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algo.hs
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algo.hs
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{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE OverloadedStrings #-}
{-#LANGUAGE MultiParamTypeClasses #-}
module Main where
import Text.ParserCombinators.Parsec
import Control.Monad
import Debug.Trace
import Data.List
import Test.QuickCheck
import System.Random
import Control.Arrow
import Control.Monad.State
import Data.Maybe
import Data.Ord
import qualified Data.Text as T
import Text.Blaze
import Text.Blaze.Html.Renderer.Text
equ21=do
ops<-[(/),(*),(+),(-)]
ops2<-[(/),(*),(+),(-)]
nums<-[0..9]
nums2<-[0..9]
nums3<-[0..9]
let expr=ops nums $ ops2 nums2 nums3
guard $ expr==21
return expr
--type Aj f g =Adjoint f g
class (Functor f, Functor g) => Adjoint f g where
counit :: f (g a) -> a
unit :: a -> g (f a)
instance Adjoint ((,) a) ((->) a) where
-- counit :: (a,a -> b) -> b
counit (x, f) = f x
-- unit :: b -> (a -> (a,b))
unit x = \y -> (y, x)
t="dsfds\n"::T.Text
main = do
--putStrLn $ show $ pacDup "adfdsdfffffaaaaa"
s<-getLine
putStrLn s
when (s/="exit") $ main
tls=[1,2,3,4,4,5,6]
xy 0 xs=head xs
xy i xs= xy (i-1) $ tail xs
len::[a]->Int
len [] = 0
len xs =(len $ tail xs) + 1
rev::[a]->[a]
rev []=[]
rev (x:xs)=(rev xs)++[x]
pldli=[1,2,2,1]
isPld xs = (\(a,b)->a==reverse b) $ if isOdd $ len xs
then splitAt ((len xsodd) `quot` 2) $ xsodd
else splitAt ((len xs)`quot`2 ) xs
where
xsodd=delAt (quot ((len xs) -1) 2) xs
isOdd i=(mod i 2 )==1
-- Problem 20 (*) Remove the K'th element from a list.
delAt::Int->[a]->[a]
delAt i xs=uncurry (++) ((\(x,y)->(init x , y)) (splitAt (i+1) xs))
data NL a=E a|L [NL a]
nls=L [E 1,L [E 1,E 2 ,E 3,L [E 789,E 45] ]]
nll::NL a->[a]
nll (L [])=[]
nll (E a)=[a]
nll (L (x:xs))=(nll x)++(nll $ L xs)
flatten (E x) = return x
flatten (L x) = x>>= flatten
tails []=[]
tails xs=tail xs
deldup::(Eq a)=>[a]->[a]
deldup []=[]
deldup (x:y:xs)=if x == y then deldup $ x:deldup xs else x:y:deldup xs
deldup [x]=[x]
mtrace=trace "dbg:"
pacDup::(Eq a,Show a)=>[a]->[[a]]
pacDup []=[]
pacDup (x:xs)=(\(a,na)->(x:a):(pacDup na)) $ span (==x) xs
encDup::(Eq a)=>[a]->[(Int,a)]
encDup =fmap (\xs->(length xs,head xs)).group
data VarLen a =Plu Int a|Sig a
deriving Show
encDupv::(Eq a)=>[a]->[VarLen a]
encDupv =fmap (\xs->case len xs of
1->Sig $ head xs
_->Plu (length xs) $ head xs ).group
decDupv::(Eq a)=>[VarLen a]->[a]
decDupv =join . fmap (\xs-> case xs of
Sig a->[a]
Plu i a->replicate i a)
dupli::Int->[a]->[a]
dupli i =join . fmap ( replicate i )
delEv _ []=[]
delEv i x=(take (i-1) x)++(delEv i $ drop i x)
