   return(x*y);
   }