From 5ffb7e02d1bf981516a3fa931ebdf50f879ca88c Mon Sep 17 00:00:00 2001
From: Robin VAN DE MERGHEL <robin.van_de_merghel@etu.uca.fr>
Date: Wed, 29 Mar 2023 22:34:34 +0200
Subject: [PATCH] New MRP course

---
 .gitmodules                                   |   9 +
 Modeliser Resolution/Automates.pdf            | Bin 0 -> 84491 bytes
 Modeliser Resolution/Exo_Graphs.py            | 174 ++++++++++++++++
 Modeliser Resolution/Special_Graphs.py        |  36 ++++
 .../Special_Graphs.cpython-311.pyc            | Bin 0 -> 2066 bytes
 Modeliser Resolution/automate.py              | 194 ++++++++++++++++++
 Modeliser Resolution/graph.dot                |  26 +++
 Modeliser Resolution/graph.png                | Bin 0 -> 64771 bytes
 Modeliser Resolution/hypercube.txt            |   8 +
 POO/ProjetV2                                  |   1 +
 Related Personal Projects/productivity        |   1 +
 Web-Serveur/Projet                            |   1 +
 12 files changed, 450 insertions(+)
 create mode 100644 Modeliser Resolution/Automates.pdf
 create mode 100644 Modeliser Resolution/Exo_Graphs.py
 create mode 100644 Modeliser Resolution/Special_Graphs.py
 create mode 100644 Modeliser Resolution/__pycache__/Special_Graphs.cpython-311.pyc
 create mode 100644 Modeliser Resolution/automate.py
 create mode 100644 Modeliser Resolution/graph.dot
 create mode 100644 Modeliser Resolution/graph.png
 create mode 100644 Modeliser Resolution/hypercube.txt
 create mode 160000 POO/ProjetV2
 create mode 160000 Related Personal Projects/productivity
 create mode 160000 Web-Serveur/Projet

diff --git a/.gitmodules b/.gitmodules
index 551204c..5b5e6cc 100644
--- a/.gitmodules
+++ b/.gitmodules
@@ -19,3 +19,12 @@
 [submodule "POO/Projet"]
 	path = POO/Projet
 	url = git@gitlab.isima.fr:rovandemer/demineur.git
+[submodule "POO/ProjetV2"]
+	path = POO/ProjetV2
+	url = git@gitlab.isima.fr:rovandemer/minesweeper.git
+[submodule "Web-Serveur/Projet"]
+	path = Web-Serveur/Projet
+	url = git@gitlab.isima.fr:rovandemer/le-konbah.git
+[submodule "Related Personal Projects/productivity"]
+	path = Related Personal Projects/productivity
+	url = git@gitlab.isima.fr:rovandemer/productivity.git
diff --git a/Modeliser Resolution/Automates.pdf b/Modeliser Resolution/Automates.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..ccadb2ac357018fa20ab5dd1d2204db3800571da
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diff --git a/Modeliser Resolution/Exo_Graphs.py b/Modeliser Resolution/Exo_Graphs.py
new file mode 100644
index 0000000..a7c2b9f
--- /dev/null
+++ b/Modeliser Resolution/Exo_Graphs.py	
@@ -0,0 +1,174 @@
+import random
+import Special_Graphs
+
+import os
+import graphviz as gv
+
+"""A vertex is a string.
+A graph is a dictionary; its keys are vertices and the value associated to a
+key/vertex u is the set of neighbors of u in G.
+"""
+
+def extract_graph_from_file(file):
+    """Takes a file name as input and extracts the graph inside it.
+    The file is composed of n lines, where n is the total number of vertices.
+    Each line is of the form u:v1:v2:...:vk where u is a vertex and the
+    vi's are its neighbors. If u has no neighbor, the corresponding line is u:
+    This function returns a dictionary representing the graph:
+    Its keys are vertices and its values are the sets of neighbors
+    of each vertex. """
+    with open(file, "r") as f:
+        d = {}
+        for line in f:
+            line = line.strip()
+            line = line.split(":")
+            if (len(line) == 1):
+                d[line[0]] = set()
+            else:
+                d[line[0]] = set(line[1:])
+        
+        return d
+
+def set_of_vertices(graph):
+    """Returns the set of vertices of the graph."""