slice::Int->Int->[a]->[a]
slice i j xs=take (j-i+1) $ drop (i-1) xs
slice1 i j xs=do
(k,x)<-zip [1..(j+1)] xs
guard $ k>=i&&k<=j
return x
range m n
| m<=n =m:(range (m+1) n)
| otherwise = []
takes is xs=fmap snd $ join $ fmap (\i->filter (\(a,b)->a==i) $ zip [1..] xs) is
rand::Int->[a]->[a]
rand 0 _=[]
--rand i xs=takes (fst $ gen (mkStdGen 13) i) xs
--gen g 0=([],g)
--gen g r =(\(a,g3)->(if a/=head as then a:as else a:fst $ gen g3 r,) ) $ randomR (1,r) g
comb::Int->[a]->[[a]]
comb 0 _=[]
comb _ []=[]
comb i xs=(fmap (\q->(take (i-1) xs)++[q]) ( drop (i-1) xs) )++(comb i $ Main.tails xs)
combinations :: Int -> [a] -> [[a]]
combinations 0 _ = []
combinations n xs = do y:xs' <- Data.List.tails xs
ys <- combinations (n-1) xs'
return (y:ys)
gp2::Int->[a]->[[[a]]]
gp2 1 xs=[ [[head xs],tail xs] ]
gp2 n xs=(gp2 (n-1) xs)++[(\(x,y)->[x,y]) $ splitAt n xs]
gpn::Int->[a]->[[[a]]]
gpn 2 xs=gp2 (len xs) xs
gpn 3 xs=fmap (\xss->(head xss) :(join $ gpn 2 $ tail xs) ) $ gpn 2 xs
combination :: Int -> [a] -> [([a],[a])]
combination 0 xs = [([],xs)]
combination _ [] = []
combination n (x:xs) = ts ++ ds
where
ts = [ (x:ys,zs) | (ys,zs) <- combination (n-1) xs ]
ds = [ (ys,x:zs) | (ys,zs) <- combination n xs ]
lsort::[[a]]->[[a]]
lsort xs=llsort ((len xs)-1) xs
where
llsort 0 lxs=lxs
llsort i (x:y:zs)=if length x>length y
then llsort (i-1) $ y:(llsort (i-1) (x:zs))
else llsort (i-1) $ x:(llsort (i-1) (y:zs))
llsort _ _=[]
prime n=pmeh (n-1) n
where
pmeh 1 _=True
pmeh i pn=if (mod pn i)==0 then False else pmeh (i-1) pn
--Problem 31 (**) Determine whether a given integer number is prime.
isPrime :: Int -> Bool
isPrime n | n < 4 = n > 1
isPrime n = all ((/=0).mod n) $ 2:3:[x + i | x <- [6,12..s], i <- [-1,1]]
where s = floor $ sqrt $ fromIntegral n
isFac fac n=fac*(quot n fac)==n
factors 1=[1]
factors x =filter (/=1) $ (head facs):factors (quot x $ head facs)
where
facs =filter (\l->isPrime l && (isFac l x )) [2..x]
factorsc =fmap (\li->(head li,len li)) . group . factors
--Problem 39 (*) A list of prime numbers. Given a range of integers by its lower and upper limit, construct a list of all prime numbers in that range.
primesR l h =filter (\x->x>l&&x<h&&(prime x)) [1..h]
adder x =addera (quot x 2) x
where
addera::Int->Int->[(Int,Int)]
addera 1 _=[]
addera n x=((x-n),n):(addera (n-1) x)
--Problem 40 (**) Goldbach's conjecture.
goldbach =filter (\(x,y)->(prime x)&&(prime y) ).adder
and1 True x=x
and1 False _=False
or1 True _=True
or1 False x=x
table1 li=do
a<-li
b<-li
return $ show a ++" " ++ show b
--Problem 46 (**) A logical expression in two variables can then be written as in the following example: and(or(A,B),nand(A,B)).
