Project Euler > Problem 31 > Coin sums (Java Solution)

Problem:

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

It is possible to make £2 in the following way:

1[×]£1 + 1[×]50p + 2[×]20p + 1[×]5p + 1[×]2p + 3[×]1p

How many different ways can £2 be made using any number of coins?

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]);
 }
 
}