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Suwako Moriya 2020-09-15 18:55:23 +02:00
commit 41d8036710
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[[source]]
name = "pypi"
url = "https://pypi.org/simple"
verify_ssl = true
[dev-packages]
[packages]
pygame = "*"
[requires]
python_version = "3.7"

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{
"_meta": {
"hash": {
"sha256": "e172a3e30534a9a0b74742497b40f2ab196a0890d1cb082eb481fb89e384456e"
},
"pipfile-spec": 6,
"requires": {
"python_version": "3.7"
},
"sources": [
{
"name": "pypi",
"url": "https://pypi.org/simple",
"verify_ssl": true
}
]
},
"default": {
"pygame": {
"hashes": [
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"sha256:4e1065577f1b29111113be5deb2ea88553551a5e1cf33e0c08fa32768f285809",
"sha256:5f052dc2975a399aa1830c1f04c5f72856aa416bf3cd4b31375a058015a5c620",
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],
"index": "pypi",
"version": "==1.9.6"
}
},
"develop": {}
}

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Le simulateur utilise pygame, pour l'installer :
pip install pygame
une fois fait, pour lancer le simulateur, executez le main.py en tant que script (Ca permet à Pyzo de lancer le script dans le bon dossier)
Comment l'utiliser :
Les touches :
PARTOUT :
ESPACE : Met en pause le jeu
C : Diminuer la fréquence de mise à jour des cellules
V : Augmenter la fréquence de mise à jour des cellules
Q : Quitter
Suppr : Effacer la grille
D : Activer le mode débogage (Affiche les compteurs des cellules à l'itération précédente)
M : Basculer en mode Clavier / Basculer en mode Souris
Mode Souris :
Clic gauche : Changer l'état de la cellule selectionnée (rester appuyé pour en changer plusieurs)
Clic droit / Clic molette (glisser) : Changer la zone visible de la grille
Molette vers le haut : Zoomer
Molette vers le bas : Dézoomer
Mode Clavier :
Touches directionnelles (Flèches) : Déplacer le pointeur (cadre jaune)
T : changer l'état de la cellule selectionnée
À propos :
La grille est infinie, et par défaut, le mode souris est activé. Le mode clavier est incomplet mais permet de faire des actions basique.

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import pygame
import time
import sys
import random
"""
Game of Life Simulator
"""
#Partie Calculatoire
RULES = {"B":3, "O":3, "U":2}
NEIGHBOURS = [(i,j) for i in (-1,0,1) for j in (-1,0,1) if (i,j) != (0,0)]
def relative(offset, cell):
"""
Fonction permettant d'obtenir une coordonnée absolue à partir d'une origine(offset) et de coordonnées relative(cell).
"""
return tuple(cell[i] + offset[i] for i in range(len(cell)))
def difference(origin, cell):
"""
Fonction permettant d'obtenir les coordonnées de cell en fixant origin comme origine
"""
return tuple(cell[i] - origin[i] for i in range(len(cell)))
def scale(cell, factor):
return tuple(int(cell[i]*factor) for i in range(len(cell)))
class Grid:
"""
Classe gérant les calculs liés à l'évolution d'une grille infinie selon le Jeu de la vie
"""
def __init__(self):
self.alive_cells = set({(i, 0) for i in range(500)})
self.active_cells = dict()
self.old_cells = set()
def tick(self):
self.old_cells.clear()
self.old_cells.update(self.alive_cells)
self.active_cells.clear()
#On s'assure que les cellules vivantes soient considérés comme actives
for cell in self.alive_cells:
self.active_cells.update({cell:0})
#On met à jour les voisins des cellules vivantes, c'est à dire incrémenter leur compteur
for cell in self.alive_cells:
for neighbour in NEIGHBOURS:
self.incr_counter(relative(cell, neighbour))
#On applique les règles du jeu selon le compteur des cellules actives
for cell in self.active_cells:
if RULES["U"] <= self.active_cells[cell] <= RULES["O"]:
if self.active_cells[cell] == RULES["B"]:
self.alive_cells.add(cell)
else:
self.alive_cells.discard(cell)
def incr_counter(self, cell):
if cell in self.active_cells:
self.active_cells[cell] +=1
else:
self.active_cells.update({cell:1})
#Interface Graphique
pygame.init()
size = width, height = 1025,1025
screen = pygame.display.set_mode(size, flags=pygame.RESIZABLE)
