blob: ffefc5a16d148bdac9b3e1225e95abf65227f14d (
plain) (
blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
|
----------------------------------------------------------------------------
--
-- Copyright : (C) 2017 Yuchen Pei
-- License : GPLv3+
--
-- Maintainer : Yuchen Pei
-- Stability : experimental
-- Portability : non-portable
--
----------------------------------------------------------------------------
module RobinsonSchensted where
import YoungTableaux
-- |Plactic monoid
instance Ord a => Monoid (SSYT a)
where
mempty = S $ repeat []
mappend s1 s2 = foldl rowInsert s1 (toRowWord s2)
-- |Row insertion algorithm
rowInsert :: Ord a => SSYT a -> a -> SSYT a
rowInsert (S t) = toSSYT . (rowInsert' t)
-- |Row insertion algorithm on an SSYT as a nested list
rowInsert' :: Ord a => [[a]] -> a -> [[a]]
rowInsert' t x =
case break (>x) (head t) of
(r, []) -> (r ++ [x]):(tail t)
(r1, r2) -> (r1 ++ x:(tail r2)):(rowInsert' (tail t) (head r2))
colInsert :: Ord a => SSYT a -> a -> SSYT a
colInsert st = transpose . (colInsert' (transpose st))
colInsert' :: Ord a => SSYT a -> a -> SSYT a
colInsert' (S t) = toSSYT . (colInsert'' t)
colInsert'' :: Ord a => [[a]] -> a -> [[a]]
colInsert'' t x =
case break (>=x) (head t) of
(r, []) -> (r ++ [x]):(tail t)
(r1, r2) -> (r1 ++ x:(tail r2)):(rowInsert' (tail t) (head r2))
-- |The Robinson-Schensted algorithm
robinsonSchensted :: Ord a => [a] -> SSYT a
robinsonSchensted = foldl rowInsert mempty
-- |The Robinson-Schensted algorithm with column insertion
robinsonSchensted' :: Ord a => [a] -> SSYT a
robinsonSchensted' = foldl colInsert mempty
prop_ReduceWord_RobinsonSchensted :: [Int] -> Bool
prop_ReduceWord_RobinsonSchensted xs = (toRowWord $ robinsonSchensted xs) == (reduceWord xs)
|
