import math
import random
import matplotlib.pyplot as plt
import seaborn as sns

# A list of g goats' floor preference.
def goatPreferences(g) :
    preferences = []
    for i in range(1, g+1):
        #Goat's preference can be any from floor 1 to floor g.
        preferences.append(random.randrange(1, g+1))
    preferences.sort()
    return(preferences)

def compareFloor(g, preferences):
    
    floors = list(range(1, g+1))
    
    for i in range(g-1, -1, -1) :
       
        #Compare goat preference with current floor.
        if preferences[i] > floors[i] :
            return(0)
        else :
            preferences.pop()
            floors.pop()
    
    return(1) 

def monteCarlo(g):
    outcomes = 0
    for i in range(1000000000):
        preferences = goatPreferences(g)
        outcome = compareFloor(g, preferences)
        outcomes += outcome
    return(outcomes)

numerators = []
for i in range(1, 12):
    print(i-1)
    outcomes = monteCarlo(i)
    numerators.append(outcomes)

0
1
2
3
4
5
6
7
8
9
10

approximations = []
for i in range(1, 12):
    a = ((i+1)**(i-1)) / i**i
    approximations.append(a)

#Plot.
sns.set()
fig = plt.figure(figsize = (14, 8))
ax = fig.add_subplot(111, xlim = (0.5, 11.5), ylim = (0, 1))

simulation = [n/1000000000 for n in numerators]

#Scatter.
ax.scatter(x = range(1, 12),
           y = simulation,
           s = 100,
           c = "#287D8E")
# ax.scatter(x = range(1, 12),
#            y = approximations,
#            s = 50,
#            alpha = 0.5,
#            c = "#481567")

#Title.
ax.set_title("Probability All Goats Will Have Their Own Floor (1,000,000,000 simulations)", fontsize = 24)

#Axes.
ax.set_xlabel("Goats", fontsize = 20)
ax.set_ylabel("Probability", fontsize = 20)
ax.tick_params(axis = 'both', labelsize = 16)

fig.savefig("2022.06.24 Classic.png")

print(numerators)
print("")
print(approximations)

[1000000000, 750004596, 592558973, 488287741, 414732100, 360210095, 318294739, 285087681, 258127130, 235781540, 217040838]

[1.0, 0.75, 0.5925925925925926, 0.48828125, 0.41472, 0.36023233882030176, 0.3183124621300891, 0.2850871682167053, 0.2581174791713197, 0.2357947691, 0.21701658432479423]

Rohan Lewis

2022.06.26