From ffa1adea1f0415427258de52b86a8fed85804489 Mon Sep 17 00:00:00 2001
From: Suwako Moriya <suwako@moriya.zapto.org>
Date: Sat, 2 May 2020 18:15:27 +0200
Subject: [PATCH] checkpoint

---
 obligatoire/TP5/main.py                       |     7 +-
 obligatoire/TP5_Bonus/TP5 listes bonus.pdf    |   Bin 0 -> 197833 bytes
 obligatoire/TP5_Bonus/main.py                 |   148 +
 obligatoire/TP6/main.py                       |   104 +
 obligatoire/TP6/sanstitre1.py                 |     8 +
 obligatoire/TP_Intégrale/main.py              |    29 +
 .../TP Cours 8.méthode de Newton.pdf          |   Bin 0 -> 206589 bytes
 obligatoire/TP_Newton/main.py                 |    94 +
 obligatoire/TP_Newton/sanstitre1.py           |    18 +
 spe/DS.ml                                     |    51 +
 spe/DS1.ml                                    |    84 +
 spe/TD2/main.ml                               |    55 +
 spe/TD3/main.ml                               |    51 +
 spe/TP1/main.ml                               |     2 +-
 spe/TP3/main.ml                               |    92 +
 spe/TP4/main.ml                               |    23 +
 spe/decomp                                    |   Bin 0 -> 796784 bytes
 spe/decomp.cmi                                |   Bin 0 -> 1023 bytes
 spe/decomp.cmx                                |   Bin 0 -> 3111 bytes
 spe/decomp.ml                                 |    53 +
 spe/decomp.o                                  |   Bin 0 -> 20960 bytes
 spe/liste.txt                                 | 24134 ++++++++++++++++
 22 files changed, 24951 insertions(+), 2 deletions(-)
 create mode 100644 obligatoire/TP5_Bonus/TP5 listes bonus.pdf
 create mode 100755 obligatoire/TP5_Bonus/main.py
 create mode 100755 obligatoire/TP6/main.py
 create mode 100755 obligatoire/TP6/sanstitre1.py
 create mode 100755 obligatoire/TP_Intégrale/main.py
 create mode 100644 obligatoire/TP_Newton/TP Cours 8.méthode de Newton.pdf
 create mode 100755 obligatoire/TP_Newton/main.py
 create mode 100755 obligatoire/TP_Newton/sanstitre1.py
 create mode 100644 spe/DS.ml
 create mode 100644 spe/DS1.ml
 create mode 100644 spe/TD2/main.ml
 create mode 100644 spe/TD3/main.ml
 create mode 100644 spe/TP3/main.ml
 create mode 100644 spe/TP4/main.ml
 create mode 100755 spe/decomp
 create mode 100644 spe/decomp.cmi
 create mode 100644 spe/decomp.cmx
 create mode 100644 spe/decomp.ml
 create mode 100644 spe/decomp.o
 create mode 100644 spe/liste.txt

diff --git a/obligatoire/TP5/main.py b/obligatoire/TP5/main.py
index aca85e1..83172b2 100755
--- a/obligatoire/TP5/main.py
+++ b/obligatoire/TP5/main.py
@@ -100,5 +100,10 @@ ajouteRoutes(plan3, [(1,6),(1,2),(2,7),(6,7),(6,5),(5,10),(10,11),(11,9),(9,8),(
 
 #Troisième partie
 
+#Préliminaire
+import random
+def entierAleatoire(k):
+    return random.randint(1,k)
+#1.
 
-
+def coloriageAleatoire(plan, couleur, k, s, t):
diff --git a/obligatoire/TP5_Bonus/TP5 listes bonus.pdf b/obligatoire/TP5_Bonus/TP5 listes bonus.pdf
new file mode 100644
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diff --git a/obligatoire/TP5_Bonus/main.py b/obligatoire/TP5_Bonus/main.py
new file mode 100755
index 0000000..b2632af
--- /dev/null
+++ b/obligatoire/TP5_Bonus/main.py
@@ -0,0 +1,148 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Feb  6 08:23:46 2020
+
+@author: suwako
+"""
+
+#Exercice 1
+#a)
+"""La fonction len permet de connaître la durée de la randonnée d'Alice."""
