java binary exponentiation
/**
* Calculate a^n in O(logn) time, instead of O(n) time with naive approach.
**/
public static long powerRecursive(int base, int exponent){
if(exponent == 0) return 1;
return (exponent % 2 == 0) ?
powerRecursive(base, exponent / 2) * powerRecursive(base, exponent / 2)
: base * powerRecursive(base, (exponent - 1) / 2) *
powerRecursive(base, (exponent - 1) / 2);
}