练习：Benford定律

# -*- coding:utf-8 -*-
# /usr/bin/python

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt


mpl.rcParams['axes.unicode_minus'] = False
mpl.rcParams['font.sans-serif'] = 'SimHei'


def top(number):
    number -= int(number)
    frequency[int(10 ** number) - 1] += 1


if __name__ == '__main__':
    N = 100000
    x = list(range(1, N+1))
    frequency = np.zeros(9, dtype=np.int)
    f = 1
    y = np.cumsum(np.log10(x))
    list(map(top, y))
    plt.figure(facecolor='w')
    t = np.arange(1, 10)
    plt.plot(t, frequency, 'r-', t, frequency, 'go', lw=2, markersize=8)
    for x,y in enumerate(frequency):
        plt.text(x+1.1, y, frequency[x], verticalalignment='top', fontsize=13)
    plt.title('%d!首位数字出现频率' % N, fontsize=18)
    plt.xlim(0.5, 9.5)
    plt.ylim(0, max(frequency)*1.03)
    plt.grid(b=True)
    plt.show()