[PYTHON] Use bubble sort to generate random numbers based on a standard normal distribution from uniform random numbers

Introduction

It's a wasteful idea that I came up with and implemented while implementing various sorting algorithms while practicing python to kill time.

Use bubble sort to generate a random number based on a standard normal distribution

When implementing bubble sort, sorting randomly generated data, and finding the average number of times, everyone naturally thinks that the number of sorts is based on a uniform standard normal distribution. Using it, I made a program to generate random numbers based on a standard normal distribution from uniform random numbers.

Is the program useful? ~~ python vector operation numpy

R = np.random.rand()

 Random numbers based on the standard normal distribution can be generated without using. ~~

 Even random

#### **`random.normalvariate(mu, sigma)`**
```normalvariate(mu, sigma)

 Random numbers can be generated based on the normal distribution by using.

 ~~ In other words, it is a useless idea that can generate random numbers based on the standard normal distribution without putting numpy in python. ~~
 Not really useful.

## The following programs
```python
# -*- coding: utf-8 -*-
import random
import matplotlib.pyplot as plt

def bubble_sort(data,data_num):
	count = 0
	for i in range(0,data_num):
		for j in range(data_num-1,i,-1):
		 	if data[j] <= data[j-1]:
		 		count += 1
		 		data[j] , data[j-1] = data[j-1] , data[j]
	return count

if __name__ == '__main__':
	t = 10 #Number of random numbers to perform each bubble sort
	n = t*(t-1)/2 #A standard normal distribution is created in the range of n
	y = [0]*n #Stores the number of times it took to sort when each bubble sort was performed.
	data = [] #T to sort data each time

	for j in range(0,100000):
		count = 0
		for i in range(0,t):
			data.append(random.randint(1,100))

		count = bubble_sort(data,t)
		y[count] = y[count] + 1
		del data[:] #Data initialization

	plt.plot(y,marker="o")
	plt.show() 

About the result

This time, we sorted a list of 10 random numbers 100,000 times, and captured the number of times each sort was performed as a newly generated random number, and counted and graphed it. As you can see from the graph, it feels like a standard normal distribution. The maximum number of sorts when n pieces of data are sorted by bubble sort is n (n-1) / 2, so this time there are 10 sorts of data, so 10 * (10-1) / 2 = The calculation is 45. The reason why it looks like a standard normal distribution is thought to be the pattern of random numbers that belong to the number of sorts.

Summary

It's just a self-satisfaction program.