+    return set(graph.keys())
+
+
+def set_of_neighbors(graph, u):
+    """Returns the set of neighbors of vertex u in the graph."""
+    return set(graph[u])
+
+
+def degree_of(graph, u):
+    """Returns the numbers of neighbors of vertex u in the graph."""
+    return len(graph[u])
+
+
+def are_neighbors(graph, u, v):
+    """Boolean function returning True if u and v are neighbors in the graph.
+     Returns False otherwise."""
+    return v in graph[u]
+
+
+def number_of_vertices(graph):
+    """Returns the number of vertices of the graph."""
+    return len(graph)
+
+
+def number_of_edges(graph):
+    """Returns the number of edges of the graph.
+    We suppose that it is NON directed."""
+    return sum([len(graph[u]) for u in graph]) // 2
+
+
+def is_symmetric(graph):
+    """Boolean function returning True if the dictionary representing the graph
+    is symmetric: u is a neighbor of v iff v is a neighbor of u.
+    Returns False otherwise and print a non symmetric couple."""
+    for u in graph:
+        for v in graph[u]:
+            if u not in graph[v]:
+                print(f"Non symmetric couple: {u}, {v}")
+                return False
+    return True
+
+
+def bfs(graph, r):
+    """Makes the BFS of the graph from vertex r. Returns a tuple
+    (parent, d, color)."""
+    parent = {r: None}
+    d = {r: 0}
+    color = {r: "gray"}
+    queue = [r]
+    while queue:
+        u = queue.pop(0)
+        for v in graph[u]:
+            if v not in color:
+                color[v] = "gray"
+                d[v] = d[u] + 1
+                parent[v] = u
+                queue.append(v)
+        color[u] = "black"
+    return parent, d, color
+
+
+def color_graph_by_list(graph, list_of_vertices):
+    """Takes as input a graph and a list of its vertices. This function colors
+    the graph with this list and returns a tuple (c, color) where:
+     + color is the constructed coloration (a dictionary whose keys are the
+     vertices and values are colors (integers > 0)) and
+     + c is the number of colors used by the coloration color."""
+    color = {}
+    c = 0
+    for u in list_of_vertices:
+        color[u] = c
+        c += 1
+    return c, color
+
+
+def color_graph_by_random_lists(graph, number_of_iterations=1):
+    """Takes as input a graph, and an integer number_of_iterations.
+    Runs number_of_iterations times the coloring function of the graph on
+    random lists of vertices of the graph and returns the best coloring found
+    (the one using the lowest number of colors)."""
+    best_coloring = {}
+    best_c = float("inf")
+    for i in range(number_of_iterations):
+        list_of_vertices = list(graph.keys())
+        random.shuffle(list_of_vertices)
+        c, color = color_graph_by_list(graph, list_of_vertices)
+        if c < best_c:
+            best_c = c
+            best_coloring = color
+    return best_coloring
+
+
+def is_stable(graph, set_s):
+    """Boolean function taking as input a graph and a set of vertices.
+    It returns True if this set is a stable of the graph (there is no edge
+     between vertices of this set in the graph).
+     Returns False otherwise."""
+    for u in set_s:
+        for v in set_s:
+            if are_neighbors(graph, u, v):
+                return False
+    return True
+
+
+def is_proper_coloring(graph, color):
+    """Takes as input a graph and a coloring (a dictionary having the set of
+    vertices as keys and colors (integers > 0) as values).
+    Returns True if color is a proper coloring of the graph.
+    Returns False otherwise and print a message to indicate the error."""
+    for u in graph:
+        for v in graph[u]:
+            if color[u] == color[v]:
+                print(f"Error: {u} and {v} have the same color.")
+                return False
+    return True
+
+def render_graph(graph, color=None, filename="graph"):
+    with open(filename + ".dot", "w") as f:
+        f.write("digraph G {\n")
+        for u in graph:
+            for v in graph[u]:
+                if color is None:
+                    f.write(f"{u} -> {v};\n")
+                else:
+                    f.write(f"{u} -> {v} [color={color[u]}];\n")
+        f.write("}\n")
+    os.system(f"dot -Tpng {filename}.dot -o {filename}.png")
+
+
+
+# Special_Graphs.hypercube_graph(3)  # To construct a hypercube(d)
+global_graph = extract_graph_from_file("hypercube.txt")
+print("------ BFS from 000:", bfs(global_graph, "000"))
+print(f"------ Is the graph symmetric? {is_symmetric(global_graph)}")
+global_coloring_of_the_graph = color_graph_by_random_lists(global_graph, 4)
+print(global_coloring_of_the_graph)
+# resultG["000"] = resultG["010"] # To force an error in H3 graph.