+#b)
+def altmax(alts):
+    res = alts[0]
+    for i in range(1, len(alts)):
+        if alts[i] > res :
+            res = alts[i]
+    return res
+#c)
+def denivmax(alts):
+    res = max(0, alts[0])
+    for i, j in enumerate(range(1, len(alts))):
+        deniv = alts[j] - alts[i]
+        if deniv > res :
+            res = deniv
+    return res
+
+def heure_denivmax(alts):
+    res = (max(0, alts[0]), 0)
+    for i, j in enumerate(range(1, len(alts))):
+        deniv = alts[j] - alts[i]
+        if deniv > res[0] :
+            res = (deniv, j)
+    return res[1]
+
+def denivtotal(alts):
+    res = max(0, alts[0])
+    for i, j in enumerate(range(1, len(alts))):
+        deniv = alts[j] - alts[i]
+        if deniv > 0:
+            res += deniv
+    return res
+
+def sommets(alts):
+    res = []
+    for a, b, c in zip(range(len(alts)-2),
+                       range(1, len(alts) - 1),
+                       range(2, len(alts))):
+        if alts[a]<alts[b] and alts[b]>alts[c]:
+            res.append(alts[b])
+    return res
+
+#Exercice 2
+
+def pgplateau(tab):
+    grand_plateau = 0
+    plateau = 0
+    for el in tab:
+        if el == 0:
+            plateau += 1
+        else:
+            grand_plateau = max(grand_plateau, plateau)
+            plateau = 0
+    return grand_plateau
+#Exercice 3:
+import random
+#a)
+def tableau_hasard(n=100): return [random.randint(0,n-1) for i in range(n)]
+#b)
+def absents(tab):
+    presents = {tab[0]}
+    for el in tab[1:]:
+        presents.update({el})
+    return(100 - len(list(presents)))
+#c)
+def moyenne(*args):
+    n=100
+    if args:
+        n = args[0]
+    somme = 0
+    for i in range(n):
+        somme += absents(tableau_hasard())
+    return somme/n
+
+#Exercice 4
+#a)
+def premiere_motie(tab):
+    return tab[:len(tab)//2 + 1]
+def deuxieme_motie(tab):
+    return tab[len(tab)//2 - 1:]
+def pairs(tab):
+    return tab[::2]
+def impairs(tab):
+    return tab[1::2]
+#b)
+
+def out_shuffle(tab):
+    tab[::2], tab[1::2] = tab[:len(tab)//2], tab[len(tab)//2:]
+    return tab
+#c)
+def nb_shuffle(n=52, shuffle=out_shuffle):
+    ori_tab = list(range(n))
+    tab = shuffle(ori_tab.copy())
+    i = 1
+    while tab != ori_tab:
+        shuffle(tab)
+        i+=1
+    return i
+#On est à 8 pour le out_shuffle
+#d)
+def in_shuffle(tab):
+    tab[::2], tab[1::2] = tab[len(tab)//2:], tab[:len(tab)//2]
+    return tab
+#On est à 52 pour le in_shuffle
+
+#Exercice 5
+def pppremier(n):
+    i = n+1
+    while True:
+        j = 2
+        while j*j <= i:
+            if i % j == 0:
+                break
+            j += 1
+        if j*j > i:
+            return i
+        i += 1
+
+def premiers1(n=1000):
+    premiers=[2]
+    while premiers[-1]<1000:
+        premiers.append(pppremier(premiers[-1]))
+    if premiers[-1] > 1000:
+        del premiers[-1]
+    return premiers
+
+def erathostene(n=1000):
+    premiers = list(range(2,1001))
+    i=0
+    while i<len(premiers):
+        j = i+1
+        while j<len(premiers):
+            if premiers[j] % premiers[i] == 0:
+                del premiers[j]
+            else:
+                j+=1
+        i+=1
+    return premiers
\ No newline at end of file
