Knuth-Morris-Pratt algorithm in Haskell

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清酒与你
清酒与你 2021-02-20 07:55

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

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  • 2021-02-20 08:14

    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.

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