In today’s Programming Praxis exercise, our goal is to list all of the ways in which a target amount can be reached given a list of coin denominations. Let’s get started, shall we?

import Data.List

We check the first remaining coin to see if it’s not bigger than the remaining target amount. If so, subtract it from the target amount and call the algorithm recursively. If not, delete it from the list of remaining coins and continue. When the remaining amount reaches 0, we have found a valid combination.

coins :: (Num a, Ord a) => [a] -> a -> [[a]] coins _ 0 = [[]] coins xs n = [c:r | (c:cs) <- tails xs, c <= n, r <- coins (c:cs) (n-c)]

Since the logic for counting the total number of options and generating the options is nigh identical, we simply ask for the length of the resulting list.

count :: (Num a, Ord a) => [a] -> a -> Int count xs = length . coins xs

Some tests to see if everything is working properly:

main :: IO () main = do print $ count [1,5,10,25] 40 == 31 mapM_ print $ coins [1,5,10,25] 40