031 Coin sums.sf

#!/usr/bin/ruby

# Author: Daniel "Trizen" Șuteu
# License: GPLv3
# Website: https://github.com/trizen

# 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?

# https://projecteuler.net/problem=31

# Runtime: 0.169s

var target = 200;
var coins = [1, 2, 5, 10, 20, 50, 100, 200];

func num_paths(startsum, lastcoin) is cached {

    return 1 if (startsum == target);

    var paths = 0;
    coins.each { |coin|
        if ((lastcoin >= coin) && (startsum <= (target - coin))) {
            paths += num_paths(startsum + coin, coin);
        }
    }

    paths;
}

say num_paths(0, target);