Hi Michael,

I think you're making your own task harder than necessary. For one thing, -XViewPatterns is nice, but in this case they hide some of the structure. Most importantly, they hide that all the special null-cases are actually unnecessary because the normal cases already cover them. I would further advise to use layout to reveal even more structure. That's especially useful when you later convert the explicit recursion into a fold.

But even then, on a different level you're still working too hard: You're parsing the string and building/correcting the tree in one step. Why not create the tree, convert the tree, and then read out the tree in three steps? It's still the same complexity class but much easier to write and read. And once you are free to think of the tree manipulations on their own it might help recognize optimizations like those the solutions of other commenters use.

I'm prepping for a coding interview, and am examining the task of correcting unbalanced parentheses. The finger tree seems to be the right data structure. As a proof of concept I've used Data.Sequence to test my idea. If this is the right direction to go, I'll write more specialized finger tree code. The code works on the few test cases I have tried. Feedback appreciated.

{-# LANGUAGE ViewPatterns #-}
module Parenthesis where
import BasicPrelude hiding (concat,null,empty)

import Data.Sequence hiding (length)
import Data.Foldable hiding (length,null)

balanceParens :: String -> String
balanceParens str = go str [] empty
  where
    go [] [] (null -> True) = []
    go [] [] parens = Data.Foldable.toList parens
    go ('(':xs) [] (null -> True) = go xs [RP] (singleton '(')
    go (')':xs) [] (null -> True) = go xs [] (fromList "()")
    go ('(':xs) debit parens = go xs (RP:debit) (parens |> '(')
    go (')':xs) [] parens = go xs [] corrected
      where corrected = ('(' <| parens) |> ')'
    go (')':xs) (RP:debit) parens = go xs debit (parens |> ')')
    go (_:xs) debit parens = go xs debit parens
    go [] (RP:debit) parens = go [] debit (parens |> ')')

example:

balanceParens "))("
"(())()"
balanceParens ")))"
"((()))"

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