CODE EXAMPLE FOR JAVA

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);
}