列表推导的奇怪行为

Question

I'm learning basics of Haskell and trying to solve project Euler's simple tasks: find largest palindrome of 3 digit numbers (100.999). I wrote this code:

palindrome = maximum $ filter (\a -> reverse a == a) $
                                    map show [ x*y :: Int | x <- [100 .. 999],
                                                            y <- [x, x+1 .. 999]]

It gives a wrong answer = 99999, when I change it to x <- [307 .. 999] answer still is wrong: 94249 (all palindromes, but not the largest) and finally when I change it to x <- [308 .. 999], it gives me right answer: 906609.

I really don't understand this behaviour: it seems there is some kind of overflow and truncation happens inside the generated list. Can someone explain me this wrong behaviour? I don't want you to answer the task: i know my solution is not very efficient. I just want you to explain this code behaviour (list truncation or memory issues). Thanks.

Answer 1

The result of filter is a list of String values, so maximum is comparing them lexicographically. You need to convert the values back to Int s first. The type signature ensures that read returns values of the correct type.

palindrome :: Int
palindrome = maximum . map read . filter ...

Another approach is to only convert a value to a String in the filter itself:

palindrome :: Int
palindrome = maximum $ filter (\a -> let sa = show a in reverse sa == sa) [ x*y | x <- [100..999], y <- [x..999]]