# first_fib-q4
# Section 10, Q.4.a) p.42, p.255

import math
import matplotlib.pyplot as plt

x = [0]*10
a = 1.0; b = 1.0
for i in range(10000):
  d = math.trunc(a)
  x[d] = x[d]+1
  b += a
  a = b-a
  if a >= 10:
    b = b/10
    a = a/10
sum = sum(x)
percents = [ x[i]/sum for i in range(10)]
print("digit  freq     %")
for i in range(10):
  print(f"{i:3} {x[i]:7} {percents[i]:8.5f}")
plt.plot([i for i in range(1,10)], percents[1::])
plt.xlabel('First digit')
plt.ylabel('Freq')
plt.title('First Digit Freq for n == 10000')
plt.show()