vault backup: 2023-09-25 14:21:29

Algo/Séminaire/Exercices seminaire.md

@@ -427,4 +427,31 @@ let power x n = match n with
 			| n -> p (x*x) (n/2) *. (if n mod 2 = 1 then x else 1.)
 			in p x n)
 ;;
-```
+```
+
+Complexity :
+$$
+x^0 -> 1 \ | \ 
+x^1 -> (x^0)^2 -> 2 \ | \ 
+x^2 -> x^1 -> 3 \ | \ 
+x^4 -> x^2 -> 4 \ | \ 
+x^8 -> x^4 -> 5 \ | \ 
+x^16 -> x^8 -> 6 \ | \ 
+x^(2^k) -> x^(2^k-1) -> k+2 \approx{k} \ | \ 
+n = 2^k -> K*log(n) \ | \ 
+log(n) = log(2^k) = k 
+$$
+$$
+= O(log(n))
+$$
+## 4.12 - Prime number
+```Ocaml
+let prime n =
+	if n < 1 then
+		invalid_args "n should not be inferior to zero"
+	else
+		let rec p n = 
+			if n = 0 then
+				1
+			else
+