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What would be a good hash function that will return a positive integer value, even if the key is an negative integer value? How do I pick a hash function? So what I would want is to associate negative numbers with some positive value so I can use them later.

UPDATE: (summary) I need to find a bijection $f: \mathbb{Z}\to\mathbb{N}$ which also has the property that: $$ f(x) + f(y) = f(x + y) $$

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  • $\begingroup$ What is the purpose of your hash function? $\endgroup$ – reinierpost Nov 12 '19 at 9:43
  • $\begingroup$ @reinierpost the purpose is to map negative numbers to some positive value and also not collide with other positive numbers from an array. so basically, I have an array with some integer values, and i want to map every integer value from that array to some other positive value so then i could use an algorithm that only works for positive values. $\endgroup$ – C. Cristi Nov 12 '19 at 9:45
  • $\begingroup$ In that case, any simple bijection from $\mathbb{Z}$ to $\mathbb{N}$ will do, right? It doesn't need to "hash" (mix up the ordering). $\endgroup$ – reinierpost Nov 12 '19 at 9:49
  • $\begingroup$ @reinierpost sure, but i cant think of any bijection like that $\endgroup$ – C. Cristi Nov 12 '19 at 9:51
  • $\begingroup$ @reinerpost nevermind, i think i found one! thanks! $\endgroup$ – C. Cristi Nov 12 '19 at 9:53
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From your comments, it appears all you need a bijection from $\mathbb{Z}$ to $\mathbb{N}$ that is easy to compute.

The simplest one I can think of: $x \mapsto 1/2 + 2 \mid\!(x - 1/4)\mid$.

This isn't really a hash function: it doesn't "hash" (scatter its consecutive function values across their range).

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  • $\begingroup$ Hello, I also need that the function to be like f(x) + f(y) = f(x + y) $\endgroup$ – C. Cristi Nov 12 '19 at 11:08
  • $\begingroup$ Can you see the edit? $\endgroup$ – C. Cristi Nov 12 '19 at 12:16
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    $\begingroup$ Yes. With that additional requirement, no such function exists: for infinitely many different $x$, you now require that $f(x)$ is positive, $f(-x)$ is positive, and $f(x) + f(-x) = f(0)$; no value for $f(0)$ can meet that requirement.. Are you sure you really need it? Or perhaps your function doesn't need to be injective? $\endgroup$ – reinierpost Nov 12 '19 at 12:27
  • $\begingroup$ @reinerpost The problem goes like this: given an array with N integer elements find the longest subsequence which sum gives K. and i thought of a linear time solution but only works for positive elements, so that's why i'm searching for something like this $\endgroup$ – C. Cristi Nov 12 '19 at 12:29
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    $\begingroup$ That's a different question ... $\endgroup$ – reinierpost Nov 12 '19 at 12:38
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Hint: map the positive numbers to the odd numbers and the negative numbers to the even numbers.

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