## 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?

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]);
}

}