diff --git a/obligatoire/TP6/main.py b/obligatoire/TP6/main.py
new file mode 100755
index 0000000..c9bb3d0
--- /dev/null
+++ b/obligatoire/TP6/main.py
@@ -0,0 +1,104 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Mar  3 10:11:04 2020
+
+@author: suwako
+"""
+"""
+import matplotlib.pyplot as plt
+import matplotlib.image as mpimg
+import numpy as np
+import copy as c
+M=np.array([[1,0,1],[0,1,1],[1,0,1],[0,1,1]])
+
+## ajoute une ligne tout autour de la matrice M
+def bord(M):
+    p=np.size(M[:,0])
+    q=np.size(M[0,:])
+    N=np.zeros((p+2,q+2))
+    c=0.3
+    N[:,0]=c
+    N[:,q+1]=c
+    N[0,:]=c
+    N[p+1,:]=c
+    N[1:p+1,1:q+1]=M[0:p,0:q]
+    return(N)
+##agrandissement de la matrice et création de l'image
+def lab(M):
+    p=np.size(M[:,0])
+    q=np.size(M[0,:])
+    r=min(512//p,512//q)
+    img=np.zeros((r*p,r*q))
+    for i in range(p):
+        for j in range(q):
+            img[i*r:i*r+r,j*r:j*r+r]=int(M[i,j]*255)
+    return(img)
+
+img=lab(bord(M))
+plt.imshow(img,cmap=plt.cm.gray)
+plt.show()
+
+##passage à la matrice des triplets et retour
+def tr1(M):
+    p=np.size(M[:,0])
+    q=np.size(M[0,:])
+    M1=np.array([[[M[i,j],0,0] for j in range(q)] for i in range(p)])
+    return M1
+
+def tr(M):
+    p=np.size(M[:,0])
+    q=np.size(M[0,:])
+    M1=np.array([[M[i,j][0] for j in range(q//3)] for i in range(p//3)])
+    return M1
+
+print(tr(tr1(M)))"""
+import numpy as np
+import matplotlib.pyplot as plt
+import random
+
+def bord(M):
+    return np.pad(np.array(M, dtype='float64'), pad_width=1, mode='constant', constant_values=0.3)
+
+def img(M):
+    return np.kron(M, np.full((512, 512), 255))
+
+
+def tr(M):
+    return np.array([[j[0] for j in i] for i in M])
+
+def tr1(M):
+    return np.array([[(j, 0, 0) for j in i] for i in M])
+
+def voisin(M, i,j):
+    cases=[case for case in [(i,j-1), (i-1,j), (i+1,j), (i,j+1)] if M[case[0]][case[1]][0]==1]
+    for case in cases:
+        M[case[0]][case[1]]=[0.5, i, j]
+    return cases
+
+def suivant(M, chemin):
+    return [vois for case in chemin for vois in voisin(M, *case)]
+
+def chemin(M, depart, fin):
+    voisins=voisin(M, *depart)
+    i=0
+    while fin not in voisins:
+        voisins = suivant(M, voisins)
+        i+=1
+        if i>1000:
+            raise
+    chemin = [fin]
+    while depart != chemin[-1]:
+        i,j=chemin[-1]
+        chemin.append(tuple(map(int,M[i][j]))[1:])
+    return chemin[::-1]
+def val(p):
+    if random.random()<p:
+        return(0)
+    else:
+        return(1)
+p=0.35
+m=15
+M=tr1(bord(np.array([[val(p) for j in range(m)] for i in range(m)])))
+print(chemin(M, (1,3), (4,2)))
+plt.imshow(img(tr(M)), cmap=plt.cm.gray)
\ No newline at end of file
diff --git a/obligatoire/TP6/sanstitre1.py b/obligatoire/TP6/sanstitre1.py
new file mode 100755
index 0000000..693a318
--- /dev/null
+++ b/obligatoire/TP6/sanstitre1.py
@@ -0,0 +1,8 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Mar  6 08:06:39 2020
+
+@author: suwako
+"""
+
diff --git a/obligatoire/TP_Intégrale/main.py b/obligatoire/TP_Intégrale/main.py
new file mode 100755
index 0000000..7b1ef4c
--- /dev/null
+++ b/obligatoire/TP_Intégrale/main.py
@@ -0,0 +1,29 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Feb  4 10:32:17 2020
