Mapping two integers to one, in a unique and deterministic way

Question

Imagine two positive integers A and B. I want to combine these two into a single integer C.

There can be no other integers D and E which combine to C. So combining

Answer 1

Although Stephan202's answer is the only truly general one, for integers in a bounded range you can do better. For example, if your range is 0..10,000, then you can do:

#define RANGE_MIN 0
#define RANGE_MAX 10000

unsigned int merge(unsigned int x, unsigned int y)
{
    return (x * (RANGE_MAX - RANGE_MIN + 1)) + y;
}

void split(unsigned int v, unsigned int &x, unsigned int &y)
{
    x = RANGE_MIN + (v / (RANGE_MAX - RANGE_MIN + 1));
    y = RANGE_MIN + (v % (RANGE_MAX - RANGE_MIN + 1));
}

Results can fit in a single integer for a range up to the square root of the integer type's cardinality. This packs slightly more efficiently than Stephan202's more general method. It is also considerably simpler to decode; requiring no square roots, for starters :)