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Funkcionalno programiranje

Funkcionalno programiranje. Čas7: Rad sa beskonačnim listama Primeri rada sa matricama. Pitagorejske trojke. Zadatak:

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Funkcionalno programiranje

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  1. Funkcionalno programiranje Čas7: Rad sa beskonačnim listama Primeri rada sa matricama

  2. Pitagorejske trojke • Zadatak: Pitagorejska trojkaje svaka trojka prirodnih brojeva (x,y,z) koja ispunjava uslov x*x+y*y=z*z. Napisati funkciju pythagTripleskoja generiše listu svih pitagorejskih trojki.

  3. pogrešno rešenje pythagTriplesWrong= [ (x,y,z) | x<-[2..], y<-[x+1..], z<-[y+1..], x*x+y*y=z*z]

  4. tačno rešenje pythagTriples = [ (x,y,z) | z<-[2..], y<-[2..z-1], x<-[2..y-1], x*x+y*y=z*z]

  5. Generisanje slučajnih brojeva • Linearni kongruentni metod: Xn+1 = (aXn+c) mod m m>0 - modulus 0<a<m – multiplier 0<=c <m – increment 0<=Xo<=m – seed

  6. Primer • rand.hs

  7. Podsećanje • funkcija all all :: (a → Bool ) → [a ] → Bool all p = and ◦ map p Npr all (>0) [1,2,3]

  8. Karijeve funkcije: • add :: (Int, Int) → Int • add’ :: Int → (Int → Int)

  9. funkcije curry: • Curry pretvara funkciju nad parovima u Karijevu funkciju: curry :: ((a, b) → c) → (a → b → c) curry f = λx y → f (x , y) Primer: curry fst 1 2

  10. funkcija uncurry: • Pretvara Karijevu funkciju u funkciju nad parovima: uncurry :: (a → b → c) → ((a, b) → c) uncurry f = λ(x , y) → f x y Npr. uncurry (+) (1,2)

  11. Funkcija zip: zip :: [a ] → [b ] → [(a, b)] Primer: > zip [’a’, ’b’, ’c’] [1, 2, 3, 4] [(’a’, 1), (’b’, 2), (’c’, 3)]

  12. Funkcija zipWith zipWith f [] _ = [] zipWith f _ [] = [] zipWith f (x:xs) (y:ys) = f x y : zipWith f xs ys Primer: zipWith (*) [1,2] [3,4]

  13. Rad sa matricama • type Matrix = [[Int]] • zadaci06.txt

  14. Rad sa matricama • primer: inverse.hs

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