如何编码/解码另一个整数中2个整数的所有组合

Question

i want to encode all possible directions of a square into an integer (except the 0,0).

i have two directions i, j each one could be {-1, 0, 1}

i need 2 functions with these signatures

int encodeToIndex(int i, int j) {
}

and

int[] decodeFromIndex(int x) {
}

We could use a Hashmap, but i need an optimized solution, we should be able to encode all the combinations (except the 0,0) in just 8 numbers from 0 to 7 (i need an index from 0 to 7).

I am working with JAVA, so a JAVA solution would be prefered (but it a mathematical problem).

folowing the @Andrea solution i choose this solution for the moment:

public static int encode(int i, int j) {
    int res = (i + 1) + (j + 1) * 3;
    return res>4?res-1:res;
}
public static int[] decode(int x) {
    if (x>3) x++;
    return new int[]{ x%3-1, x/3-1 };
}

Answer 1

You have 3 values for each, so one way to store that is to use 2 bits, eg use i + 1 (0-2) and j + 1 (0-2), then combined them using bit-manipulation:

(i + 1) | (j + 1) << 2

A more condensed result can be done by multiply by 3 instead:

(i + 1) + (j + 1) * 3

For the various values of i and j that would produce:

   Bit-shift        Factor of 3
   i -1  0  1        i -1  0  1
 j ┌─────────      j ┌─────────
-1 │  0  1  2     -1 │  0  1  2
 0 │  4  5  6      0 │  3  4  5
 1 │  8  9 10      1 │  6  7  8

The reverse operation is simple enough too, using either bit-shift/-mask, or division/remainder.