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(ns funciones.recursivas)
;; Fuentes:
;; http://www.cs.us.es/~jalonso/cursos/i1m-15/temas/tema-6.html
;; http://www.glc.us.es/~jalonso/vestigium/i1m2015-ejercicios-de-definiciones-por-recursion/
;; Recursión numérica
(defn factorial01
[n]
(if (= n 0)
1
(*' n (factorial01 (- n 1)))))
(defn factorial02
[n]
(letfn [(factorial
[i t]
(if (> i n)
t
(factorial (inc i) (* i t))))]
(factorial 1 1)))
(defn productomn01
[m n]
(if (= n 0)
0
(+ m (producto01 m (- n 1)))))
(defn productomn02
[m n]
(letfn [(producto
[i t]
(if (= i m)
t
(producto (inc i) (+ n t))))]
(if (> m 0)
(producto 1 n))))
(defn potencia01
[m n]
(if (= n 0)
1
(* m (potencia01 m (dec n)))))
(defn mcd01
[a b]
(if (= b 0)
a
(mcd01 b (rem a b))))
;; Recursión sobre listas
(defn productons01
[ns]
(if (= (count ns) 0)
1
(* (first ns) (producto03 (rest ns)))))
(defn productons02
[ns]
(if (nil? (first ns))
1
(* (first ns) (producto04 (rest ns)))))
(defn productons03
[ns]
(letfn [(producto
[i t]
(if (>= i (count ns))
t
(producto (inc i) (* t (ns i)))))]
(producto 0 1)))
(defn length01
[xs]
(if (= (count xs) 0)
0
(+ 1 (length01 (rest xs)))))
(defn length02
[xs]
(if (nil? (first xs))
0
(+ 1 (length02 (rest xs)))))
(defn length03
[xs]
(letfn [(lengthinterno
[i]
(if (>= i (count xs))
i
(lengthinterno (inc i))))]
(lengthinterno 0)))
(defn reverse01
[xs]
(if (= (count xs) 0)
[]
(conj (reverse01 (rest xs)) (first xs))))
(defn reverse02
[xs]
(if (nil? xs)
[]
(conj (reverse01 (rest xs)) (first xs))))
(defn reverse03
[xs]
(letfn [(reverseinterno
[i t]
(if (< i 0)
t
(reverseinterno (dec i) (conj t (xs i)))))]
(reverseinterno (- (count xs) 1) [])))
(defn concat01
[xs ys]
(if (nil? (first ys))
xs
(concat01 (conj xs (first ys)) (rest ys))))
(defn concat02
[xs ys]
(letfn [(concatinterno
[i t]
(if (= i (count ys))
t
(concatinterno (inc i) (assoc t (+ (count xs) i) (ys i)))))]
(concatinterno 0 xs)))
(defn pertenece01
[x xs]
(if (= (count xs) 0)
false
(or
(= x (first xs))
(pertenece01 x (rest xs)))))
;; Recursión mutua
(defn par01
[n]
(if (= n 0)
true
(impar01 (dec n))))
(defn impar01
[n]
(if (= n 0)
false
(par01 (dec n))))
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