+
+@author: suwako
+"""
+
+
+def rectangle(f, a, b, n):
+    h = (b - a) / n
+    aire = 0
+    for i in range(n):
+        aire += f(a+i*h)
+    return aire*h
+
+def trapeze(f, a, b, n):
+    h = (b - a) / n
+    aire = 0
+    for i in range(n):
+        aire += (f(i*h) + f((i+1)*h))
+    return aire*h/2
+
+def milieu(f, a, b, n):
+    h = (b - a) / n
+    aire = 0
+    for i in range(n):
+        aire += f((a+h*i + a + h*(i+1))/2)
+    return aire*h
diff --git a/obligatoire/TP_Newton/TP Cours 8.méthode de Newton.pdf b/obligatoire/TP_Newton/TP Cours 8.méthode de Newton.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..3b9f79dccffdf818c5526d19464dc0f3482827fb
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diff --git a/obligatoire/TP_Newton/main.py b/obligatoire/TP_Newton/main.py
new file mode 100755
index 0000000..9cd6464
--- /dev/null
+++ b/obligatoire/TP_Newton/main.py
@@ -0,0 +1,94 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Mar  6 08:06:39 2020
+
+@author: suwako
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+def newton(f, df, u, xtol=1e-12, Nmax=100):
+    n = 1
+    v = u - f(u) / df(u)
+    while abs(u - v) >= xtol:
+        u, v = v, v - f(v) / df(v)
+        n += 1
+        if n > Nmax:
+            return None
+    return v, n
+
+def secante(f, u, v, xtol=1e-12, Nmax=100):
+    n = 1
+    while abs(u - v) >= xtol:
+        u, v = v, (u * f(v) - v * f(u)) / (f(v) - f(u))
+        n += 1
+        if n > Nmax:
+            return None
+    return v, n
+
+def f(x): return x**3 - 2 * x - 5
+def df(x): return 3 * x * x - 2
+plt.figure(0)
+X = np.linspace(-3, 3, 256)
+Y = [f(x) for x in X]
+plt.plot(X,Y)
+plt.grid()
+plt.show()
+
+for u in range(-3, 4):
+    x, n = newton(f, df, u)
+    print(f"Pour u0 = {u} on obtient {x} au bout de {n} itérations'")
+
+nmax = 0
+for u in range(-3, 4):
+    for v in range(-3, 4):
+        if u != v:
+            x, n = secante(f, u, v)
+            if n > nmax:
+                nmax = n
+                (a, b) = (u, v)
+print(f"pour u0 = {a} et u1 = {b}, {nmax} itérations sont nécéssaires")
+
+print(secante(df, 0, 1)[0])
+print(newton(f, df, secante(df, 0, 1)[0], Nmax=200))
+
+def f(x): return 3 * np.sin(4*x)+x*x - 2
+def df(x): return 12*np.cos(4*x)+2*x
+plt.figure(1)
+X = np.linspace(-3, 3, 256)
+Y = [f(x) for x in X]
+plt.plot(X,Y)
+plt.grid()
+plt.show()
+
+def zeros(f, df, a, b, n=100):
+    zer = []
+    for k in range(n):
+        u = a + np.random.random() * (b - a)
+        x = newton(f, df, u)
+        if x is not None and round(x[0], 12) not in zer:
+            zer.append(round(x[0], 12))
+    return zer
+from scipy.integrate import quad
+
+def f(x): 
+    return quad(lambda t : np.sqrt(1-t*t)*np.cos(x*t),-1,1)[0]
+def df(x):
+    return quad(lambda t : -t*np.sqrt(1-t*t)*np.sin(x*t),-1,1)[0]
+plt.figure(2)
+X = np.linspace(0, 16, 256)
+Y = [f(x) for x in X]
+plt.plot(X,Y)
+plt.grid()
+plt.show()
+
+def derivee(f,x,h):
+    return (f(x+h)-f(x-h)/(2*h))
+def delta(p):
+    return abs(np.cos(1)-derivee(np.sin,1,10**(-p)))
+plt.figure(3)
+P= np.arange(4,8,.1)
+D=[delta(p) for p in P]
+print(D)
+plt.plot(P,D)
+plt.show()
\ No newline at end of file