tablebn size expf=mapM_ putStrLn $ do
a<-blns size
return $ tostr a ++"-->" ++ expf a
where
blns n=replicateM n [True,False]
tostr a=show a
-- Questions 54A to 60: Binary trees,Questions 61 to 69: Binary trees, continued
data Tr a =Nd a (Tr a) (Tr a)|Lf a|Nil
deriving (Eq)
--depth of a tree
dptTr Nil=0
dptTr (Lf _)=1
dptTr (Nd _ t1 t2)=1+(max (dptTr t1) (dptTr t2) )
--Problem 56 (**) Symmetric binary trees
symTr (Nd _ l r)=mirrTr l==r
where
mirrTr::Tr a->Tr a
mirrTr (Lf a)=Lf a
mirrTr Nil=Nil
mirrTr (Nd l a b)=Nd l (mirrTr b) (mirrTr a)
-- Problem 55 (**) Construct completely balanced binary trees
cbTr 0=[Nil]
cbTr n=do
i<-[q..q+r]
l<-cbTr i
r<-cbTr (n1-i)
return $ Nd 1 l r
where
n1=n-1
(q,r)=quotRem n1 2
symcbTr n=(cbTr n1)>>=(\x->[Nd 1 x (mirrTr x)])
where
n1=quot (n-1) 2
-- Problem 59 (**) Construct height-balanced binary trees
hbTr::Int->[Tr Int]
hbTr 0=[Nil]
hbTr 1=[Nd 1 Nil Nil]
hbTr n=do
(ln,rn)<-[(n-1,n-2),(n-2,n-1),(n-1,n-1)]
l<-hbTr ln
r<-hbTr rn
return $ Nd 1 l r
cardTr::Tr a->Int
cardTr (Nd _ l r)=1 + cardTr l +cardTr r
cardTr _=0
minLi (x:y:xs)=if x<y then minLi (x:xs) else minLi $ y:xs
minLi [x]=x
minHbTr::Int->(Tr Int,Int)
minHbTr =minimumBy (comparing snd) . fmap (\xs->(xs,cardTr xs)) . hbTr
iHbTr::Int->(Tr Int,Int)
iHbTr x=head.filter (\(t,c)->c==x) . fmap (\xs->(xs,cardTr xs)) . hbTr $ x
-- Problem 61 Count the leaves of a binary tree
cardTrLf (Nd _ Nil Nil)=1
cardTrLf Nil=0
cardTrLf (Nd _ a b)=cardTrLf a + cardTrLf b
--Problem 61A Collect the leaves of a binary tree in a list
tr2li (Nd x Nil Nil)=[x]
tr2li Nil=[]
tr2li (Nd _ a b)=tr2li a ++ tr2li b
-- Problem 62 Collect the internal nodes of a binary tree in a list
intTr (Nd _ Nil Nil)=[]
intTr Nil=[]
intTr (Nd x a b)=[x]++intTr a ++ intTr b
levTr 0 (Nd x _ _)=[x]
levTr n (Nd x a b)=levTr (n-1) a ++ levTr (n-1) b
levTr _ _=[]
coorTr::Int->Tr String->Tr String
coorTr _ Nil=Nil
coorTr 0 (Nd x l r)=Nd (show (x,0)) l r
coorTr n (Nd x l r)=Nd (show (x,n)) (coorTr (n-1) l) $ coorTr (n-1) r
coorTr1 t=coorTr (dptTr t) t
instance Show a=>Show (Tr a) where
show (Nd x Nil Nil)="Lf "++show x
show t=sho 0 t
where
nl="\n"
ql="("
qr=")"
spac=" "
dptC=dptTr t::Int
sho1 Nil="_"
sho1 (Lf x)="Lf "++ show x
sho1 (Nd x a b)="Nd "++show x ++ nl ++ spac++show a ++ nl ++ spac++show b
sho n (Nd x Nil Nil)=nl++(unwords $ replicate n spac )++ "Nd "++show x ++ " _ _"
sho n (Nd x l r)=nl++(unwords $ replicate n spac )++ "Nd "++show x ++ (sho (n+1) l )++ (sho (n+1) r)
sho dptC tr=nl++(unwords $ replicate dptC spac )++ sho1 tr
