Just compute two rolling checksums while traversing the list, one forwards and one backwards, and compare them at the end.ĭata RKHash = RKHash Update: The problem could be actually solved in a genuine one pass using a rolling checksum, at the cost of having false positives in (rare) cases of hash collisions. We'd have to do some measurements, for example using the criterion package. Since all suggested algorithms are O(n), it's hard to decide which one will be more efficient just by reasoning. The combined length of ss and xs is always n and if we find out in the middle a difference, like in "aaabcaaa", we finish and release resources early. When we hit the middle after n/2 steps, we just compare the accumulated reversed first half with the rest. During that we compute the reverse of the traversed part in ss. We're traversing the list at two different "speeds" at the same time in a tail-recursive loop, to get to the middle. My attempt to solve this problem would look like this: isPal' :: (Eq a) => -> Bool > case () ofįurthermore, since walk calls itself recursively and examines the result of the recursive call, it can't be optimized to tail recursion, so you're building a chain of n calls on the stack.Īnother thing to notice is that the whole original list is kept in memory until the whole chain of walks finishes. (The above nested ifs can be rewritten as. Where we're traversing ys as walk returns to its parent call. (if n > 0 then Left (Right ys) else Right True) And the second traversal is occurring in the line Left (Right (y:ys)) -> if y = x then The first pass is the recursive call to walk, which gets to the end of the list. In your case, you're also traversing the list twice, although it's somewhat hidden. So we'll always have to either get to the last element at the beginning, or keep the elements as we traverse the list, to have them for comparison when we get to the end, So we can't get to the situation when we just traverse the list from the beginning to the end, releasing the elements already traversed. Obviously we can't avoid checking the last element, if the list is a palindrome, and we need to have the first element to compare it to. In general, I'd say that it's not really possible to make a genuine single-pass solution. A small improvement is also replacing nested ifs with a case statement. You should also document the function better, it's not clear what the Int argument is without thoroughly inspecting the code. Not only it'll be simpler, but the constructor names will also be more descriptive and it'll be easier to understand what's going on. Also instead of having Either (Either X Y) Z, declare your own data type with 3 constructors. Is there a better way to check if a string is a palindrome using only one pass? Is it worth trying to write a single pass check?įrom the readability point of view, I'd suggest to keep some maximum line length, like 72 or 80 characters. IsPalindrome x = ans where (Right ans) = walk x 0 Left (Right (y:ys)) -> if y = x then (if n > 0 then Left (Right ys) else Right True) else Right False | back = n -> let (y:ys) = xs in if y = x then (if null ys then Right True else Left (Right ys)) else Right False Left (Left back) | (back + 1) = n -> Left (Right xs) walk :: (Eq a) => -> Int -> Either (Either Int ) Bool I wanted to write a single pass palindrome check. All of them use two passes - one for building reverse list and one more for =. There are several other solutions with some kind of reverse. It's obvious solution is isPalindrome x = x = reverse x There is a problem to check if a list if a palindrome. I am learning Haskell and I am doing 99 Haskell problems.
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