Check if one integer is an integer power of another

Question

This is an interview question: \"Given 2 integers x and y, check if x is an integer power of y\" (e.g. for x = 8 and y = 2 the answer is \"true\", and for x = 10 and y = 2 \

Answer 1

This looks for the exponent in O(log N) steps:

#define MAX_POWERS 100

int is_power(unsigned long x, unsigned long y) {
  int i;
  unsigned long powers[MAX_POWERS];
  unsigned long last;
  last = powers[0] = y;

  for (i = 1; last < x; i++) {
    last *= last; // note that last * last can overflow here!
    powers[i] = last;
  }
  while (x >= y) {
    unsigned long top = powers[--i];
    if (x >= top) {
      unsigned long x1 = x / top;
      if (x1 * top != x) return 0;
      x = x1;
    }
  }
  return (x == 1);
}

Negative numbers are not handled by this code, but it can be done easyly with some conditional code when i = 1