Don't update current x and y on each iteration.

Save the total number of jumps of one direction.
Ex:
int toSouthWest = 0;
for (int i = 0; i < a.legth; i++) {
 if (a[i] == '1'){
   toSouthWest++;
 }
 if (a[i] == '9'){
   toSouthWest--;
 }
 if (a[i] == '8'){
   toSouth++
 }
 ...
}

then you sum diractions vectors and get the answer

double y = toSouth + (toSouthWest + toSouthEast)*(1/2)^(1/2);
double x = ...

good luck!!