DEBUG = False #Affichage de variables de débogage à l'écran
TICK_RATE = 10 #Fréquence de rafraîchissement du jeu
FRAME_RATE = 60 #Fréquence de rafraîchissement de l'interface
camera = [0, 0] #Permettant choisir quelle zone de la grille on visualise
true_camera = camera
MOUSE = True #Mode souris : On pointe avec les cellules avec la souris et pas les flèches directionnelles
grid = Grid() #On initialise une grille
#On charge les assets
source_assets = {
"alive_cell": pygame.image.load("assets/alive_cell.png"),
"dead_cell": pygame.image.load("assets/dead_cell.png"),
"highlight": pygame.image.load("assets/highlight.png")}
SCALE = .25 #Facteur de taille variable (zoom)
CELL_SIDE = int(source_assets["highlight"].get_rect().width * SCALE) #Mesure en pixel d'un côté d'une cellule
assets = {asset:pygame.transform.scale(source_assets[asset],(CELL_SIDE,CELL_SIDE)) for asset in source_assets}
font = pygame.font.SysFont(pygame.font.get_default_font(), CELL_SIDE)
class Unit(pygame.sprite.Sprite):
"""
Classe représentant une unité d'affichage (cellule)
Il est à noter que cette unité peut représenter différentes cellules en fonction de camera
"""
def __init__(self, offset):
super().__init__()
self.offset = offset
def draw(self, screen, camera, grid):
self.image = assets[("dead_cell","alive_cell")[relative(camera, self.offset) in grid.alive_cells]]
self.position = self.image.get_rect()
self.position.x = self.offset[0]*CELL_SIDE #On positionne la cellule sur l'écran
self.position.y = self.offset[1]*CELL_SIDE #On positionne la cellule sur l'écran
screen.blit(self.image, self.position) #On dessine la cellule
if DEBUG and relative(camera, self.offset) in grid.active_cells:
text = font.render(str(grid.active_cells[relative(camera, self.offset)]), False, (0,255,0))
posi = text.get_rect()
posi.center = self.position.center
screen.blit(text, posi)
class Pointer(pygame.sprite.Sprite):
"""
Classe représentant le pointeur de cellule sélectionnée (pour l'éditer)
"""
def __init__(self, pos):
super().__init__()
self.pos = pos
def draw(self, screen, camera, grid):
self.image = assets["highlight"]
self.position = self.image.get_rect()
self.position.x = self.pos[0]*CELL_SIDE #On positionne le pointeur sur l'écran
self.position.y = self.pos[1]*CELL_SIDE #On positionne le pointeur sur l'écran
screen.blit(self.image, self.position) #On dessine le pointeur
def draw_grid(screen, camera, grid, units):
for unit in units:
units[unit].draw(screen, camera, grid)
#Boucle principale
def get_units():
return {(i,j):Unit((i,j)) for i in range(width//(CELL_SIDE) +1) for j in range(height//(CELL_SIDE) +1)}
units = get_units() #Liste de cellules à afficher à l'écran
relatives = {unit:relative(camera, unit) for unit in units}
pointer = Pointer((0,0)) #Permettant de sélectionner une cellule précisément pour l'éditer
running = True
pause = True
last_tick = time.time()
last_frame = time.time()
KEYSDOWN = set()
MOUSEBUTTONSDOWN = set()
visited_cells = set()
drag_origin = (0,0) #Position du curseur à la préssion du bouton du milieu de la souris
last_pointer_move = time.time()
redraw = True
while running:
frame = (last_frame + 1/FRAME_RATE) - time.time() < 0
if frame:
for event in pygame.event.get():
if event.type == pygame.VIDEORESIZE:
size = width, height = event.size
screen =screen = pygame.display.set_mode(size,
flags=pygame.RESIZABLE)
units = get_units()
redraw = True
if event.type == pygame.QUIT:
sys.exit()
if event.type == pygame.KEYDOWN:
KEYSDOWN.add(event.key)
if event.key in [275,276,273,274] and not MOUSE: #Touches directionnelles pour déplacer le pointeur
new_pos = list(pointer.pos)
exec("new_pos" + ("[0]+","[0]-","[1]-","[1]+")[[275,276,273,274].index(event.key)] + "=1")
if pointer.pos in units: units[pointer.pos].draw(screen, camera, grid)
pointer.pos = tuple(new_pos)
last_pointer_move = time.time()
if event.key == 116 and not MOUSE: #T: Changer l'état d'une cellule
if relative(camera, pointer.pos) in grid.alive_cells:
grid.alive_cells.discard(relative(camera, pointer.pos))
else:
grid.alive_cells.add(relative(camera, pointer.pos))
