Python data structures and algorithms 17th Day "Probabilistic algorithm"

1. Classical probabilities

For example: Mahjong starts to touch the 14 cards without the probability, two identical cards will be, then there are:

All cases: Choose 14 cards from 136 cards for C136-14

No will: The different cards grouped, a total of 34 groups, then take 14 cards, the first time the extraction of c34-1 * 4, the second time for the c33-1 * 4

Total (C34-1 * 4) * (C33-1 * 4) * .... * (C21-1 * 4) = c34-14 * 4^14

Then the probability of no will is c34-14 * 4^14/c136-14

2. From 1!, 2!, 3!, 4!, to n! All the numbers in the first place is 1 probability, the first is the probability of 2, the first is the probability of 3, until the first is the probability of 9

The code is implemented as follows:

#!/usr/bin/env python#! _*_ coding:utf-8 _*_deffirst_number (n):" "First Digit" "     whileN >= 10: N= N/10returnNdefsecond_number (n):" "Second Digit" "     whileN >= 100: N= N/10returnN% 10defthird_number (n):" "Third Digit" "     whileN >= 1000: N= N/10returnN% 100if __name__=="__main__":    #initializes the frequency list, Requency[i] represents the number of occurrences of the first 1frequency = [0 forIinchRange (0, 10, 1)] I= 1#do factorial operations, from 1! , 2! , 3! , until 100! The Operation     forNinchRange (1, 100, 1): I= n *i m=First_number (i) frequency[m]= Frequency[m] + 1PrintFrequency

Results:

/users/liudaoqiang/pycharmprojects/numpy/venv/bin/python/users/liudaoqiang/project/python_project/bat_day17/  7, 7, 7, 3, ten, 4]process finished with exit code 0

3. Ben Ford's Law:

In life, the probability of the first digit being 1 is nearly 1/3, which is 3 times times the 1/9.

Practical application:

(1) factorial, Prime number series, Fibonacci series first

(2) Residential address number,

(3) Economic data anti-fraud, vote anti-fraud

Python data structures and algorithms 17th Day "Probabilistic algorithm"