diff --git a/obligatoire/TP_Newton/sanstitre1.py b/obligatoire/TP_Newton/sanstitre1.py
new file mode 100755
index 0000000..2c12951
--- /dev/null
+++ b/obligatoire/TP_Newton/sanstitre1.py
@@ -0,0 +1,18 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Mar 28 09:14:39 2020
+
+@author: suwako
+"""
+
+def genere(n):
+    u=[83 for _ in range(n)]
+    l=[83%2 for _ in range(n)]
+    for i in range(1,n):
+        u[i] = (16365*u[i-1]) % 65521
+        l[i] = u[i]%2
+    return l
+
+def palindrome(s):
+    return s[:len(s)//2] == s[:len(s)//2:-1]
\ No newline at end of file
diff --git a/spe/DS.ml b/spe/DS.ml
new file mode 100644
index 0000000..2e9149e
--- /dev/null
+++ b/spe/DS.ml
@@ -0,0 +1,51 @@
+let indice_ming t =
+	let min = ref t.(0) in
+	let imin = ref 0 in
+	for i=1 to (Array.length t) - 1 do
+		if t.(i) <= !min then
+			begin
+			min := t.(i);
+			imin := i
+			end
+	done;
+	!imin;;
+
+indice_ming [|1;5;3;2;-1;9|];;
+[|1;5;3;2;-1;9|].(4);;
+
+let premier_indice_minl t = 
+	let i = ref 0 in
+	let n = Array.length t in
+	let continue = ref true in
+	while !continue do
+		if !i = (n - 1) then
+			continue := false
+		else if (!i = 0) then
+			if (t.(!i) <= t.(!i + 1)) then
+				continue := false
+			else i := !i + 1
+		else if (t.(!i) <= t.(!i - 1)) && (t.(!i) <= t.(!i + 1)) then
+			continue := false
+		else
+			i := !i + 1
+	done;
+	!i;;
+premier_indice_minl [|7;5;3;2;1;|];;
+
+let indice_minl t = 
+	let rec aux is ie =
+		let k = (is + ie)/2 in
+		if (ie - is) <= 1 then
+			if t.(is) <= t.(ie) then
+				is
+			else ie
+		else if t.(k) >= t.(k-1) then
+			aux is (k - 1)
+		else if t.(k) >= t.(k+1) then
+			aux (k + 1) ie
+		else
+			k in
+	aux 0 (Array.length t - 1);;
+let t = [|0;1;2;3;4;|];;
+indice_minl t;;
+t.(indice_minl t);;
\ No newline at end of file
diff --git a/spe/DS1.ml b/spe/DS1.ml
new file mode 100644
index 0000000..7598226
--- /dev/null
+++ b/spe/DS1.ml
@@ -0,0 +1,84 @@
+(* Exercice 1 *)
+
+let dichotomie x t = ();;
+
+(* Exercice 2 *)
+
+let rec f x n = match n with
+	| 0 -> 1
+	| _ -> x * (f x (n - 1));;
+
+f 10 2;;
+
+let puissance x n = 
+	let res = ref 1 in
+	for i=0 to n-1 do
+		res := !res * x
+	done;
+	!res;;
+
+puissance 2 2;;
+
+(* Exercice 3 *)
+
+(* 5 *)
+let rec pgcd a b = match min (abs a) (abs b) with
+	| 0 -> max (abs a) (abs b)
+	| 1 -> 1
+	| _ -> pgcd ((max (abs a) (abs b)) mod (min (abs a) (abs b))) (min (abs a) (abs b));;
+
+let rec pgcd a b = match b with
+	| 0 -> a
+	| -> pgcd b (a mod b);;
+	
+
+(* 7 *)
+let bezout a b =
+	let rec aux u0 v0 u1 v1 r0 r1 = match r0 mod r1 with
+		| 0 -> r1,u1,v1
+		| _ -> aux u1 v1 (u0 - ( (r0 / r1) * u1 ) ) (v0 - ( (r0 / r1) * v1 )) r1 (r0 mod r1) in
+		aux 1 0 0 1 a b;;
+
+bezout 24 65;;
+bezout 6 6;;
+
+pgcd (-1024) 4096;;
+
+max (abs 1) (abs 2) ;;
+abs;;
+
+(* Exercice 4 *)
+
+let next n = match n mod 2 with
+	| 0 -> n/2
+	| _ -> 3 * n + 1;;
+let 
+next 1;;
+
+let rec syracuse n = match n with
+	| 1 -> [1]
+	| _ -> n::syracuse (next n);;
+syracuse 5;;
+
+let rec altitude_maximale n = match n with
+	| 1 -> 1
+	| _ -> max n (altitude_maximale (next n));;
+
+syracuse 9;;
+altitude_maximale 9;;
+
+let dav n = 
+	let vmax = ref 0 in
+	let v = ref 0 in
+	let i = ref n in
+	while !i <> 1 do
+		i := next !i;
