问题
I have a trouble with understanding this implementation of the Knuth-Morris-Pratt algorithm in Haskell.
http://twanvl.nl/blog/haskell/Knuth-Morris-Pratt-in-Haskell
In particular I don't understand the construction of the automaton. I know that it uses the "Tying the Knot" method to construct it, but it isn't clear to me and I also don't know why it should have the right complexity.
Another thing I would like to know is whether you think that this implementation could be easily generalized to implement the Aho-Corasick algorithm.
Thanks for your answers!
回答1:
So here's the algorithm:
makeTable :: Eq a => [a] -> KMP a
makeTable xs = table
where table = makeTable' xs (const table)
makeTable' [] failure = KMP True failure
makeTable' (x:xs) failure = KMP False test
where test c = if c == x then success else failure c
success = makeTable' xs (next (failure x))
Using that, let's look at the table constructed for "shoeshop":
makeTable "shoeshop" = table0
table0 = makeTable' "shoeshop" (const table0)
= KMP False test0
test0 c = if c == 's' then success1 else const table0 c
= if c == 's' then success1 else table0
success1 = makeTable' "hoeshop" (next (const table0 's'))
= makeTable' "hoeshop" (next table0)
= makeTable' "hoeshop" test0
= KMP False test1
test1 c = if c == 'h' then success2 else test0 c
success2 = makeTable' "oeshop" (next (test0 'h'))
= makeTable' "oeshop" (next table0)
= makeTable' "oeshop" test0
= makeTable' "oeshop" test0
= KMP False test2
test2 c = if c == 'o' then success3 else test0 c
success3 = makeTable' "eshop" (next (test0 'o'))
= makeTable' "eshop" (next table0)
= makeTable' "eshop" test0
= KMP False test3
test3 c = if c == 'e' then success4 else test0 c
success4 = makeTable' "shop" (next (test0 'e'))
= makeTable' "shop" (next table0)
= makeTable' "shop" test0
= KMP False test4
test4 c = if c == 's' then success5 else test0 c
success5 = makeTable' "hop" (next (test0 's'))
= makeTable' "hop" (next success1)
= makeTable' "hop" test1
= KMP False test5
test5 c = if c == 'h' then success6 else test1 c
success6 = makeTable' "op" (next (test1 'h'))
= makeTable' "op" (next success2)
= makeTable' "op" test2
= KMP False test6
test6 c = if c == 'o' then success7 else test2 c
success7 = makeTable' "p" (next (test2 'o'))
= makeTable' "p" (next success3)
= makeTable' "p" test3
= KMP False test7
test7 c = if c == 'p' then success8 else test3 c
success8 = makeTable' "" (next (test3 'p'))
= makeTable' "" (next (test0 'p'))
= makeTable' "" (next table0)
= makeTable' "" test0
= KMP True test0
Note how success5
uses the consumed 's' to retrace the initial 's' of the pattern.
Now walk through what happens when you do isSubstringOf2 "shoeshop" $ cycle "shoe"
.
See that when test7
fails to match 'p', it falls back to test3
to try to match 'e', so that we cycle through success4
, success5
, success6
and success7
ad infinitum.
来源:https://stackoverflow.com/questions/16694306/knuth-morris-pratt-algorithm-in-haskell