visited_cells.add(relative(camera, pointer.pos))
if event.type == pygame.KEYUP:
print(event.key)
if event.key in KEYSDOWN:
if event.key == 32: #ESPACE : pause
pause = not pause
if event.key in (109,59): #M : Mode souris
MOUSE = not MOUSE
if event.key == 100: #D : Mode de déboggage
DEBUG = not DEBUG
if event.key in (113,97): #Q : Quitter
sys.exit()
if event.key == 127: #Suppr : Effacer la grille
grid.alive_cells.clear()
redraw = True
if event.key == 99: #C: Diminuer le TICK_RATE
TICK_RATE = TICK_RATE/2
if event.key == 118: #V : Augmenter le TICK_RATE
TICK_RATE = TICK_RATE*2
if event.key == 116 and not MOUSE: #T: Changer l'état d'une cellule
visited_cells.clear()
if event.key == 114 : #R : Remplir aléatoirement l'écran
redraw = True
for unit in units:
if random.randint(0,3) == 0:
grid.alive_cells.add(relatives[unit])
else:
grid.alive_cells.discard(relatives[unit])
KEYSDOWN.discard(event.key)
if event.type == pygame.MOUSEBUTTONDOWN:
if MOUSE:
if event.button in (2,3): #Bouton de la molette / Clic droit : Glisser
print(event.pos)
true_camera = camera
drag_origin = event.pos
if event.button == 1: #Clic gauche : Éditer la cellule selectionnée
if relative(camera, pointer.pos) in grid.alive_cells:
grid.alive_cells.discard(relative(camera, pointer.pos))
else:
grid.alive_cells.add(relative(camera, pointer.pos))
visited_cells.add(relative(camera, pointer.pos))
MOUSEBUTTONSDOWN.add(event.button)
if event.type == pygame.MOUSEBUTTONUP:
if event.button in (2,3):
camera = difference(scale(difference(drag_origin, event.pos), 1/CELL_SIDE), true_camera)
redraw = True
if event.button == 1:
visited_cells.clear()
if event.button == 4: #Molette vers le haut #Zoom
if CELL_SIDE*2 <= min(size):
SCALE *= 2 #Facteur de taille variable (zoom)
CELL_SIDE = int(source_assets["highlight"].get_rect().width * SCALE) #Mesure en pixel d'un côté d'une cellule
assets = {asset:pygame.transform.scale(source_assets[asset],(CELL_SIDE,CELL_SIDE)) for asset in source_assets}
units = get_units() #Liste de cellules à afficher à l'écran
font = pygame.font.SysFont(pygame.font.get_default_font(), CELL_SIDE)
redraw = True
if event.button == 5: #Molette vers le bas #"Dézoom"
if CELL_SIDE/2 >= 3:
SCALE *= 1/2 #Facteur de taille variable (zoom)
CELL_SIDE = int(source_assets["highlight"].get_rect().width * SCALE) #Mesure en pixel d'un côté d'une cellule
assets = {asset:pygame.transform.scale(source_assets[asset],(CELL_SIDE,CELL_SIDE)) for asset in source_assets}
units = get_units() #Liste de cellules à afficher à l'écran
font = pygame.font.SysFont(pygame.font.get_default_font(), CELL_SIDE)
redraw = True
print(event.button)
MOUSEBUTTONSDOWN.discard(event.button)
if event.type == pygame.MOUSEMOTION:
if 2 in MOUSEBUTTONSDOWN or 3 in MOUSEBUTTONSDOWN:
camera = difference(scale(difference(drag_origin, event.pos), 1/CELL_SIDE),true_camera)
redraw = True
if MOUSE:
if pointer.pos in units: units[pointer.pos].draw(screen, camera, grid)
pointer.pos = scale(event.pos, 1/CELL_SIDE)
if 1 in MOUSEBUTTONSDOWN:
if pointer.pos in units: units[pointer.pos].draw(screen, camera, grid)
pointer.pos = scale(event.pos, 1/CELL_SIDE)
if relative(camera, pointer.pos) not in visited_cells:
if relative(camera, pointer.pos) in grid.alive_cells:
grid.alive_cells.discard(relative(camera, pointer.pos))
else:
grid.alive_cells.add(relative(camera, pointer.pos))
visited_cells.add(relative(camera, pointer.pos))
if not MOUSE and (time.time() - (last_pointer_move + 5/FRAME_RATE) > 0):
for key in KEYSDOWN:
if key in [275,276,273,274]:
new_pos = list(pointer.pos)
exec("new_pos" + ("[0]+","[0]-","[1]-","[1]+")[[275,276,273,274].index(event.key)] + "=1")
if pointer.pos in units: units[pointer.pos].draw(screen, camera, grid)
pointer.pos = tuple(new_pos)
last_pointer_move = time.time()
if redraw:
relatives = {unit:relative(camera, unit) for unit in units}
draw_grid(screen, camera, grid, units)
redraw = False
if (last_tick + 1/TICK_RATE) - time.time() < 0:
last_tick = time.time()
if not pause:
grid.tick()
if True:
for unit in units:
if (relatives[unit] in grid.alive_cells) != (relatives[unit] in grid.old_cells):