+		if !i > n then
+			v := !v + 1
+		else
+			v := 0;
+		if !v > !vmax then
+			vmax := !v
+	done;
+	!vmax;;
+dav 9;;
\ No newline at end of file
diff --git a/spe/TD2/main.ml b/spe/TD2/main.ml
new file mode 100644
index 0000000..8491d3e
--- /dev/null
+++ b/spe/TD2/main.ml
@@ -0,0 +1,55 @@
+(* Exercice 1 *)
+(* 1 *)
+let selection t = 
+	let rec maxi fin =
+		if fin = 0 then
+			0
+		else
+			begin
+			let m = maxi (fin - 1) in
+			if t.(fin) > t.(m) then
+				fin
+			else
+				m
+			end in
+
+	let rec aux fin = 
+		if fin = 0 then ()
+		else
+			begin
+			let f = t.(fin) in
+			let m = maxi fin in
+			t.(fin) <- t.(m);
+			t.(m) <- f;
+			aux (fin - 1)
+			end in
+
+	aux (Array.length t - 1);;
+
+let a = [|1;4;2;-1;2;3;4;2;9|];;
+selection a;;
+a;;
+(* 2 *)
+(* Dans le pire des cas, la fonction effectuera en tout n! comparaisons *)
+(* 3 *)
+(* Dans le meilleur des cas, la fonction effectuera également n! comparaisons *)
+
+(* Exercice 2 *)
+let rec min_liste l = match l with
+	| [] -> failwith "La liiste estttt"
+	| [a] -> (a, [])
+	| h::t -> 
+		let m, l = min_liste t in
+		if h < m then
+			(h, t)
+		else
+			(m, h::l);;
+min_liste [4;2;4;1;5];;
+let rec l_selection l = match l with
+	| [] -> []
+	| [a] -> [a]
+	| _ -> let m, lst = min_liste l in m::(l_selection lst);;
+l_selection [1;2;6;7;3;2;-6;3];;
+
+let rec insertion l = match l with
+	
\ No newline at end of file
diff --git a/spe/TD3/main.ml b/spe/TD3/main.ml
new file mode 100644
index 0000000..045f7de
--- /dev/null
+++ b/spe/TD3/main.ml
@@ -0,0 +1,51 @@
+(* Exercice 1 *)
+
+let scinder l =
+	let rec aux acc1 acc2 n l = match l with
+		| [] -> (acc1, acc2)
+		| h::t -> if n = 0 then aux (h::acc1) acc2 1 t
+					 else aux acc1 (h::acc2) 0 t in
+		aux [] [] 0 l;;
+scinder [8;5;4;3;1];;
+
+let fusionner l1 l2 = 
+	let rec aux acc l1 l2 = match (l1,l2) with
+		|([],[]) -> acc
+		|([],h::t) -> aux h::acc [] t
+		|(h::t,[]) -> aux h::acc t []
+		|(h1::t1,h2::t2) -> if h1>h2 then aux (h2::acc) l1 t2
+								  else aux (h1::acc) t1 l2 in
+	let rec reverse acc l = match l with
+		| [] -> acc
+		| h::t -> reverse (h::acc) t in
+	reverse [] (aux [] l1 l2);;
+
+fusionner [5;7;11] [2;4;8;10];;
+
+let rec tri_fusion l = match l with
+	|[] -> []
+	|[a] -> [a]
+	|_ -> let (l1,l2) = scinder l in fusionner (tri_fusion l1)  (tri_fusion l2);;
+
+tri_fusion [3;1;2;666];;
+
+(* Exerice 2 *)
+
+let partition k l = 
+	let rec aux acc1 acc2 l = match l with
+		|[] -> (acc1,acc2)
+		|h::t -> if h>=k then aux acc1 (h::acc2) t
+					else aux (h::acc1) acc2 t in
+	aux [] [] l;;
+
+partition2 2 [3;1;666;2;0;-1];;
+
+let rec tri_pivot l = match l with
+	|[] -> []
+	|h::t -> let (l1,l2) = partition h t in (tri_pivot l1)@(h::(tri_pivot l2));;
+
+tri_pivot [3;1;666;2;0;-1];;
+
+let a = ref 1;;
+decr a;;
+a;;
\ No newline at end of file
diff --git a/spe/TP1/main.ml b/spe/TP1/main.ml
index 1bd2654..d78ee8b 100644
--- a/spe/TP1/main.ml
+++ b/spe/TP1/main.ml
@@ -55,7 +55,7 @@ let rec recherche_dicho d f a v =
 let recherche_dichotomique a v =
 	recherche_dicho 0 (Array.length v) a v;;
 
-recherche_dichotomique (-5) [|1;2;3;4;5;6;7;8;9;10;11|];;
+recherche_dichotomique (-5) [|1;2;3;4;5;6;7;8;9;10;5|];;
 
 
 (*Exercice 5*)