tr1=(Nd "a"
(Nd "b" Nil Nil)
(Nd "c"
(Nd "d" Nil Nil)
Nil))
-- Problem 64 : As a preparation for drawing the tree, a layout algorithm is required to determine the position of each node in a rectangular grid
layout :: Tr a -> Tr (a, (Int,Int))
layout = fst . layoutAux 1 1
where layoutAux x y Nil = (Nil, x)
layoutAux x y (Nd a l r) = (Nd (a, (x',y)) l' r', x'')
where (l', x') = layoutAux x (y+1) l
(r', x'') = layoutAux (x'+1) (y+1) r
layout1 :: Tr a -> Tr (a, (Int,Int))
layout1 t = layoutAux 1 1 sep1 t
where d = dptTr t ::Int
sep1 = 2^(d-2)
layoutAux x y sep Nil = Nil
layoutAux x y sep (Nd a l r) =
Nd (a, (x,y))
(layoutAux (x-sep) (y+1) (sep `div` 2) l)
(layoutAux (x+sep) (y+1) (sep `div` 2) r)
readTr t=case parse tr "" t of
Left e->show e
Right v->show v
where
tr:: Parser (Tr Char)
tr=try bch<|>try lf <|>(return Nil)
lf=do
a<-letter
--char ','
--tr
return $ Nd a Nil Nil
bch:: Parser (Tr Char)
bch=do
a<-letter
char '('; l<-tr; char ',';r<-tr;char ')'
return $ Nd a l r
bch'= do
a<-letter
(do char '(';
l<-tr; char ','; r<-tr;char ')'
return $ Nd a l r)
<|> (return ( Nd a Nil Nil))
tr2ds Nil="."
tr2ds (Nd x l r) =x++ tr2ds l ++ tr2ds r
parse1 s parser=case parse parser "" s of
Left e->show e
Right v->show v
ds2tr s=parse1 s tr
where
tr=nd<|>(char '.'>>return Nil)
nd=do
a<-letter
l<-tr
r<-tr
return $ Nd a l r
--99 questions/70B to 73, Multiway Trees
data MTr a =MNd a [MTr a]
deriving Show
mMTr1::MTr Char
mMTr1=MNd 'a' [MNd 'b' [MNd 'd' []] ,MNd 'c' []]
--Problem 70C (*) Count the nodes of a multiway tree.
cardMTr (MNd a [])=1
cardMTr (MNd a li)=1+(foldr1 (+) $ fmap (cardMTr) li)
--Problem 71 (*) Determine the internal path length of a tree.
iplMTr (MNd a (x:xs))=1+(foldr1 (+) $ fmap (iplMTr) $ xs)
--Problem 72 (*) Construct the bottom-up order sequence of the tree nodes.
btrMTr (MNd a [])=[a]
btrMTr (MNd a xs)=(xs>>=btrMTr)++ [a]
--brace s="("++s++")"
-- graph algo
data Graph a=Gcan [a] [(a,a)]|Gadj [(a,[a])]|Ghum [(a,a)]
gr2a::Eq a=>[(a,a)]->[(a,[a])]
gr2a li=fmap (maxtp) $ groupBy (\x y->fst x==fst y) $ fmap (head) $ group $ g2a li
where
maxtp::[(a,[a])]->(a,[a])
maxtp (x:y:[])=if (len $ snd x )>(len $ snd y) then x else y
maxtp [x]=x
maxtp (x:y:xs)=if (len $ snd x )>(len $ snd y) then maxtp (x:xs) else maxtp $ y:xs
g2a::Eq a=>[(a,a)]->[(a,[a])]
g2a li=do
a<-li
b<-li
guard $ a/=b
return (fst a,if (fst a==fst b )then [snd a]++[snd b] else [snd a])
a2gr::[(a,[a])]->[(a,a)]
a2gr li=do
(a,as)<-li
b<-as
return (a,b)