units[unit].draw(screen, camera, grid)
if frame:
if pointer.pos in units:
units[pointer.pos].draw(screen, camera, grid)
pointer.draw(screen, camera, grid)
pygame.display.flip()
last_frame = time.time()
time.sleep(max(0,min((last_frame + 1/FRAME_RATE) - time.time(), (last_tick + 1/TICK_RATE) - time.time()))) #On attend avant la prochaine image / le prochain tick pour ne pas surcharger le CPU inutilement

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0 -> 1 en 1. :
0 -> 1
0 -> 0 -> 1
0 -> 1 -> 1
0 -> 0 -> 1 -> 1
0 -> 2 en 2. :
0 -> 2
0 -> 0 -> 2
0 -> 2 -> 2
0 -> 0 -> 2 -> 2
0 -> 3 en 2. :
0 -> 1 -> 3
0 -> 0 -> 1 -> 3
0 -> 1 -> 3 -> 3
0 -> 0 -> 1 -> 3 -> 3
0 -> 4 en 4. :
0 -> 2 -> 4
0 -> 0 -> 2 -> 4
0 -> 2 -> 4 -> 4
0 -> 0 -> 2 -> 4 -> 4
0 -> 5 en 6. :
0 -> 1 -> 3 -> 5
0 -> 0 -> 1 -> 3 -> 5
0 -> 1 -> 3 -> 5 -> 5
0 -> 0 -> 1 -> 3 -> 5 -> 5
0 -> 6 en 3. :
0 -> 1 -> 3 -> 6
0 -> 0 -> 1 -> 3 -> 6
0 -> 1 -> 3 -> 6 -> 6
0 -> 0 -> 1 -> 3 -> 6 -> 6
0 -> 7 en 18. :
0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
0 -> 8 en 17. :
0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8
0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
0 -> 9 en 6. :
0 -> 1 -> 3 -> 6 -> 9
0 -> 0 -> 1 -> 3 -> 6 -> 9
0 -> 1 -> 3 -> 6 -> 9 -> 9
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 9
0 -> 10 en 9. :
0 -> 1 -> 3 -> 6 -> 9 -> 10
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 10
0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 10
0 -> 0 -> 1 -> 3 -> 6 -> 9 -> 10 -> 10
1 -> 0 en 17. :
1 -> 3 -> 6 -> 9 -> 10 -> 0
1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
1 -> 2 en 19. :
1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2
1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
1 -> 3 en 1. :
1 -> 3
1 -> 1 -> 3
1 -> 3 -> 3
1 -> 1 -> 3 -> 3
1 -> 4 en 21. :
1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
1 -> 5 en 5. :
1 -> 3 -> 5
1 -> 1 -> 3 -> 5
1 -> 3 -> 5 -> 5
1 -> 1 -> 3 -> 5 -> 5
1 -> 6 en 2. :
1 -> 3 -> 6
1 -> 1 -> 3 -> 6
1 -> 3 -> 6 -> 6
1 -> 1 -> 3 -> 6 -> 6
1 -> 7 en 17. :
1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
1 -> 8 en 16. :
1 -> 3 -> 6 -> 9 -> 10 -> 8
1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
1 -> 9 en 5. :
1 -> 3 -> 6 -> 9
1 -> 1 -> 3 -> 6 -> 9
1 -> 3 -> 6 -> 9 -> 9
1 -> 1 -> 3 -> 6 -> 9 -> 9
1 -> 10 en 8. :
1 -> 3 -> 6 -> 9 -> 10
1 -> 1 -> 3 -> 6 -> 9 -> 10
1 -> 3 -> 6 -> 9 -> 10 -> 10
1 -> 1 -> 3 -> 6 -> 9 -> 10 -> 10
2 -> 0 en 19. :
2 -> 3 -> 6 -> 9 -> 10 -> 0
2 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 0
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
2 -> 4 -> 6 -> 9 -> 10 -> 0
2 -> 4 -> 6 -> 9 -> 10 -> 0 -> 0
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 0
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 0 -> 0
2 -> 1 en 8. :
2 -> 3 -> 5 -> 1
2 -> 3 -> 5 -> 1 -> 1
2 -> 2 -> 3 -> 5 -> 1
2 -> 2 -> 3 -> 5 -> 1 -> 1
2 -> 3 en 3. :
2 -> 3
2 -> 2 -> 3
2 -> 3 -> 3
2 -> 2 -> 3 -> 3
2 -> 4 en 2. :
2 -> 4
2 -> 2 -> 4
2 -> 4 -> 4
2 -> 2 -> 4 -> 4
2 -> 5 en 7. :
2 -> 3 -> 5
2 -> 2 -> 3 -> 5
2 -> 3 -> 5 -> 5
2 -> 2 -> 3 -> 5 -> 5
2 -> 6 en 4. :
2 -> 3 -> 6
2 -> 2 -> 3 -> 6
2 -> 4 -> 6
2 -> 2 -> 4 -> 6
2 -> 3 -> 6 -> 6
2 -> 2 -> 3 -> 6 -> 6
2 -> 4 -> 6 -> 6
2 -> 2 -> 4 -> 6 -> 6
2 -> 7 en 19. :
2 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
2 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
2 -> 4 -> 6 -> 9 -> 10 -> 8 -> 7
2 -> 4 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 8 -> 7
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
2 -> 8 en 18. :
2 -> 3 -> 6 -> 9 -> 10 -> 8
2 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 8
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
2 -> 4 -> 6 -> 9 -> 10 -> 8
2 -> 4 -> 6 -> 9 -> 10 -> 8 -> 8
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 8
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 8 -> 8
2 -> 9 en 7. :
2 -> 3 -> 6 -> 9
2 -> 2 -> 3 -> 6 -> 9
2 -> 4 -> 6 -> 9
2 -> 2 -> 4 -> 6 -> 9
2 -> 3 -> 6 -> 9 -> 9
2 -> 2 -> 3 -> 6 -> 9 -> 9
2 -> 4 -> 6 -> 9 -> 9
2 -> 2 -> 4 -> 6 -> 9 -> 9
2 -> 10 en 10. :
