Solution to Project Euler Problem 31: Coin sums - In the United Kingdom the currency is made up of pound (£) and pence (p). 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?

• Java Code

package sikademy;
/**
 *
 * @author Archangel Macsika
 * Copyright (c) Sikademy. All rights reserved
 */

public class SikademyEulerSolution {
	
	private static final int TOTAL = 200;
	private static int[] COINS = {1, 2, 5, 10, 20, 50, 100, 200};
	
	public String run() {
		int[][] ways = new int[COINS.length + 1][TOTAL + 1];
		ways[0][0] = 1;
		for (int i = 0; i < COINS.length; i++) {
			int coin = COINS[i];
			for (int j = 0; j <= TOTAL; j++)
				ways[i + 1][j] = ways[i][j] + (j >= coin ? ways[i + 1][j - coin] : 0);
		}
		return Integer.toString(ways[COINS.length][TOTAL]);
	}

	public static void main(String[] args) {
                SikademyEulerSolution solution = new SikademyEulerSolution();
		System.out.println(solution.run());
	}	
}

• Python Code

# 
# @author Archangel Macsika
# Copyright (c) Sikademy. All rights reserved.
# 

def compute():
	TOTAL = 200

	ways = [1] + [0] * TOTAL
	for coin in [1, 2, 5, 10, 20, 50, 100, 200]:
		for i in range(len(ways) - coin):
			ways[i + coin] += ways[i]
	return str(ways[-1])


if __name__ == "__main__":
	print(compute())