--Problem 81 (**) Path from one node to another one
paths :: Eq a =>a -> a -> [(a,a)] -> [[a]]
paths source sink edges
| source == sink = [[sink]]
| otherwise = do
edge<-edges
guard $ (fst edge) == source
path<-paths (snd edge) sink (edges\\[edge])
return $ source:path
--Problem 82 (*) Cycle from a given node
--gcycle::Eq a=>a->[(a,a)]->[[a]]
gcycle _ _ []=[]
gcycle x (l,r) eg
|x==r=[[r]]
|otherwise=do
(a,b)<-eg
guard $ x==a
y<-eg\\[(a,b)]
cyc<-gcycle b y (eg\\[(a,b)])
-- guard $ x==snd y
return $ b:cyc
cyclebi :: (Eq a) => a -> [(a, a)] -> [[a]]
cyclebi a xs = [a : path | e <- xs, fst e == a, path <- paths (snd e) a (xs\\[e])]
++[a : path | e <- xs, snd e == a, path <- paths (fst e) a (xs\\[e])]
isog1=[(1,[2,3]),(2,[3,1])]
isog2=[(2,[1,3]),(1,[2,3])]
--Problem 85 (**) Graph isomorphism
isogrh::Eq a=>[(a,[a])]->[(a,[a])]->Bool
isogrh l r =(deleteFirstsBy (\x y-> (fst x==fst y)&&(snd x\\snd y==[])) l r)==[]
ls [] []=[]
ls [] a=[a]
ls a []=[a]
ls xs ys =do
x<-xs
y<-ys
guard $ x==y
ls (xs\\[x]) (ys\\[y])
-- where
--class SimpleGraph where
--nodes::Graph a->[a]
gadj=[('b',['c','f']), ('c',['b','f']), ('d',['a','k']), ('f',['b','c']),('a',"dk"),('k',"ad")]
clrgph::Eq a=>[(a,[a])]->Int->[(a,[a],Int)]
clrgph [] _=[]
clrgph ghs n=do
gs<-gphs
gs2<-gphs
guard $ not $ elem (fst gs2) (snd gs)
tl<-clrgph (gphs\\[gs,gs2]) (n+2)
{-}(do
gss<-gphs
guard $ not $ elem (fst gs2) (snd gss)
return gss)-}
(fst gs,snd gs,n):(fst gs2,snd gs2,n+1):tl:[]
where
--gphs::[(a,[a])]
gphs=sortBy (comparing (length.snd)) ghs
reachable::(Eq a)=>[(a,[a])]->[a]->[a]
reachable [] _=[]
reachable grh as=do
g<-grh
a<-as
guard $ (fst g)==a
(snd g)++(reachable [g1|g1<-grh,(fst g1)/=a] (snd g))
delete1::(Eq a)=>a->[a]->[a]
delete1 _ []=[]
delete1 x (z:zs)=if x==z then delete1 z zs else z:(delete1 x zs)
--group1::(Eq a)=>[a]->[[a]]
sameset xs ys=(nub xs)\\(nub ys)==[]
partitiongrh g=nubBy sameset $ partitiong g --h88
where
partitiong grh=do
(x,xs)<-grh
return $ nub $ reachable grh [x]
--queens::Int->[[Int]]
--queens n=
qbool::[(Int,Int)]->[(Int,Int)]
qbool is=do
(x1,y1)<-is
(x2,y2)<-is
guard $ x1/=x2 && y1/=y2 && (x1-x2)/=(y1-y2)
return (x1,y1)
--queens n=qbool pos
-- where
pos n=do
p<-permutations [1..n]
return $ zip [1..n] p
q2 xxs=do
xs<-xxs
xy@(x1,y1)<-xs
(x2,y2)<-xs
guard $ (abs $ x1-x2)/=(abs $ y1-y2)
return xy
--delim::(Eq a)=>a->[a]->[[a]]
wordsWhen :: (Char -> Bool) -> String -> [String]
wordsWhen p s = case dropWhile p s of
"" -> []
s' -> w : wordsWhen p s''
where (w, s'') = break p s'