Récursivité 1 Exercices

fact
let fact n = 1
let fact n =
if n=0then
1
else
n*(fact (n - 1))
fact 10 fact n n
fact
let rec fact n =
if n=0then
1
else
n*fact n - 1
fact 1
pair impair
let rec pair n = if n=0then true else not (impair n)
and impair n = if n=0then false else not (pair n)
pair 1
pair
pair
let rec pair n =
if n=0then true
else pair (n - 2)

let rec mccarthy n =
if n > 100 then n - 10
else mccarthy (mccarthy (n + 11))
nmccarthy n
90 ≤n≤100
n≤100
a b
a a + 1
a a −1
a a = 0 a > 0a < 0
a b
a b a +b
a a −1
a a = 0
n n ∈N
a
a b a ×b
a a −1
a a = 0
a= 119 b= 544
119 = 544 ×0 + 119
544 = 119 ×4 + 68
119 = 68 ×1 + 51
68 = 51 ×1 +
51 = ×3 + 0

a b
amod ba
pgcd 119 (-544)
pgcd
n≥p≥0n
p=n! p!(n−p)!
n > p > 0
n+ 1
p+ 1=n p+n p+ 1
n= 5 p= 2
radar elle été ici
String.sub string →int →int →string
nb_occurrences
string →char →int
#nb_occurrences "abcdebdb" ’z’ ;;
-:int=0
#nb_occurrences "abcdebdb" ’b’ ;;
-:int=3

String.sub
indice
string →char →int
Failure "indice
indice String index
let indice = String.index
String.index Not_found
s
s s eadbc
abcde
s|s|!s
s
|s|!−1s
eadbc abcde
n s
s
s
’0’ ’1’ ’9’
’+’
"" "12+" "+12" "12++12"
evalue_somme
string →int
#evalue_somme "123" ;;
- : int = 123
#evalue_somme "123+15" ;;
- : int = 138
#evalue_somme "123+15+1" ;;
- : int = 139
#evalue_somme "123+15+1+2000" ;;
- : int = 2139

String.sub String.index
int_of_string
A(xA, yA)B(xB, yB)
[A, B]
plot x y (x, y)