#We simulate the Stemann parallel algorithm
import random
import math
#The principal variables are defined here
#k is the parameter that appears in the description of the algorithm
#Bins answer to all the messages if they received less than k and else 0
k = 3
n = 1000000
#Balls choose the bins they are communicating with at the beginning
#Choices is the list of their initial choices
choices = range(n)
#Balls[i]=j means that the ball i is in the bin j (if j is -1 then i hasn't commited)
Balls = range(n)
#Bins[i] is the load of the bin i
Bins = range(n)
#Bins_round[i] is the list of the balls that have sent a message to bin i during the round simulated
bins_round = range(n)
#Balls_round[i] is the list of bins that have answered to the ball i during the round simulated
balls_round = range(n)
#An useful list
l = range(n)
#It puts k in all the cases of the list l
def place(k,l):
for i in range(len(l)):
l[i] = k
#It begins a simulation by defining the different lists according to the number of balls
def change_n(k):
global n
global Balls
global Bins
global bins_round
global balls_round
global l
n = k
l = range(n)
Balls = range(n)
Bins = range(n)
bins_round = range(n)
balls_round = range(n)
l = range(n)
#It allows to begin a new simulation
def remise_zero():
place(-1,Balls)
place(0,Bins)
for i in l:
choices[i] = random.sample(l,2)
#This function simulates a round of the algorithm without priority
#nb_balls is the number of balls left
#Current_ball lists the balls that are still her : we have nb_balls = len(current_balls)
def round(nb_balls,current_balls):
place([],balls_round)
place([],bins_round)
for i in range(nb_balls):
#The choices are defined before by remise_zero
for b in choices[current_balls[i]]:
bins_round[b] = bins_round[b] + [current_balls[i]]
#If the balll i got less than k messages it answers
for i in range(n):
len_i = len(bins_round[i])
if len_i <= k:
for j in bins_round[i]:
balls_round[j] = balls_round[j] + [i]
#If a ball can commit, it commits
for i in range(n):
if len(balls_round[i]) != 0:
choice_commit = random.choice(balls_round[i])
Balls[i] = choice_commit
Bins[choice_commit] = Bins[choice_commit] + 1
#It sumulates one time the algorithm
def simulation():
current_balls = range(n)
remise_zero()
nb_balls = n
nb_rounds = 0
while nb_rounds < 3:
round(nb_balls,current_balls)
current_balls = [b for b in range(n) if Balls[b] == -1]
nb_balls = len(current_balls)
nb_rounds = nb_rounds +1
print(nb_balls)
return(nb_balls)
def nb_moy(essais):
nb_balls_moy = 0.
for i in range(essais):
remise_zero()
nb_balls_moy = nb_balls_moy + (float(simulation()))/(float(essais))
print(nb_balls_moy)
nb_moy(10)