#!/usr/bin/python3
"""
Exponential ranking
"""
import numpy as np
import matplotlib.pyplot as plt

# Population size
u = 20
ui = range(u)
# Normalization constant:
c = u - (1 - (1 / np.exp(u))) / (1 - np.exp(-1))
fitnesses = []
for i in range(u):
    e = np.exp(1)
    P_i = (1 - (e**-i)) / c
    print(f"Fitness of {i}, P_i is {P_i}")
    fitnesses.append(P_i)
print(sum(fitnesses))
plt.plot(ui, fitnesses)
plt.show()