2 -> 3 -> 6 -> 9 -> 10
2 -> 2 -> 3 -> 6 -> 9 -> 10
2 -> 4 -> 6 -> 9 -> 10
2 -> 2 -> 4 -> 6 -> 9 -> 10
2 -> 3 -> 6 -> 9 -> 10 -> 10
2 -> 2 -> 3 -> 6 -> 9 -> 10 -> 10
2 -> 4 -> 6 -> 9 -> 10 -> 10
2 -> 2 -> 4 -> 6 -> 9 -> 10 -> 10
3 -> 0 en 16. :
3 -> 6 -> 9 -> 10 -> 0
3 -> 6 -> 9 -> 10 -> 0 -> 0
3 -> 3 -> 6 -> 9 -> 10 -> 0
3 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
3 -> 1 en 5. :
3 -> 5 -> 1
3 -> 5 -> 1 -> 1
3 -> 3 -> 5 -> 1
3 -> 3 -> 5 -> 1 -> 1
3 -> 2 en 18. :
3 -> 6 -> 9 -> 10 -> 0 -> 2
3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
3 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2
3 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
3 -> 4 en 20. :
3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
3 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
3 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
3 -> 5 en 4. :
3 -> 5
3 -> 3 -> 5
3 -> 5 -> 5
3 -> 3 -> 5 -> 5
3 -> 6 en 1. :
3 -> 6
3 -> 3 -> 6
3 -> 6 -> 6
3 -> 3 -> 6 -> 6
3 -> 7 en 16. :
3 -> 6 -> 9 -> 10 -> 8 -> 7
3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
3 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
3 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
3 -> 8 en 15. :
3 -> 6 -> 9 -> 10 -> 8
3 -> 6 -> 9 -> 10 -> 8 -> 8
3 -> 3 -> 6 -> 9 -> 10 -> 8
3 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
3 -> 9 en 4. :
3 -> 6 -> 9
3 -> 3 -> 6 -> 9
3 -> 6 -> 9 -> 9
3 -> 3 -> 6 -> 9 -> 9
3 -> 10 en 7. :
3 -> 6 -> 9 -> 10
3 -> 3 -> 6 -> 9 -> 10
3 -> 6 -> 9 -> 10 -> 10
3 -> 3 -> 6 -> 9 -> 10 -> 10
4 -> 0 en 17. :
4 -> 6 -> 9 -> 10 -> 0
4 -> 6 -> 9 -> 10 -> 0 -> 0
4 -> 4 -> 6 -> 9 -> 10 -> 0
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 0
4 -> 1 en 18. :
4 -> 6 -> 9 -> 10 -> 0 -> 1
4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 1
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
4 -> 2 en 19. :
4 -> 6 -> 9 -> 10 -> 0 -> 2
4 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 2
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
4 -> 3 en 19. :
4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
4 -> 5 en 23. :
4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
4 -> 4 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
4 -> 6 en 2. :
4 -> 6
4 -> 4 -> 6
4 -> 6 -> 6
4 -> 4 -> 6 -> 6
4 -> 7 en 17. :
4 -> 6 -> 9 -> 10 -> 8 -> 7
4 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
4 -> 4 -> 6 -> 9 -> 10 -> 8 -> 7
4 -> 4 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
4 -> 8 en 16. :
4 -> 6 -> 9 -> 10 -> 8
4 -> 6 -> 9 -> 10 -> 8 -> 8
4 -> 4 -> 6 -> 9 -> 10 -> 8
4 -> 4 -> 6 -> 9 -> 10 -> 8 -> 8
4 -> 9 en 5. :
4 -> 6 -> 9
4 -> 4 -> 6 -> 9
4 -> 6 -> 9 -> 9
4 -> 4 -> 6 -> 9 -> 9
4 -> 10 en 8. :
4 -> 6 -> 9 -> 10
4 -> 4 -> 6 -> 9 -> 10
4 -> 6 -> 9 -> 10 -> 10
4 -> 4 -> 6 -> 9 -> 10 -> 10
5 -> 0 en 18. :
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 0
5 -> 1 en 1. :
5 -> 1
5 -> 1 -> 1
5 -> 5 -> 1
5 -> 5 -> 1 -> 1
5 -> 2 en 20. :
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
5 -> 3 en 2. :
5 -> 1 -> 3
5 -> 1 -> 3 -> 3
5 -> 5 -> 1 -> 3
5 -> 5 -> 1 -> 3 -> 3
5 -> 4 en 22. :
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
5 -> 6 en 3. :
5 -> 1 -> 3 -> 6
5 -> 5 -> 1 -> 3 -> 6
5 -> 1 -> 3 -> 6 -> 6
5 -> 5 -> 1 -> 3 -> 6 -> 6
5 -> 7 en 18. :
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
5 -> 8 en 17. :
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 8 -> 8
5 -> 9 en 6. :
5 -> 1 -> 3 -> 6 -> 9
5 -> 5 -> 1 -> 3 -> 6 -> 9
5 -> 1 -> 3 -> 6 -> 9 -> 9
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 9
5 -> 10 en 9. :
5 -> 1 -> 3 -> 6 -> 9 -> 10
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10
5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 10
5 -> 5 -> 1 -> 3 -> 6 -> 9 -> 10 -> 10
6 -> 0 en 15. :
6 -> 9 -> 10 -> 0
6 -> 9 -> 10 -> 0 -> 0
6 -> 6 -> 9 -> 10 -> 0
6 -> 6 -> 9 -> 10 -> 0 -> 0
6 -> 1 en 16. :
6 -> 9 -> 10 -> 0 -> 1
6 -> 9 -> 10 -> 0 -> 1 -> 1
6 -> 6 -> 9 -> 10 -> 0 -> 1
6 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
6 -> 2 en 17. :
6 -> 9 -> 10 -> 0 -> 2
6 -> 9 -> 10 -> 0 -> 2 -> 2
6 -> 6 -> 9 -> 10 -> 0 -> 2