+print(f"-- Is it a valid coloring? "
+      f"{is_proper_coloring(global_graph, global_coloring_of_the_graph)}")
+
+render_graph(global_graph)
diff --git a/Modeliser Resolution/Special_Graphs.py b/Modeliser Resolution/Special_Graphs.py
new file mode 100644
index 0000000..54323ce
--- /dev/null
+++ b/Modeliser Resolution/Special_Graphs.py	
@@ -0,0 +1,36 @@
+# This file must be renamed Special_Graphs.py
+
+# ------ Hypercube graphs -------
+
+
+def hypercube_graph(d):
+    """Constructs the hypercube graph of dimension d and write it in file Hd.
+    Each vertex is associated to a binary word of length d.
+    For example '001101' is a vertex of hypercube of dimension 6.
+    Two vertices are neighbors iff they differ on exactly one bit.
+    For example, 01001 and 01101 are neighbors in hypercube(5)."""
+    with open("H" + str(d), "w") as f:
+        for i in range(2 ** d):
+            f.write("{0:b}".format(i).zfill(d) + ":")
+            for j in range(d):
+                f.write("{0:b}".format(i ^ (1 << j)).zfill(d) + ":")
+            f.write("\n")
+
+
+# ------ Complete graphs -------
+
+def complete_graph(n):
+    """Constructs a complete graph of n vertices and write it in file Kn."""
+    pass
+
+# ------ Grid graphs -------
+
+def grid_graph(p, q):
+    """Constructs a grid pXq and write it in file GridpXq."""
+    pass
+
+# ------ Torus graphs -------
+
+def torus_graph(p, q):
+    """Constructs a torus pXq and write it in file ToruspXq."""
+    pass
diff --git a/Modeliser Resolution/__pycache__/Special_Graphs.cpython-311.pyc b/Modeliser Resolution/__pycache__/Special_Graphs.cpython-311.pyc
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diff --git a/Modeliser Resolution/automate.py b/Modeliser Resolution/automate.py
new file mode 100644
index 0000000..f50f1e2
--- /dev/null
+++ b/Modeliser Resolution/automate.py	
@@ -0,0 +1,194 @@
+"""Automates finis deterministes (AFD).
+Un état est une chaine de caractères.
+Un caractère est une chaine de longueur 1.
+Un alphabet est un ensemble de catactères. 
+Une fonction de transition delta est un dictionnaire dont les clés sont des
+tuples (q,c), avec q un état et c un caractère, et donc les valeurs sont
+des états.
+Un automate est un tuple :
+(alphabet, ens. des états, état initial, ens. de états accepteurs, delta) 
+Rappels : 
+Déterministe = pour tout état p et tout caractère c de l'alphabet, il
+existe exactement un état q tel que : delta(p,c)=q.
+L'automate a exactement un état initial.
+Un mot est accepté ssi en partant de l'état initial l'automate est dans un
+état accepteur après avoir traité l'intégralité du mot. 
+"""
+
+
+def alphabet(automate):
+    """Retourne l'alphabet de l'automate."""
+    return automate[0]
+
+
+def ens_etats(automate):
+    """Retourne l'ens. des états de l'automate."""
+    return automate[1]
+
+
+def etat_initial(automate):
+    """Retourne l'état initial de l'automate."""
+    return automate[2]
+
+
+def ens_etats_accepteurs(automate):
+    """Retourne l'ens. des états accepteurs de l'automate."""
+    return automate[3]
+
+
+def delta(automate):
+    """Retourne la fonction de transition de l'automate."""
+    return automate[4]
+
+
+def construit_alphabet_a_partir_de_delta(dico_delta):
+    """Extrait et retourne l'ens. alphabet de l'automate dont la fonction
+    delta est donnée sous forme de dictionnaire."""
