The function groupBy from haskell’s standard library is defined in terms of span, the effect being that the supplied predicate function is used to compare the first element of a group with successive elements.
This isn’t clear from the docs, and you might try to do this and wonder at the output you got:
*Main> groupBy (< =) [3,4,5,3,2,1,4,4,1,1,2,3,4,5,4,5,6,7] [[3,4,5,3],[2],[1,4,4,1,1,2,3,4,5,4,5,6,7]]
I’ve been thinking quite a bit lately about a category of functions that are always a bit awkward to define: they involve cases where we would like to traverse a recursive data structure and do something with the data that we have passed over but which is “gone now”.
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Here is some code I whipped up in response to an interesting problem posted on reddit.com/r/coding/. It was a really interesting algorithm to work out:
import Data.List (sortBy)
-- takes an inversion list and converts it to the list of permuted
-- elements:
decode = dec [] . sortBy lowHi . zip [1..] where
dec as [] = as
dec as ((a,_):is) = let is' = sortBy lowHi (decrementGT a is)
in dec (a:as) is'
-- decrement every inversion number by 1, for every tuple in which
-- the element is greater than `a`:
decrementGT a = map (\(a',i) -> (a', if a'>a then i-1 else i) )
-- we sort by the inversion number, low to high. For elements with
-- the same inversion number, we say that the greater element tuple
-- should go before a lesser element:
lowHi (a,i) (a',i')
| i == i' = if a>a' then LT else GT
| otherwise = compare i i'
It’s not the prettiest code I’ve written, but it’s pretty straight-forward and concise. Thanks for looking!
