-----------------------------------------------------------------------------
-- |
-- Module : Data.OrdList
-- Copyright : (c) Leon P Smith 2009
-- License : BSD3
--
-- Maintainer : leon at melding-monads dot com
-- Stability : experimental
-- Portability : portable
--
-- This module implements bag and set operations on ordered lists.
-- Except for variations of the 'sort' and 'isSorted' functions,
-- every function assumes that any list arguments are sorted lists.
-- Assuming this precondition is met, every resulting list is also
-- sorted.
--
-- Note that these functions handle multisets, and are left-biased.
-- Thus, even assuming the arguments are sorted, 'isect' may not be a
-- return the same results as Data.List.intersection, due to multiplicity.
--
-----------------------------------------------------------------------------
module Data.OrdList
( member, memberBy, has, hasBy
, isSorted, isSortedBy
, insertBag, insertBagBy
, insertSet, insertSetBy
, isect, isectBy
, union, unionBy
, minus, minusBy
, xunion, xunionBy
, merge, mergeBy
, subset, subsetBy
, sort, sortBy
, sortOn, sortOn'
, nubSort, nubSortBy
, nubSortOn, nubSortOn'
, nub, nubBy
) where
import Data.List(sort,sortBy)
-- | Returns 'True' if the elements of a list occur in non-descending order, equivalent to 'isSortedBy' '(<=)'
isSorted :: (Ord a) => [a] -> Bool
isSorted = isSortedBy (<=)
-- | Returns 'True' if the predicate returns true for all adjacent pairs of elements in the list
isSortedBy :: (a -> a -> Bool) -> [a] -> Bool
isSortedBy lte = loop
where
loop [] = True
loop [_] = True
loop (x:y:zs) = (x `lte` y) && loop (y:zs)
-- | Returns 'True' if the element appears in the list
member :: (Ord a) => a -> [a] -> Bool
member = memberBy compare
memberBy :: (a -> a -> Ordering) -> a -> [a] -> Bool
memberBy cmp x = loop
where
loop [] = False
loop (y:ys) = case cmp x y of
LT -> False
EQ -> True
GT -> loop ys
-- | Returns 'True' if the element appears in the list
has :: (Ord a) => [a] -> a -> Bool
has xs y = memberBy compare y xs
hasBy :: (a -> a -> Ordering) -> [a] -> a -> Bool
hasBy cmp xs y = memberBy cmp y xs
-- | Inserts an element into a list, allowing for duplicate elements
insertBag :: (Ord a) => a -> [a] -> [a]
insertBag = insertBagBy compare
insertBagBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
insertBagBy cmp = loop
where
loop x [] = [x]
loop x (y:ys)
= case cmp x y of
LT -> y:loop x ys
_ -> x:y:ys
-- | Inserts an element into a list only if it is not already there.
insertSet :: (Ord a) => a -> [a] -> [a]
insertSet = insertSetBy compare
insertSetBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
insertSetBy cmp = loop
where
loop x [] = [x]
loop x (y:ys) = case cmp x y of
LT -> y:loop x ys
EQ -> y:ys
GT -> x:y:ys
-- | Intersection of two ordered lists.
--
-- > isect [1,3,5] [2,4,6] == []
-- > isect [2,4,6,8] [3,6,9] == [6]
-- > isect [1,2,2,2] [1,1,1,2,2] == [1,2,2]
isect :: (Ord a) => [a] -> [a] -> [a]
isect = isectBy compare
isectBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
isectBy cmp = loop
where
loop [] _ys = []
loop _xs [] = []
loop (x:xs) (y:ys)
= case cmp x y of
LT -> loop xs (y:ys)
EQ -> x : loop xs ys
GT -> loop (x:xs) ys
-- | Union of two ordered lists.