+    return {el for _, el in dico_delta.keys()}
+
+
+def construit_ens_etats_a_partir_de_delta(dico_delta):
+    """Extrait et retourne l'ens. des états de l'automate dont la fonction
+    delta est donnée sous forme de dictionnaire."""
+    return {el for el, _ in dico_delta.keys()}
+
+
+def est_mot_compatible(automate, mot_w):
+    """Fonction Booléenne retournant True ssi les caractères du mot sont tous
+    dans l'alphabet de l'automate."""
+    return {x for x in mot_w}.issubset(alphabet(automate))
+
+
+def delta_etoile(automate, etat_q, mot_w):
+    """Retourne l'état de l'automate après le traitement du mot à partir de
+    l'état etat_q de l'automate."""
+    etat_courant = etat_q
+    delta_automate = delta(automate)
+    for caractere in mot_w:
+        etat_courant = delta_automate[(etat_courant, caractere)]
+
+    return etat_courant
+
+
+def est_accepte(automate, mot_w):
+    """Fonction Booléenne retournant True ssi mot_w est accepté par l'automate
+    déterministe."""
+    q_0 = etat_initial(automate)
+
+    # On récupère l'état final après le traitement du mot
+    etat_final = delta_etoile(automate, q_0, mot_w)
+
+    # On vérifie que l'état final est un état accepteur
+    if etat_final in ens_etats_accepteurs(automate):
+        return True
+
+    return False
+
+
+# Cette fonction sera utilisée dans affiche_facteur_dans_mot
+def affiche_facteur(mot, indice_deb, indice_fin):
+    """Affiche le facteur du mot entre des deux indices donnés,
+    encadré par [...]"""
+    print(f"{mot[:indice_deb]}[{mot[indice_deb:indice_fin]}]{mot[indice_fin:]}")
+
+
+# Cette fonction sera utilisée dans affiche_tous_les_facteurs
+def affiche_facteur_dans_mot(automate, mot_m, indice_i):
+    """Affiche tous les facteurs f du mot mot_m, à partir de l'indice indice_i
+    de celui-ci, avec la propriété que f est un mot (non vide) accepté par
+    l'automate."""
+    p = etat_initial(automate)
+    delt = delta(automate)
+    long = 0
+
+    for x in mot_m[indice_i:]:
+        p = delt.get((p, x))
+        long += 1
+        
+        if p != None and p in ens_etats_accepteurs(automate):
+            affiche_facteur(mot_m, indice_i, indice_i + long)
+        elif p == None:
+            return None
+
+
+
+def affiche_tous_les_facteurs(automate, mot_w):
+    """Affiche tous les facteurs f du mot mot_w tels que f est un mot (non
+    vide) accepté par l'automate. L'affichage est de la forme ...[...]...
+    Le mot mot_w peut contenir des caractères qui ne sont pas dans l'alphabet
+    de l'automate."""
+    for indice in range(len(mot_w)):
+        affiche_facteur_dans_mot(automate, mot_w, indice)
+
+
+def est_automate_deterministe(automate):
+    """Fonction Booléenne retournant True ssi l'automate est déterministe."""
+    for etat in ens_etats(automate):
+        for caractere in alphabet(automate):
+            # On récupère les états suivants pour chaque couple (état,
+            # caractère)
+            etats_suivants = [delta(automate)[(etat, caractere)]]
+
+            # On vérifie que tous les états suivants sont différents
+            if len(etats_suivants) != len(set(etats_suivants)):
+                return False
+
+    return True
+
+
+# ---- Construction de l'automate 1
+etat_initial_1 = 'q1'
+ensemble_etats_accepteurs_1 = {'q3'}
+delta_1 = {('q1', 'a'): 'q3', ('q1', 'b'): 'q1',
+           ('q2', 'a'): 'q2', ('q2', 'b'): 'q1',
+           ('q3', 'a'): 'q2', ('q3', 'b'): 'q3'}
+automate_1 = (construit_alphabet_a_partir_de_delta(delta_1),
+              construit_ens_etats_a_partir_de_delta(delta_1),
+              etat_initial_1, ensemble_etats_accepteurs_1, delta_1)
+
+
+# ---- Construction de l'automate 2 : mots contenant un nombre pair de a dans
+# ---- ceux composés de a et de b uniquement.
