# Mitchell Approximation

A method of computer multiplication and division is proposed which uses binary logarithms. The logarithm of a binary number may be determined approximately from the number itself by simple shifting and counting. A simple add or subtract and shift operation is all that is required to multiply or divide.

```#include<stdio.h>

int main() {
float a = 12.3f;
float b = 4.56f;
int c = *(int*)&a + *(int*)&b - 0x3f800000;
printf("Approximate result：%f\n", *(float*)&c);
printf("Accurate result：%f\n", a * b);
return 0;
}```

# How to renew your Let’s encrypt

Step 1. Suspend your web server (nginx for example)
`sudo service nginx stop`

`sudo letsencrypt certonly --standalone --email {email address} -d elfsong.cn -d {web address}`

Step 3. Restart your web server
`sudo service nginx start`

Step 4. Check the status
`sudo service nginx status`

# Semiring

```import numpy as np
import networkx as nx
from functools import reduce
import matplotlib.pyplot as plt

connect_graph = np.array([[0, 1, 0, 0, 0],
[0, 0, 0, 1, 0],
[0, 0, 0, 1, 0],
[0, 0, 0, 0, 1],
[0, 0, 1, 0, 0]])

return a or b

def ring_multi(a, b):
return a and b

def dot_product(i, j):
row = connect_graph[i]
column = connect_graph[:,j]
return reduce(ring_add, [ring_multi(a, b) for a, b in zip(row, column)])

def next_generation(connect_graph):
candidate_number = connect_graph.shape

new_connect_graph = np.zeros((candidate_number, candidate_number))

for i in range(candidate_number):
for j in range(candidate_number):
new_connect_graph[i][j] = dot_product(i,j)

return new_connect_graph

new_connect_graph = next_generation(connect_graph)

def draw_graph(connect_graph):
G = nx.DiGraph()

candidate_number = connect_graph.shape

node_name = list(range(candidate_number))

for i in range(candidate_number):
for j in range(candidate_number):
if connect_graph[i][j]:

nx.draw(G, with_labels=True)

plt.show()

draw_graph(new_connect_graph)```

## Lemme try

### Status # Heap sort

```class Test():
def heap_sort(self, nums):
i, l = 0, len(nums)
self.nums = nums

# 构造大顶堆，从非叶子节点开始倒序遍历，因此是l//2 -1 就是最后一个非叶子节点
for i in range(l//2-1, -1, -1):
self.build_heap(i, l-1)

print(nums)

# 上面的循环完成了大顶堆的构造，那么就开始把根节点跟末尾节点交换，然后重新调整大顶堆
for j in range(l-1, -1, -1):
nums, nums[j] = nums[j], nums
self.build_heap(0, j-1)

return nums

def build_heap(self, i, l):
"""构建大顶堆"""
nums = self.nums
left, right = 2*i+1, 2*i+2 ## 左右子节点的下标

large_index = i

if left <= l and nums[i] < nums[left]:
large_index = left

if right <= l and nums[left] < nums[right]:
large_index = right

# 通过上面跟左右节点比较后，得出三个元素之间较大的下标，如果较大下表不是父节点的下标，说明交换后需要重新调整大顶堆
if large_index != i:
nums[i], nums[large_index] = nums[large_index], nums[i]
self.build_heap(large_index, l)```

# Is a Balanced Binary Tree

For this problem, a height-balanced binary tree is defined as:

a binary tree in which the left and right subtrees of every node differ in height by no more than 1.

This problem is an easy-level at Leetcode. I probably did it more than five times, once and once again. Just like a muscle memory.

However, I found an interesting solution today, which literally changed my mind about Python…

Here is the code:

```# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

class Solution:
def isBalanced(self, root: TreeNode, h = 1) -> bool:
if not root: return h
l = self.isBalanced(root.left, h + 1)
r = self.isBalanced(root.right, h + 1)
return abs(l - r) <= 1 and max(l, r)```

I am very confused at the last line, the max(l, r) part.

I thought that max(l, r) should be converted as a bool value even it returns a integer type value, because as the second component of the operation AND, max(l, r) should represent as a bool variable.

Following by my worst idea, I supposed that the function isBalanced would return either 1 (True) or 0 (False). However, I found a crazy truth after experiments, that Python executor actually return a integer value (the maximum value of l and r) if abs(l – r) <= 1 is matched.

So, it really makes sense. Gain new knowledge of Python 🙂

# Median of interval

There are two methods to calculate the median of an interval [low, high].

• m = ( l + h ) / 2
• m = l + ( h – l ) / 2

l + h may have addition overflow, but h-l will not. Therefore, it is best to use the second method of calculation.

# The Discrete Fourier Transform

This week, I welcomed a new apartment-mate, who was a brilliant theoretical physicist/ Product Manager/ Programmer/etc. In one word, he is amazing!

After a cheerful chat with him, I got known that he has extremely abundant experience spans many fields. He was used to be a postgraduate student at UCAS majored in theoretical physics, and RA at sustech, and be PM at MeiTuan (A Chinese take-away services pioneer), and be visit student at MPI.

And, you can’t imagine that, he is a very good programmer at BtyeDance currently XD.

Back to our points, I’d grasp this opportunity to learn some very fundamental knowledge about Quantum Computing. Speaking of which, I really wanna figure out the Shor’s Algorithm.

The most important concept of the Shor’s Algorithm should be how to find the period, in which we can take advantages of Quantum Computing.

Fine, my mentor calls me back… I will do this article lately. STAY TUNED!