-- Practico 10

--Ejercicio 1

resto :: Int -> Int -> Int
resto a 0 = error "Divisor no valido"
resto 0 a = 0
resto a b  | a<b = a
                | a==b = 0
               | otherwise = resto (a-b) b


--Ejercicio 2


divi :: Int -> Int -> Int
divi a 0 = error "popopopopof"
divi 0 a = 0
divi a b | a==b = 1
	 | b>a = 0
	 | otherwise = divi (a-b) b + 1


--Ejercicio 3


sumdeshas :: Int -> Int -> Int
sumdeshas 0 0 = 0
sumdeshas 0 a = sumdeshas 0 (a - 1) + a
sumdeshas a 0 = error "no"
sumdeshas a b | a==b = a
	      | a>b = error "no"
	      | otherwise = sumdeshas a (b - 1) + b


--ejercicio 4

prodehas :: Int -> Int -> Int
prodehas 0 0 = 0
prodehas 0 a = 0
prodehas 1 1 = 1
prodehas 1 a = prodehas 1 (a - 1) * a
prodehas a b | a==b = a
	     | a>b =error "no es posible"
	     | otherwise = prodehas a (b - 1) * b



--ejercicio 5

arreglos:: Int -> Int -> Int
arreglos a 0 =1
arreglos a b | a<0 || b>0 = error "."
             | a>b = error "."
             | divi(facto a) (facto (a-b))



facto:: Int -> Int
facto 0 = 1
facto n = n * facto(n-1)



--ejercicio 10

divide:: Int -> [Int]
divide 0 = error "."
divide 1 = [1]
divide a = [x/x<-[1...a], resto x a == 0]



--ejercicio 11

mcd:: Int -> Int -> Int
mcd a b | a == b = a
        | mod a b == 0 = b
        |otherwise = mcd b(resto a b)


--ejercicio 12

esprimo:: Int -> Bool
esprimo a = largo (divide a) == 2

--Se agradece a la estudiante Bettina Battagliese por estos ejercicios.