Project Euler > Problem 131 > Prime cube partnership (Java Solution)

Problem:

There are some prime values, p, for which there exists a positive integer, n, such that the expression n3 + n2p is a perfect cube.

For example, when p = 19, 83 + 82[×]19 = 123.

What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred.

How many primes below one million have this remarkable property?

Solution:

73682

Code:
The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}

/* 
 * Solution to Project Euler problem 31
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p031 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p031().run());
	}
	
	
	private static final int TOTAL = 200;
	private static int[] COINS = {1, 2, 5, 10, 20, 50, 100, 200};
	
	public String run() {
		// Knapsack problem. ways[i][j] is the number of ways to use
		// any of the first i coin values to form an unordered sum of j.
		int[][] ways = new int[COINS.length + 1][TOTAL + 1];
		ways[0][0] = 1;
		for (int i = 0; i < COINS.length; i++) {
			for (int j = 0; j <= TOTAL; j++)
				ways[i + 1][j] = ways[i][j] + (j >= COINS[i] ? ways[i + 1][j - COINS[i]] : 0);  // Dynamic programming
		}
		return Integer.toString(ways[COINS.length][TOTAL]);
	}
	
}