diff --git a/spe/TP3/main.ml b/spe/TP3/main.ml
new file mode 100644
index 0000000..97d9c00
--- /dev/null
+++ b/spe/TP3/main.ml
@@ -0,0 +1,92 @@
+(* Exercice 1 *)
+let rec fibo n = match n with
+	|0 -> 0
+	|1 -> 1
+	|_ -> (fibo (n-1)) + (fibo (n-2));;
+let fibot n =
+	let rec aux acc1 acc2 n = match n with
+		| 0 -> acc1
+		| _ -> aux acc2 (acc2+acc1) (n-1) in
+	aux 0 1 n;;
+
+let comp fa fb i j =
+	let debuta =Sys.time () in
+	fa i j;
+	let fina = Sys.time () in
+	let debutb = Sys.time () in
+	fb i j;
+	let finb = Sys.time() in
+	print_float (fina -. debuta);
+	print_newline ();
+	print_float (finb -. debutb);;
+fibo 20;;
+Sys.time ();;
+comp fibot fibot 50000000;;
+
+(* Exercice 2 *)
+
+let rec numero x y = match y with
+	|0 when x = 0 -> 0
+	|0 -> numero 0 (x-1) + 1
+	|_ -> numero (x+1) (y-1) + 1;;
+let numero_ter x y =
+	let rec aux acc x y = match y with
+		|0 when x = 0 -> acc
+		|0 -> aux (acc+1) 0 (x-1)
+		|_ -> aux (acc+1) (x+1) (y-1) in
+	aux 0 x y;;
+numero_ter 2 2;;
+let rec suite x y = match x with
+	|0 -> [numero_ter 0 y]
+	|_ -> (numero_ter x y)::(suite (x-1) y);;
+suite 100 0;;
+let numero_formule x y = (x+y)*(x+y+1)/2 + y ;;
+numero 6 2;;
+
+(* Exercice 3 *)
+
+let binome k n =
+	let m = Array.make_matrix (n+1) (k+1) 0 in
+	for i = 0 to n do
+		for j = 0 to k do
+			if j = 0 then m.(i).(j) <- 1
+			else if  i = 0 then m.(i).(j) <- 0
+			else m.(i).(j) <- m.(i-1).(j) + m.(i-1).(j-1)
+		done
+	done;
+	m.(n).(k);;
+let rec binrec k n = match (k,n) with
+	| (0,n) -> 1
+	| (k,0) -> 0
+	| _ -> binrec (k-1) (n-1) + binrec k (n-1);;
+binrec 2 7;;
+binome 2 7;;
+
+comp binrec binome 12 22;;
+(* La version itérative est plus rapide. *)
+(* En effet, la version itérative ne calcule qu'une seule fois chacun
+des coefficients là où la version récursive calcule à plusieures reprises
+les mêmes coefficients *)
+
+(* Exo Bonus *)
+
+let rec binr n = match n with
+	| 0 -> [""]
+	| _ -> List.map (fun s -> "1"^s) (binr (n-1)) @ List.map (fun s -> "0"^s) (binr (n-1));;
+binr 5;;
+
+let binit n = 
+	let rec puis x n = match n with
+		| 0 -> 1
+		| _ -> x * (puis x (n-1)) in
+	let aux = fun x -> match x with | true -> 0 | false -> 1 in
+	let res = Array.make (puis 2 n) "" in
+	for i = 0 to (puis 2 n) - 1 do
+		let cur = ref "" in
+		for j = n downto 1 do
+			cur:= !cur ^ string_of_int (aux ( (i / (j)) mod 2  = 0))
+			done;
+		res.(i) <- !cur
+	done;
+	res;;
+binit 3;;
\ No newline at end of file
diff --git a/spe/TP4/main.ml b/spe/TP4/main.ml
new file mode 100644
index 0000000..3848241
--- /dev/null
+++ b/spe/TP4/main.ml
@@ -0,0 +1,23 @@
+(* Exercice 1 *)
+
+let rec invnaif l =
+	let rec perm c l = match l with
+		| [] -> 0
+		| h::t -> if c > h then (perm c t) + 1 else (perm c t) in
+ 	match l with
+	| [] -> 0
+	| h::t -> (perm h t) + (invnaif t);;
+
+invnaif [3;2;1];;
+
+(* Exercice 2 *)
+
+let scinder l =
+	let rec aux acc1 c l = match l with
+		| [] -> ((List.rev acc1), [])
+		| h::t when c=0 -> ((List.rev acc1), t)
+		| h::t -> aux (h::acc1) (c-1) t
+		in
+	aux [] ((List.length l)/2) l ;;
+scinder [1;2;3;4;5;6;7];;
+
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new file mode 100755
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diff --git a/spe/decomp.cmi b/spe/decomp.cmi
