1
0
1
1
1
0
0
0
1
0
0
 
0
 
0
0
 
 
1
0
1
 
0
1
1
 
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
 
0
1
0
0
1
0
 
1
0
0
1
 
1
0
0
1
0
1
0
0
1
 
 
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
 
1
1
0
1
0
1
 
 
0
 
0
0
0
1
 
0
 
1
0
 
1
1
1
0
 
1
1
1
 
1
1
1
0
 
1
1
0
0
1
 
0
1
0
 
0
0
0
1
1
 
1
 
 
1
0
 
 
1
1
0
0
 
1
0
0
0
1
0
 
1
0
0
 
1
0
0
0
1
0
1
1
 
1
0
 
1
0
 
1
 
0
0
 
1
0
0
 
 
0
1
1
1
0
 
1
1
0
0
0
0
1
0
1
 
0
0
0
0
 
1
 
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
 
0
1
1
1
0
0
0
0
1
1
1
1
0
1
 
 
0
1
0
1
0
1
0
0
 
1
0
0
0
1
1
0
 
0
1
0
 
 
0
0
 
 
1
 
1
1
0
0
0
0
0
1
0
 
 
0
0
0
1
1
0
0
0
 
0
1
0
0
0
1
0
 
0
0
1
1
1
1
1
1
 
1
0
1
0
0
1
 
 
0
1
1
0
 
0
0
 
0
 
 
0
0
1
0
1
1
 
 
1
 
1
0
1
 
0
 
1
0
1
0
1
1
0
1
1
1
1
1
0
 
0
 
0
1
1
1
1
0
0
1
1
1
 
0
0
1
 
 
1
1
0
0
 
0
1
1
0
0
 
0
 
1
 
0
1
0
1
0
1
0
1
 
0
1
1
1
1
1
0
0
 
1
 
0
0
1
0
 
0
1
1
 
 
1
0
 
1
1
1
0
1
0
0
0
1
0
 
0
0
1
0
0
0
 
 
 
0
1
0
 
1
 
0
0
0
1
 
0
1
 
1
1
1
1
1
0
1
 
1
 
1
1
1
1
 
1
1
 
0
1
 
0
1
1
1
1
 
 
1
0
0
 
1
 
1
 
1
1
 
 
1
1
1
0
0
1
1
1
1
1
1
 
0
0
0
1
1
0
 
0
0
1
1
0
0
1
 
1
 
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
 
0
1
1
0
1
 
 
0
1
0
1
0
1
1
 
1
0
1
0
0
0
0
0
0
 
0
 
1
1
1
1
 
 
0
0
0
 
1
0
1
 
0
0
0
0
0
 
0
0
0
1
1
 
0
 
0
0
0
0
 
1
1
1
1
0
1
0
0
1
 
0
1
1
0
0
 
1
0
1
1
0
1
1
0
1
1
1
0
1
 
1
0
0
1
0
1
1
0
0
 
1
0
1
 
1
 
1
1
1
 
1
0
0
1
1
0
0
1
0
1
1
1
0
1
 
0
 
1
0
 
1
 
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
 
0
 
1
 
0
0
0
 
1
1
1
0
 
1
1
1
1
1
0
0
0
1
1
1
1
1
 
0
0
1
1
0
 
1
1
1
1
0
1
 
 
0
0
0
1
0
1
 
1
 
 
1
0
0
0
 
1
0
 
0
0
1
1
 
 
1
1
0
1
1
 
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
 
0
1
 
 
 
1
 
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
 
0
 
1

信息论课程笔记

Information Theory · 2025 Spring

H[X] = -∑i p(xi) log p(xi)

Lecture 7

2025 / 4 / 1

Lecture 6

2025 / 3 / 25

Lecture 5

2025 / 3 / 18

Lecture 4

2025 / 3 / 11

Lecture 3

2025 / 3 / 4

Lecture 2

2025 / 2 / 25