Java get pow with BigInteger

Question

Find the last ten digits of the series, 1^1 + 2^2 + 3^3 + ... + 1000^1000

I'm using Java.. I think I can modpow function for this question. (BigInteger) Here is my Java code but it isnt work. How can I do that?

 public static void main(String[] args) {
    BigInteger a;
    BigInteger b = null;
    BigInteger c = new BigInteger("10000000000");
    for (int i = 0; i <= 1000; i++) {
        a = new BigInteger("" + i);
        b.add(a.modPow(a, c));
    }
    System.out.println(b);
}

I get the error of NullPointerException.. Sorry my english, thanks.

Answer 1

BigInteger b = null;

therefore, in the first iteration, when you do b.add(a.modPow(a, c)); , b is null

Answer 2

I think you have two basic errors, first you never initialized b - that could be

BigInteger b = BigInteger.ZERO;

Then you need to assign the result of the b.add(a.modPow(a, c)); to b (since BigInteger add doesn't modify in-place). That is,

b = b.add(a.modPow(a, c));

When I make those two changes I get the output

4629110846701

Answer 3

null is not a zero value. Initialize your variable with 0 like this

BigInteger b = new BigInteger("0");

Even if, as peter.petrov said, this problem could be solved with one more simple solution without using big integers

Answer 4

import java.math.BigInteger;

class Main {
    public static void main(String[] args) {
        BigInteger num = BigInteger.ZERO;
        for (int i = 1; i <= 1000; i++) {
            num = num.add(BigInteger.valueOf(i).pow(i));
        }
        BigInteger res = num.mod(new BigInteger("10000000000"));
        System.out.println(res);
    }
}

output :

9110846700

More efficient solution taken from http://www.mathblog.dk/project-euler-48-last-ten-digits/ as biginteger gets very slow on very large numbers

import java.io.InputStream;

class Main {
    public static void main(String[] args) {
        long result = 0;
        long modulo = 10000000000L;

        for (int i = 1; i <= 1000; i++) {
            long temp = i;
            for (int j = 1; j < i; j++) {
                temp *= i;
                temp %= modulo;
            }

            result += temp;
            result %= modulo;
        }
        System.out.println(result);
    }

output :

9110846700