6 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
6 -> 3 en 17. :
6 -> 9 -> 10 -> 0 -> 1 -> 3
6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
6 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
6 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
6 -> 4 en 19. :
6 -> 9 -> 10 -> 0 -> 2 -> 4
6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
6 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
6 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
6 -> 5 en 21. :
6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
6 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
6 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
6 -> 7 en 15. :
6 -> 9 -> 10 -> 8 -> 7
6 -> 9 -> 10 -> 8 -> 7 -> 7
6 -> 6 -> 9 -> 10 -> 8 -> 7
6 -> 6 -> 9 -> 10 -> 8 -> 7 -> 7
6 -> 8 en 14. :
6 -> 9 -> 10 -> 8
6 -> 9 -> 10 -> 8 -> 8
6 -> 6 -> 9 -> 10 -> 8
6 -> 6 -> 9 -> 10 -> 8 -> 8
6 -> 9 en 3. :
6 -> 9
6 -> 6 -> 9
6 -> 9 -> 9
6 -> 6 -> 9 -> 9
6 -> 10 en 6. :
6 -> 9 -> 10
6 -> 6 -> 9 -> 10
6 -> 9 -> 10 -> 10
6 -> 6 -> 9 -> 10 -> 10
7 -> 0 en 19. :
7 -> 6 -> 9 -> 10 -> 0
7 -> 6 -> 9 -> 10 -> 0 -> 0
7 -> 7 -> 6 -> 9 -> 10 -> 0
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 0
7 -> 1 en 20. :
7 -> 6 -> 9 -> 10 -> 0 -> 1
7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
7 -> 2 en 21. :
7 -> 6 -> 9 -> 10 -> 0 -> 2
7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
7 -> 3 en 21. :
7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
7 -> 4 en 23. :
7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
7 -> 5 en 25. :
7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
7 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
7 -> 6 en 4. :
7 -> 6
7 -> 6 -> 6
7 -> 7 -> 6
7 -> 7 -> 6 -> 6
7 -> 8 en 18. :
7 -> 6 -> 9 -> 10 -> 8
7 -> 6 -> 9 -> 10 -> 8 -> 8
7 -> 7 -> 6 -> 9 -> 10 -> 8
7 -> 7 -> 6 -> 9 -> 10 -> 8 -> 8
7 -> 9 en 7. :
7 -> 6 -> 9
7 -> 7 -> 6 -> 9
7 -> 6 -> 9 -> 9
7 -> 7 -> 6 -> 9 -> 9
7 -> 10 en 10. :
7 -> 6 -> 9 -> 10
7 -> 7 -> 6 -> 9 -> 10
7 -> 6 -> 9 -> 10 -> 10
7 -> 7 -> 6 -> 9 -> 10 -> 10
8 -> 0 en 20. :
8 -> 7 -> 6 -> 9 -> 10 -> 0
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 0
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 0
8 -> 1 en 21. :
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 1
8 -> 2 en 22. :
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 2
8 -> 3 en 22. :
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
8 -> 4 en 24. :
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
8 -> 5 en 26. :
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
8 -> 6 en 5. :
8 -> 7 -> 6
8 -> 7 -> 6 -> 6
8 -> 8 -> 7 -> 6
8 -> 8 -> 7 -> 6 -> 6
8 -> 7 en 1. :
8 -> 7
8 -> 7 -> 7
8 -> 8 -> 7
8 -> 8 -> 7 -> 7
8 -> 9 en 8. :
8 -> 7 -> 6 -> 9
8 -> 8 -> 7 -> 6 -> 9
8 -> 7 -> 6 -> 9 -> 9
8 -> 8 -> 7 -> 6 -> 9 -> 9
8 -> 10 en 11. :
8 -> 7 -> 6 -> 9 -> 10
8 -> 8 -> 7 -> 6 -> 9 -> 10
8 -> 7 -> 6 -> 9 -> 10 -> 10
8 -> 8 -> 7 -> 6 -> 9 -> 10 -> 10
9 -> 0 en 12. :
9 -> 10 -> 0
9 -> 10 -> 0 -> 0
9 -> 9 -> 10 -> 0
9 -> 9 -> 10 -> 0 -> 0
9 -> 1 en 13. :
9 -> 10 -> 0 -> 1
9 -> 10 -> 0 -> 1 -> 1
9 -> 9 -> 10 -> 0 -> 1
9 -> 9 -> 10 -> 0 -> 1 -> 1
9 -> 2 en 14. :
9 -> 10 -> 0 -> 2
9 -> 10 -> 0 -> 2 -> 2
9 -> 9 -> 10 -> 0 -> 2
9 -> 9 -> 10 -> 0 -> 2 -> 2
9 -> 3 en 14. :
9 -> 10 -> 0 -> 1 -> 3
9 -> 10 -> 0 -> 1 -> 3 -> 3
9 -> 9 -> 10 -> 0 -> 1 -> 3
9 -> 9 -> 10 -> 0 -> 1 -> 3 -> 3
9 -> 4 en 16. :
9 -> 10 -> 0 -> 2 -> 4
9 -> 10 -> 0 -> 2 -> 4 -> 4
9 -> 9 -> 10 -> 0 -> 2 -> 4
9 -> 9 -> 10 -> 0 -> 2 -> 4 -> 4
9 -> 5 en 18. :
9 -> 10 -> 0 -> 1 -> 3 -> 5
9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
9 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5
9 -> 9 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
9 -> 6 en 15. :
9 -> 10 -> 0 -> 1 -> 3 -> 6
9 -> 10 -> 0 -> 1 -> 3 -> 6 -> 6
9 -> 9 -> 10 -> 0 -> 1 -> 3 -> 6
9 -> 9 -> 10 -> 0 -> 1 -> 3 -> 6 -> 6
9 -> 7 en 12. :
9 -> 10 -> 8 -> 7
9 -> 10 -> 8 -> 7 -> 7
9 -> 9 -> 10 -> 8 -> 7
9 -> 9 -> 10 -> 8 -> 7 -> 7
9 -> 8 en 11. :
9 -> 10 -> 8
9 -> 10 -> 8 -> 8
9 -> 9 -> 10 -> 8
9 -> 9 -> 10 -> 8 -> 8
