Problem:
A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k.
For example, R(10) = 1111111111 = 11[×]41[×]271[×]9091, and the sum of these prime factors is 9414.
Find the sum of the first forty prime factors of R(109).
For example, R(10) = 1111111111 = 11[×]41[×]271[×]9091, and the sum of these prime factors is 9414.
Find the sum of the first forty prime factors of R(109).
Solution:
45228
Code:
The solution may include methods that will be found here: Library.java .
public interface EulerSolution{
public String run();
}
/*
* Solution to Project Euler problem 32
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/
import java.util.Arrays;
public final class p032 implements EulerSolution {
public static void main(String[] args) {
System.out.println(new p032().run());
}
public String run() {
// A candidate product has at most 4 digits. This is because if it has 5 digits,
// then the two multiplicands must have at least 5 digits put together.
int sum = 0;
for (int i = 1; i < 10000; i++) {
if (hasPandigitalProduct(i))
sum += i;
}
return Integer.toString(sum);
}
private static boolean hasPandigitalProduct(int n) {
// Find and examine all factors of n
for (int i = 1; i <= n; i++) {
if (n % i == 0 && isPandigital("" + n + i + n/i))
return true;
}
return false;
}
private static boolean isPandigital(String s) {
if (s.length() != 9)
return false;
char[] temp = s.toCharArray();
Arrays.sort(temp);
return new String(temp).equals("123456789");
}
}
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