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diff --git a/spe/decomp.cmx b/spe/decomp.cmx
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diff --git a/spe/decomp.ml b/spe/decomp.ml
new file mode 100644
index 0000000..bbdfc8c
--- /dev/null
+++ b/spe/decomp.ml
@@ -0,0 +1,53 @@
+open Format
+let premiers = [1;2;4;8;16;32;64;128;256;512;1024;2048;4096;8192];;
+let rec print_int_list l = match l with
+	|[] -> printf "\n"
+	|h::t -> begin printf "%d " h;print_int_list t end;;
+let print_sum l =
+	let rec aux l = match l with
+		| [] -> printf "\n"
+		| h::t -> begin printf " + %d" h;aux t end in
+	match l with
+		|[] -> printf "0\n"
+		|h::t -> begin printf "%d" h;aux t end;;
+let rec sum l = match l with
+    | [] -> 0
+    | h::t -> h + sum t;;
+let rec dans a l = match l with
+	| [] -> false
+	| h::t -> if h=a then true else dans a t ;;
+let rec retirer acc base modulo = match base with
+	| [] -> acc
+	| h::t -> if dans h modulo then retirer acc t modulo
+  				 else retirer (h::acc) t modulo ;;
+let rec somme accn accl ban lim l = match l with
+	| [] -> (accn,accl,true)
+  	| h::t -> if accn < lim then somme (accn+h) (h::accl) ban lim t
+  	          else if dans (accn - lim) ban then somme (accn+h) (h::accl) ban lim t
+				 else (accn,accl,false);;
+let decomp n =
+	 let imp = ref [1] in
+    let rec aux impp n =
+        if dans n !imp then raise Not_found else
+        if dans n premiers then [n] else
+        let (a,l,f) = somme 0 [] !imp n premiers in
+        print_int_list (n::a::0::l);
+        match a - n with
+            |0 -> l
+            |d (*when d < n*) -> begin try retirer [] l (aux impp d) with
+            						| Not_found when f -> raise Not_found
+                              | Not_found -> begin imp:=(d::(!imp)); aux (d::impp) n end end
+            (*|d -> raise Not_found*) in
+    aux [1] n;;
+for i = 0 to sum premiers do
+	try begin let d = decomp i in printf "%d = " i; print_sum d end with
+		| Not_found -> printf "%d : Pas de decomposition\n" i done;;
+(*
+let max = ref 0 in
+let imax = ref 0 in
+for i = 0 to sum premiers do
+	let c = ref 0 in
+	try let a=sum (decomp c i) in printf "Oui :%d : %d\n" i !c with
+		| Not_found -> printf "Non :%d : %d\n" i !c;
+	if !c > !max then begin max := !c; imax := i end done;
+printf "%d : %d" !imax !max;; *)
diff --git a/spe/decomp.o b/spe/decomp.o
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diff --git a/spe/liste.txt b/spe/liste.txt
new file mode 100644
index 0000000..0ae0173
--- /dev/null
+++ b/spe/liste.txt
@@ -0,0 +1,24134 @@
+0 = 0
+1 : Pas de décoxmposition
+2 = 2
+3 = 3
+4 : Pas de décoxmposition
+5 = 3 + 2
+6 : Pas de décoxmposition
+7 = 2 + 5
+8 = 3 + 5
+9 = 2 + 7
+10 = 5 + 3 + 2
+11 = 11
+12 = 5 + 7
+13 = 13
+14 = 2 + 5 + 7
+15 = 3 + 5 + 7
+16 = 2 + 3 + 11
+17 = 7 + 5 + 3 + 2
+18 = 7 + 11
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+23 = 5 + 7 + 11
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+24127 : Pas de décoxmposition
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+24129 : Pas de décoxmposition
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+24132 : Pas de décoxmposition
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