HireAssistant.py

import random
import matplotlib.pyplot as plt
import math

def askingNewAssistant():
    # getting new assistant ability
    return random.random()

def hireAssistant(n):
    # hire assistant for n applications
    best = -1
    hired =0
    
    for a in range(n):
        
        new_assistant = askingNewAssistant()
        # if new assistant has more ability than the previous we hire it
        if new_assistant > best:
            best = new_assistant
            hired+=1
    # returning number of hired + number of applicants
    return hired, n

hire1 = hireAssistant(100)
hire2 = hireAssistant(10)
hire3 = hireAssistant(5)
# tests
assert hire1[0] <= hire1[1]
assert hire2[0] <= hire2[1]
assert hire3[0] <= hire3[1]

def probabilityOne(n, numberApplicants):
    # probability of only hiring one
    one = 0
    for a in range(n):
        if hireAssistant(numberApplicants)[0] == 1:
            one+=1
    return one/n

def produceArray(starting, end):
    applicants = []
    hires = []
    for a in range(starting,end):
        app = hireAssistant(a)
        applicants.append(app[1])
        hires.append(app[0])
    return hires, applicants

def produceProbOne(starting, end):
    applicants = []
    percentage = []
    for a in range(starting, end):
        app = probabilityOne(1000, a)
        applicants.append(a)
        percentage.append(app)
    return percentage, applicants

def produceMeanArray(starting, end, n):
    # producing the mean hire/number of applicant array to be graphed
    applicants = []
    hires = []
    mean_hires = []
    # range of number of applicants that we want to run
    for a in range(starting,end):
        mean_hires = []
        # getting the average number of hired based on the output of
        # running hireAssistant 'n' times
        for b in range(n):
            app = hireAssistant(a)
            mean_hires.append(app[0])
        # calculating the averages
        hires.append(sum(mean_hires)/len(mean_hires))
        applicants.append(a)
    return hires, applicants

# graphing number of hired X applicants
graph = produceArray(1,1000)
graph1 = produceMeanArray(1,1000,1000)
plt.plot(graph[1], graph[0], 'ro')
plt.plot(graph1[1], graph1[0])
# graphing the theoretical line (ln n)
plt.plot([a for a in range(1,1000)], [math.log2(a) for a in range(1,1000)])
plt.legend(['Individual points', 'Mean of points', 'theoretical line'])
plt.title('Applicants X Hires')
plt.xlabel('Applicants')
plt.ylabel('Hired')
plt.show()

#graphing the probability of only hiring one applicant
graph = produceProbOne(1,100)
plt.plot(graph[1], graph[0])
plt.title('Applicants X Probability of one applicant being hired')
plt.xlabel('Number of Applicants')
plt.ylabel('Probability of only one applicant being hired')
plt.show()