9 -> 10 en 3. :
9 -> 10
9 -> 9 -> 10
9 -> 10 -> 10
9 -> 9 -> 10 -> 10
10 -> 0 en 9. :
10 -> 0
10 -> 0 -> 0
10 -> 10 -> 0
10 -> 10 -> 0 -> 0
10 -> 1 en 10. :
10 -> 0 -> 1
10 -> 0 -> 1 -> 1
10 -> 10 -> 0 -> 1
10 -> 10 -> 0 -> 1 -> 1
10 -> 2 en 11. :
10 -> 0 -> 2
10 -> 0 -> 2 -> 2
10 -> 10 -> 0 -> 2
10 -> 10 -> 0 -> 2 -> 2
10 -> 3 en 11. :
10 -> 0 -> 1 -> 3
10 -> 0 -> 1 -> 3 -> 3
10 -> 10 -> 0 -> 1 -> 3
10 -> 10 -> 0 -> 1 -> 3 -> 3
10 -> 4 en 13. :
10 -> 0 -> 2 -> 4
10 -> 0 -> 2 -> 4 -> 4
10 -> 10 -> 0 -> 2 -> 4
10 -> 10 -> 0 -> 2 -> 4 -> 4
10 -> 5 en 15. :
10 -> 0 -> 1 -> 3 -> 5
10 -> 0 -> 1 -> 3 -> 5 -> 5
10 -> 10 -> 0 -> 1 -> 3 -> 5
10 -> 10 -> 0 -> 1 -> 3 -> 5 -> 5
10 -> 6 en 12. :
10 -> 0 -> 1 -> 3 -> 6
10 -> 0 -> 1 -> 3 -> 6 -> 6
10 -> 10 -> 0 -> 1 -> 3 -> 6
10 -> 10 -> 0 -> 1 -> 3 -> 6 -> 6
10 -> 7 en 9. :
10 -> 8 -> 7
10 -> 8 -> 7 -> 7
10 -> 10 -> 8 -> 7
10 -> 10 -> 8 -> 7 -> 7
10 -> 8 en 8. :
10 -> 8
10 -> 8 -> 8
10 -> 10 -> 8
10 -> 10 -> 8 -> 8
10 -> 9 en 15. :
10 -> 0 -> 1 -> 3 -> 6 -> 9
10 -> 0 -> 1 -> 3 -> 6 -> 9 -> 9
10 -> 10 -> 0 -> 1 -> 3 -> 6 -> 9
10 -> 10 -> 0 -> 1 -> 3 -> 6 -> 9 -> 9

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MPSI/spe/cours/floyd_warshall.cmi Normal file
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let ii = infinity;;
let g = [|
(* 0 1 2 3 4 5 6 7 8 9 10*)
(*0*) [|0.;1.;2.;ii;ii;ii;ii;ii;ii;ii;ii|];
(*1*) [|ii;0.;ii;1.;ii;ii;ii;ii;ii;ii;ii|];
(*2*) [|ii;ii;0.;3.;2.;ii;ii;ii;ii;ii;ii|];
(*3*) [|ii;ii;ii;0.;ii;4.;1.;ii;ii;ii;ii|];
(*4*) [|ii;ii;ii;ii;0.;ii;2.;ii;ii;ii;ii|];
(*5*) [|ii;1.;ii;ii;ii;0.;ii;ii;ii;ii;ii|];
(*6*) [|ii;ii;ii;ii;ii;ii;0.;ii;ii;3.;ii|];
(*7*) [|ii;ii;ii;ii;ii;ii;4.;0.;ii;ii;ii|];
(*8*) [|ii;ii;ii;ii;ii;ii;ii;1.;0.;ii;ii|];
(*9*) [|ii;ii;ii;ii;ii;ii;ii;ii;ii;0.;3.|];
(*10*)[|9.;ii;ii;ii;ii;ii;ii;ii;8.;ii;0.|];|];;
let copie_matrice m =
let p = Array.length m and q = Array.length m.(0) in
let c = Array.make_matrix p q m.(0).(0) in
for i = 0 to p-1 do
for j = 0 to q-1 do
c.(i).(j) <- m.(i).(j)
done;
done;
c;;
let ecraser_matrice m1 m2 =
let p = Array.length m2 and q = Array.length m2.(0) in
for i = 0 to p-1 do
for j = 0 to q-1 do
m1.(i).(j) <- m2.(i).(j)
done;
done;;
let floyd_warshall g =
let n = Array.length g in
(* w^(k) pour k=-1 *)
let w = copie_matrice g in
for k = 0 to n-1 do
(* mise ŕ jour de w^(k) *)
let c = Array.make_matrix n n 0. in
for i = 0 to n-1 do
for j = 0 to n-1 do
c.(i).(j) <- min w.(i).(j) (w.(i).(k)+.w.(k).(j))
done;
done;
ecraser_matrice w c;
done;
(* on retourne w^(n-1) *)
w;;
let transfo_matrice m =
let p = Array.length m and q = Array.length m.(0) in
let c = Array.make_matrix p q (m.(0).(0),[[(0,0)]]) in
for i = 0 to p-1 do
for j = 0 to q-1 do
c.(i).(j) <- (m.(i).(j), [[(i,j)]])
done;
done;
c;;
let rec joindre_chemins l1 l2 =
let rec aux chemin li = match li with
| [] -> []
| h::t -> (chemin@h)::(aux chemin t) in
match l1 with
| [] -> []
| h::t -> (aux h l2)@(joindre_chemins t l2);;
let floyd_warshall_complet g =
let n = Array.length g in
(* w^(k) pour k=-1 *)
let w = transfo_matrice g in
for k = 0 to n-1 do
(* mise ŕ jour de w^(k) *)
let c = Array.make_matrix n n w.(0).(0) in
for i = 0 to n-1 do
for j = 0 to n-1 do
let ((db,cb), (ds,cs), (dt,ct)) = (w.(i).(j), w.(i).(k), w.(k).(j)) in
if db = ds +. dt then
if db <> infinity then
c.(i).(j) <- (db,cb@(joindre_chemins cs ct))
else
c.(i).(j) <- (db, cb)
else if db > ds +. dt then
c.(i).(j) <- (ds +. dt, joindre_chemins cs ct)
else
c.(i).(j) <- (db, cb);
done;
done;
ecraser_matrice w c;
done;
(* on retourne w^(n-1) *)
w;;
open Format;;
let tous_les_chemins g =
let mat = floyd_warshall_complet g in
let rec affiche_chemin last l = match l with
| [] -> printf "%d\n" last
| (i,j)::t -> (printf "%d -> " i); affiche_chemin j t in
for i = 0 to Array.length mat - 1 do
for j = 0 to Array.length mat.(0) -1 do
if i<>j then
let (d,c) = mat.(i).(j) in printf "%d -> %d en %F :\n" i j d; List.iter (fun li -> printf " "; affiche_chemin j li) c;
print_newline ()
done
done;;
tous_les_chemins g;;

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[General]