+etat_initial_2 = 'q1'
+ensemble_etats_accepteurs_2 = {'q1'}
+delta_2 = {('q1', 'a'): 'q2', ('q1', 'b'): 'q1',
+           ('q2', 'a'): 'q1', ('q2', 'b'): 'q2'}
+automate_2 = (construit_alphabet_a_partir_de_delta(delta_2),
+              construit_ens_etats_a_partir_de_delta(delta_2),
+              etat_initial_2, ensemble_etats_accepteurs_2, delta_2)
+
+
+# ---- Tests de diverses fonctions.
+w = "abbaabbXYba"
+if est_mot_compatible(automate_1, w):
+    print(f'Le mot "{w}" est ' + 'accepté' if est_accepte(automate_1, w) else
+          'refusé')
+else:
+    print(f'Le mot "{w}" contient des caractères qui ne sont pas '
+          'dans l\'alphabet')
+
+print("--"*10 + f'Facteurs de "{w}" de l\'Automate 1 :')
+affiche_tous_les_facteurs(automate_1, w)
+
+print("--"*10 + f'Facteurs de "{w}" de l\'Automate 2 :')
+affiche_tous_les_facteurs(automate_2, w)
+
+# --- Pour vous aider, voici ce que doit afficher cette dernière ligne :
+# --------------------Facteurs de "abbaabbXYba" de l'Automate 2 :
+# [abba]abbXYba
+# a[b]baabbXYba
+# a[bb]aabbXYba
+# a[bbaa]bbXYba
+# a[bbaab]bXYba
+# a[bbaabb]XYba
+# ab[b]aabbXYba
+# ab[baa]bbXYba
+# ab[baab]bXYba
+# ab[baabb]XYba
+# abb[aa]bbXYba
+# abb[aab]bXYba
+# abb[aabb]XYba
+# abbaa[b]bXYba
+# abbaa[bb]XYba
+# abbaab[b]XYba
+# abbaabbXY[b]a
diff --git a/Modeliser Resolution/graph.dot b/Modeliser Resolution/graph.dot
new file mode 100644
index 0000000..95da9d3
--- /dev/null
+++ b/Modeliser Resolution/graph.dot	
@@ -0,0 +1,26 @@
+digraph G {
+000 -> 010;
+000 -> 100;
+000 -> 001;
+001 -> 011;
+001 -> 000;
+001 -> 101;
+010 -> 110;
+010 -> 011;
+010 -> 000;
+011 -> 010;
+011 -> 111;
+011 -> 001;
+100 -> 110;
+100 -> 000;
+100 -> 101;
+101 -> 111;
+101 -> 100;
+101 -> 001;
+110 -> 010;
+110 -> 111;
+110 -> 100;
+111 -> 110;
+111 -> 011;
+111 -> 101;
+}
diff --git a/Modeliser Resolution/graph.png b/Modeliser Resolution/graph.png
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diff --git a/Modeliser Resolution/hypercube.txt b/Modeliser Resolution/hypercube.txt
new file mode 100644
index 0000000..833fda0
--- /dev/null
+++ b/Modeliser Resolution/hypercube.txt	
@@ -0,0 +1,8 @@
+000:100:010:001
+001:101:011:000
+010:110:000:011
+011:111:001:010
+100:000:110:101
+101:001:111:100
+110:010:100:111
+111:011:101:110
diff --git a/POO/ProjetV2 b/POO/ProjetV2
new file mode 160000
index 0000000..91724c4
--- /dev/null
+++ b/POO/ProjetV2
@@ -0,0 +1 @@
+Subproject commit 91724c4b3eda66d87a5cad5faccac7a91242c45b
diff --git a/Related Personal Projects/productivity b/Related Personal Projects/productivity
new file mode 160000
index 0000000..135d82b
--- /dev/null
+++ b/Related Personal Projects/productivity	
@@ -0,0 +1 @@
+Subproject commit 135d82b35a158bddc3645f245d009983181ba7bb
diff --git a/Web-Serveur/Projet b/Web-Serveur/Projet
new file mode 160000
index 0000000..5d9a0fd
--- /dev/null
+++ b/Web-Serveur/Projet
@@ -0,0 +1 @@
+Subproject commit 5d9a0fd9779637bbb91d412cf888e3533f3ab6cf
-- 
GitLab