Question

I am facing the problem of having several integers, and I have to generate one using them. For example.

Int 1: 14 Int 2: 4 Int 3: 8 Int 4: 4  Hash Sum: 43 

I have some restriction in the values, the maximum value that and attribute can have is 30, the addition of all of them is always 30. And the attributes are always positive.

The key is that I want to generate the same hash sum for similar integers, for example if I have the integers, 14, 4, 10, 2 then I want to generate the same hash sum, in the case above 43. But of course if the integers are very different (4, 4, 2, 20) then I should have a different hash sum. Also it needs to be fast.

Ideally I would like that the output of the hash sum is between 0 and 512, and it should evenly distributed. With my restrictions I can have around 5K different possibilities, so what I would like to have is around 10 per bucket.

I am sure there are many algorithms that do this, but I could not find a way of googling this thing. Can anyone please post an algorithm to do this?.

Some more information

The whole thing with this is that those integers are attributes for a function. I want to store the values of the function in a table, but I do not have enough memory to store all the different options. That is why I want to generalize between similar attributes.

The reason why 10, 5, 15 are totally different from 5, 10, 15, it is because if you imagine this in 3d then both points are a totally different point

Some more information 2

Some answers try to solve the problem using hashing. But I do not think this is so complex. Thanks to one of the comments I have realized that this is a clustering algorithm problem. If we have only 3 attributes and we imagine the problem in 3d, what I just need is divide the space in blocks.

In fact this can be solved with rules of this type

if (att[0] < 5 && att[1] < 5 && att[2] < 5 && att[3] < 5)      Block = 21   if ( (5 < att[0] < 10) &&  (5 < att[1] < 10) &&  (5 < att[2] < 10) &&  (5 < att[3] < 10))      Block = 45 

The problem is that I need a fast and a general way to generate those ifs I cannot write all the possibilities.

Answer 1

Given the inputs a, b, c, and d, each ranging in value from 0 to 30 (5 bits), the following will produce an number in the range of 0 to 255 (8 bits).

bucket = ((a & 0x18) << 3) | ((b & 0x18) << 1) | ((c & 0x18) >> 1) | ((d & 0x18) >> 3) 

Whether the general approach is appropriate depends on how the question is interpreted. The 3 least significant bits are dropped, grouping 0-7 in the same set, 8-15 in the next, and so forth.

0-7,0-7,0-7,0-7 -> bucket 0 0-7,0-7,0-7,8-15 -> bucket 1 0-7,0-7,0-7,16-23 -> bucket 2 ... 24-30,24-30,24-30,24-30 -> bucket 255 

Trivially tested with:

for (int a = 0; a <= 30; a++)     for (int b = 0; b <= 30; b++)         for (int c = 0; c <= 30; c++)             for (int d = 0; d <= 30; d++) {                 int bucket = ((a & 0x18) << 3) |                              ((b & 0x18) << 1) |                              ((c & 0x18) >> 1) |                              ((d & 0x18) >> 3);                 printf('%d, %d, %d, %d -> %d\n',                          a,  b,  c,  d,   bucket);             }