LintCode-Fast Power

Calculate the aⁿ % b where a, b and n are all 32bit integers.

Example

For 2³¹ % 3 = 2

For 100¹⁰⁰⁰ % 1000 = 0

Challenge

O(logn)

Solution:

 class Solution {
     /*
      * @param a, b, n: 32bit integers
      * @return: An integer
      */
     public int fastPower(int a, int b, int n) {
         if (n==0) return 1%b;

         int res = fastPowerRecur(a,b,n);
         return res;
     }

     public int fastPowerRecur(int a, int b, int n){
         if (n==1)
             return a%b;

         long temp = fastPowerRecur(a,b,n/2);
         temp = temp*temp%b;
         int res = (n%2==0) ? (int) temp: (int)(temp*a%b);
         return res;
     }
 };