#Number of floors to stop at.
def EV(f):
    
    if f==1:
        return(0)
    
    elif f==2:
        return(1)
    
    else:
        sum = 0
        for n in range(1, f):
            sum += 1 + EV(n)
        
        ev = sum / (f-1)
        return(ev)
    
#Get list of average by floor.
def EVs(f):
    
    evs = [0,1]
    
    if f==1:
        pass
    
    elif f==2:
        pass
        
    else:
        
        for n in range(3, f+1) :
            sum = 0
            for ev in evs:
                
                sum += 1 + ev
                new_ev = sum / (n-1)
            
            evs.append(new_ev)
        
    return(evs[0:f])

EVs(10)[9]

2.8289682539682537

7129/2520

2.828968253968254

import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
import math

#Plot.
sns.set()
fig = plt.figure(figsize = (14, 8))
ax = fig.add_subplot(111, xlim = (0, 100), ylim = (0, 6))

#Data.
floors = list(range(1,10001))
stops = EVs(10000)
estimate = [math.log(x)+ 0.577 for x in floors]


#Scatter.
ax.scatter(x = floors,
           y = stops,
           s = 15,
           c = "#287D8E")
#ax.scatter(x = floors,
#           y = estimate,
#           s = 10,
#           c = "#481567")

#Title.
ax.set_title("Average Number of Stops from Top of Tower to 1st Floor", fontsize = 24)

#Axes.
ax.set_xlabel("Tower Height (floors)", fontsize = 18)
ax.set_ylabel("Average Number of Stops", fontsize = 18)
ax.tick_params(axis = 'both', labelsize = 16)

ax.annotate("Stops ≈ ln(floors) + γ", (75, 4.5), color = "#481567", fontsize = 18)


fig.savefig("2022.05.06 Express1.png")

Rohan Lewis

2022.05.06