--
-- > union [1,3,5] [2,4,6] == [1..6]
-- > union [2,4,6,8] [3,6,9] == [2,3,4,6,8,9]
-- > union [1,2,2,2] [1,1,1,2,2] == [1,1,1,2,2,2]
union :: (Ord a) => [a] -> [a] -> [a]
union = unionBy compare
unionBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
unionBy cmp = loop
where
loop [] ys = ys
loop xs [] = xs
loop (x:xs) (y:ys)
= case cmp x y of
LT -> x : loop xs (y:ys)
EQ -> x : loop xs ys
GT -> y : loop (x:xs) ys
-- | Difference
--
-- > minus [1,3,5] [2,4,6] == [1,3,5]
-- > minus [2,4,6,8] [3,6,9] == [2,4,8]
-- > minus [1,2,2,2] [1,1,1,2,2] == [2]
minus :: (Ord a) => [a] -> [a] -> [a]
minus = minusBy compare
minusBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
minusBy cmp = loop
where
loop [] _ys = []
loop xs [] = xs
loop (x:xs) (y:ys)
= case cmp x y of
LT -> x : loop xs (y:ys)
EQ -> loop xs ys
GT -> loop (x:xs) ys
-- | Exclusive union
--
-- > xunion [1,3,5] [2,4,6] == [1..6]
-- > xunion [2,4,6,8] [3,6,9] == [2,3,4,8]
-- > xunion [1,2,2,2] [1,1,1,2,2] == [1,1,2]
xunion :: (Ord a) => [a] -> [a] -> [a]
xunion = xunionBy compare
xunionBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
xunionBy cmp = loop
where
loop [] ys = ys
loop xs [] = xs
loop (x:xs) (y:ys)
= case cmp x y of
LT -> x : loop xs (y:ys)
EQ -> loop xs ys
GT -> y : loop (x:xs) ys
{-
genSectBy cmp p = loop
where
loop [] ys | p False True = ys
| otherwise = []
loop xs [] | p True False = xs
| otherwise = []
loop (x:xs) (y:ys)
= case cmp x y of
LT | p True False -> x : loop xs (y:ys)
| otherwise -> loop xs (y:ys)
EQ | p True True -> x : loop xs ys
| otherwise -> loop xs ys
GT | p False True -> y : loop (x:xs) ys
| otherwise -> loop (x:xs) ys
-}
-- | Merge two ordered lists
--
-- > merge [1,3,5] [2,4,6] == [1,2,3,4,5,6]
-- > merge [2,4,6,8] [3,6,9] == [2,3,4,6,6,8,9]
-- > merge [1,2,2,2] [1,1,1,2,2] == [1,1,1,1,2,2,2,2,2]
merge :: (Ord a) => [a] -> [a] -> [a]
merge = mergeBy compare
mergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
mergeBy cmp = loop
where
loop [] ys = ys
loop xs [] = xs
loop (x:xs) (y:ys)
= case cmp x y of
GT -> y : loop (x:xs) ys
_ -> x : loop xs (y:ys)
-- | Returns true if the first list is a sub-list of the second
subset :: (Ord a) => [a] -> [a] -> Bool
subset = subsetBy compare
subsetBy :: (a -> a -> Ordering) -> [a] -> [a] -> Bool
subsetBy cmp = loop
where
loop [] _ys = True
loop _xs [] = False
loop (x:xs) (y:ys)
= case cmp x y of
LT -> False
EQ -> loop xs ys
GT -> loop (x:xs) ys
{-
sort :: Ord a => [a] -> [a]
sort = sortBy compare
sortBy :: (a -> a -> Ordering) -> [a] -> [a]
sortBy cmp = loop . map (\x -> [x])
where
loop [] = []
loop [xs] = xs
loop xss = loop (merge_pairs xss)
merge_pairs [] = []
merge_pairs [xs] = [xs]
merge_pairs (xs:ys:xss) = mergeBy cmp xs ys : merge_pairs xss
-}
-- | decorate-sort-undecorate, aka the \"Schwartzian transform\"
sortOn :: Ord b => (a -> b) -> [a] -> [a]
sortOn f = map snd . sortOn' fst . map (\x -> (f x, x))
-- | Recomputes instead; better for some things such as projections.
sortOn' :: Ord b => (a -> b) -> [a] -> [a]
sortOn' f = sortBy (\x y -> compare (f x) (f y))
-- | Equivalent to nub . sort, except somewhat more efficient
nubSort :: Ord a => [a] -> [a]
nubSort = nubSortBy compare
nubSortBy :: (a -> a -> Ordering) -> [a] -> [a]
nubSortBy cmp = loop . map (\x -> [x])
where
loop [] = []
loop [xs] = xs
loop xss = loop (union_pairs xss)
union_pairs [] = []
union_pairs [xs] = [xs]
union_pairs (xs:ys:xss) = unionBy cmp xs ys : union_pairs xss
nubSortOn :: Ord b => (a -> b) -> [a] -> [a]
nubSortOn f = map snd . nubSortOn' fst . map (\x -> (f x, x))
nubSortOn' :: Ord b => (a -> b) -> [a] -> [a]
nubSortOn' f = nubSortBy (\x y -> compare (f x) (f y))
-- | Equivalent to nub on ordered lists, except faster; on unordered
-- lists it also removes elements that are smaller than any preceding element.
--
-- > nub [2,0,1,3,3] == [2,3]
nub :: (Ord a) => [a] -> [a]
nub = nubBy (>)
nubBy :: (a -> a -> Bool) -> [a] -> [a]
nubBy p xs = case xs of
[] -> []
(x:xs') -> x : loop x xs'
where
loop _ [] = []
loop x (y:ys)
| p x y = loop x ys
| otherwise = y : loop y ys