题目链接

 

Java程序

package projecteuler51to60;

import java.math.BigInteger;
import java.util.Iterator;
import java.util.Set;
import java.util.TreeSet;

class level56{    
    void solve0(){
        int maxsum=0;
        for(int a=2;a<100;a++){
            for(int b=2;b<100;b++){
                BigInteger bigNum = BigInteger.valueOf(a).pow(b);
                maxsum=Math.max(digitSum(bigNum), maxsum);
//                System.out.println(maxsum);
            }
        }
        System.out.println(maxsum);
    }
    private  int digitSum(BigInteger n) {
        int sum = 0;
        String s = n.toString();
        for (int i = 0; i < s.length(); i++)
            sum += s.charAt(i) - '0';
        return sum;
    }
    int sumDigits(BigInteger num){
        int sum=0;
        BigInteger ten = BigInteger.valueOf(10);
        while(num.equals(0)){
            sum+=(num.mod(ten)).intValue();
            num = num.divide(ten);
        }
        return sum;
    }

    
}
public class Problem56 {


    public static void main(String[] args){
        long begin= System.currentTimeMillis();
        new level56().solve0();
        long end = System.currentTimeMillis();
        long Time = end - begin;
        System.out.println("Time:"+Time/1000+"s"+Time%1000+"ms");
    }

}
由于上面程序写的时间有点长了，不做过多分析，只贴程序