kile_livePreviewEnabled=true
kile_livePreviewStatusUserSpecified=false
kile_livePreviewTool=LivePreview-PDFLaTeX
lastDocument=Questions
[document-settings,item:Questions]
Bookmarks=
Encoding=
Highlighting=LaTeX
Highlighting Set By User=false
Indentation Mode=normal
Mode=LaTeX
Mode Set By User=false
[item:Questions]
open=true
order=0
[item:réponseauxquestions.kilepr]
open=false
order=-1
[view-settings,view=0,item:Questions]
CursorColumn=25
CursorLine=3
Dynamic Word Wrap=true
JumpList=
TextFolding=[]
ViMarks=

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[General]
kile_livePreviewEnabled=true
kile_livePreviewStatusUserSpecified=false
kile_livePreviewTool=LivePreview-PDFLaTeX
lastDocument=Questions.tex
[document-settings,item:Questions.tex]
Bookmarks=
Encoding=
Highlighting=LaTeX
Highlighting Set By User=false
Indentation Mode=normal
Mode=LaTeX
Mode Set By User=false
[item:Questions.tex]
open=true
order=0
[item:tp2.kilepr]
open=false
order=-1
[view-settings,view=0,item:Questions.tex]
CursorColumn=14
CursorLine=35
Dynamic Word Wrap=true
JumpList=
TextFolding=[]
ViMarks=.,55,44,[,55,40,],55,44

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\relax
\@writefile{toc}{\contentsline {section}{\numberline {III}Forme normale disjonctive}{1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {III.1}Question :}{1}\protected@file@percent }

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This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020 Gentoo Linux) (preloaded format=pdflatex 2020.9.3) 12 SEP 2020 10:32
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
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Package: calc 2017/05/25 v4.3 Infix arithmetic (KKT,FJ)
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@ -0,0 +1,59 @@
\documentclass[a4paper,10pt]{article}
%\documentclass[a4paper,10pt]{scrartcl}
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\title{Questions du TP2}
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\begin{document}
\maketitle
\sectioni{3}{Forme normale disjonctive}
\subsectioni{1}{Question :}
On se sert du code écrit aux questions précédentes,
\begin{lstlisting}
# table_de_verite 3 g;;
- : bool array = [|true; false; true; false; true; false; false; true|]
\end{lstlisting}
$\mathcal{G} =
(\neg V_2 \wedge \neg V_1 \wedge \neg V_0) \vee
(\neg V_2 \wedge V_1 \wedge \neg V_0) \vee
(V_2 \wedge \neg V_1 \wedge \neg V_0) \vee
(V_2 \wedge V_1 \wedge V_0)
$
\end{document}

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SPE/OPT/TP 2/main.ml
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@ -19,15 +19,20 @@ let rec evaluer_tab t form = match form with
| Or (h::tail) -> (evaluer_tab t h) || (evaluer_tab t (Or tail));; | Or (h::tail) -> (evaluer_tab t h) || (evaluer_tab t (Or tail));;
5 lsr 1;; 5 lsr 1;;
let evaluer n c f = let contexte_from_int n c =
let contexte = Array.make n false in let contexte = Array.make n false in
let j = ref c in let j = ref c in
for i = 0 to n-1 do for i = 0 to n-1 do
contexte.(i) <- !j mod 2 = 0; contexte.(i) <- !j mod 2 <> 0;
j := !j lsr 1 j := !j lsr 1
done; done;
contexte;;
let evaluer n c f =
let contexte = contexte_from_int n c in
evaluer_tab contexte f;; evaluer_tab contexte f;;
evaluer 3 0 f;;
evaluer 3 3 g;;
let table_de_verite n f = let table_de_verite n f =
let rec puis n a = match n with let rec puis n a = match n with
@ -40,3 +45,23 @@ let table_de_verite n f =
res;; res;;
table_de_verite 3 g;; table_de_verite 3 g;;
let forme_normale_disjonctive n f =
let rec puis n a = match n with
| 0 -> 1
| _ -> a * (puis (n-1) a) in
let rec disjonction c conjs =
let rec conjonction cont conj n = match n with
| -1 -> And conj
| _ -> conjonction cont ((if cont.(n) then (Var n) else Not (Var n))::conj) (n-1) in
match c with
| -1 -> Or conjs
| _ -> let contexte = context_from_int n c in
if evaluer_tab contexte f then
disjonction (c-1) ((conjonction contexte [] (n-1))::conjs)
else
disjonction (c-1) conjs in
disjonction ((puis n 2) -1) [];;
forme_normale_disjonctive 3 g;;

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