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I am proceeding with my attempt at Project Euler Problem #254[1]. It revolves around reversing functions. *g(i)* is basically the reverse of *sf(n)*. What I am doing is taking an Integer (*i*) and returning every number *k* with the following property: If one adds up the digits in *k*, one comes up with *i*. Here is my code so far (see if you can spot the obvious error before I continue!):
listToInteger :: [Integer] -> Integer
listToInteger xs = listToInteger' $ reverse xs
where listToInteger' [] = 0
listToInteger' (x:xs) = x + 10 * listToInteger' xs
integersAddToInteger :: Int -> [Integer]
integersAddToInteger i = sort . map listToInteger . digitsAddTo . take i $ cycle [1]
digitsAddTo :: [Integer] -> [[Integer]]
digitsAddTo [] = []
digitsAddTo [x] = [[x]]
digitsAddTo xs = thirdSet xs ++ secondSet xs
where secondSet xs = digitsAddTo $ [first xs] ++ rest xs
thirdSet (x:xs) = map (x:) . digitsAddTo $ xs
first (a:b:xs) = a + b
rest (a:b:xs) = xs
When I call, for example, `integersAddToInteger 5`, I get this:
[5,14,23,32,41,113,122,131,212,221,311,1112,1121,1211,2111,11111]
Now, the obvious error is that if I want to find all *k* for an *i* greater than 9, the function `digitsAddTo` will begin using double digit numbers. I shall now attempt to fix this problem.
1: http://projecteuler.net/index.php?section=problems&id=254
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