From 3f37a1ccb515919c934af24298b968b4c44786d7 Mon Sep 17 00:00:00 2001
From: Louis <me@louisgallet.fr>
Date: Fri, 15 Sep 2023 16:17:18 +0200
Subject: [PATCH] vault backup: 2023-09-15 16:17:18

---
 .obsidian/workspace.json                  | 10 +++++-----
 Algo/Séminaire/Chapter 5 - Recursivity.md | 18 +++++++++++++++++-
 Algo/Séminaire/Exercices seminaire.md     | 10 +++++++++-
 3 files changed, 31 insertions(+), 7 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 03e1625..43c79c4 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -13,7 +13,7 @@
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md",
+                "file": "Algo/Séminaire/Exercices seminaire.md",
                 "mode": "source",
                 "source": false
               }
@@ -97,7 +97,7 @@
             "state": {
               "type": "backlink",
               "state": {
-                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md",
+                "file": "Algo/Séminaire/Exercices seminaire.md",
                 "collapseAll": false,
                 "extraContext": false,
                 "sortOrder": "alphabetical",
@@ -114,7 +114,7 @@
             "state": {
               "type": "outgoing-link",
               "state": {
-                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md",
+                "file": "Algo/Séminaire/Exercices seminaire.md",
                 "linksCollapsed": false,
                 "unlinkedCollapsed": true
               }
@@ -137,7 +137,7 @@
             "state": {
               "type": "outline",
               "state": {
-                "file": "Algo/Séminaire/Chapter 5 - Recursivity.md"
+                "file": "Algo/Séminaire/Exercices seminaire.md"
               }
             }
           },
@@ -170,8 +170,8 @@
   },
   "active": "0d2d422aa24bb900",
   "lastOpenFiles": [
-    "Algo/Séminaire/Exercices seminaire.md",
     "Algo/Séminaire/Chapter 5 - Recursivity.md",
+    "Algo/Séminaire/Exercices seminaire.md",
     "Algo/Séminaire/Introduction.md",
     "Algo/Séminaire/Chapter 3 - Case analysis.md",
     "Algo/Séminaire/Chapter 2 - Functions.md",
diff --git a/Algo/Séminaire/Chapter 5 - Recursivity.md b/Algo/Séminaire/Chapter 5 - Recursivity.md
index e30396f..56db4f9 100644
--- a/Algo/Séminaire/Chapter 5 - Recursivity.md	
+++ b/Algo/Séminaire/Chapter 5 - Recursivity.md	
@@ -119,6 +119,12 @@ Exemple with egypt (4.10) vs multiply (4.6):
 The best algorithm in term of complexity is the parameter that is constant/linear or logarithmic. If you have an exponential algorithm, you can put it in trash :)
 
 **Exemple with fibonacci algorithm**
+```Ocaml
+# let rec fibo = function 
+	0|1 -> 1
+	| n -> fibo (n-1) + fibo(n-2);;
+```
+
 
 | |res|how (for human) ?|How (for function) ?|
 |:----:|:----:|:----:|:----:|
@@ -133,4 +139,14 @@ The best algorithm in term of complexity is the parameter that is constant/linea
 
 
 <center><img src="https://imgur.com/6OWREOm.png" height=400 width=auto/></center>
-This function is not optimize because the number of calls is growing exponentially
\ No newline at end of file
+This function is not optimize because the number of calls is growing exponentially. 
+A good function will be:
+```Ocaml
+# let fibo n = 
+	let rec fib i fi fi_1 = 
+		if n <= i then
+			fi
+		else
+			fib (i+1)(fi+fi_1)fi
+	in fib 1 1 1
+```
diff --git a/Algo/Séminaire/Exercices seminaire.md b/Algo/Séminaire/Exercices seminaire.md
index 503adf3..97be547 100644
--- a/Algo/Séminaire/Exercices seminaire.md	
+++ b/Algo/Séminaire/Exercices seminaire.md	
@@ -1,5 +1,5 @@
 
-|## Exercise 2.2 (Power)
+## Exercise 2.2 (Power)
 
 ```Ocaml
 (*First version ; 6 multiplications*)
@@ -366,3 +366,11 @@ let rec multiply x y =
 	eg b;;
 	
 ```
+
+## Exercise 4.11
+```Ocaml
+let rec puissance = function
+	|n when n = 0 -> 1
+	|n when n = 1 -> x
+	|n -> 
+```
\ No newline at end of file