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en/docs/chapter_data_structure/summary.md
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### 1.   Key Review
- Data structures can be classified from two perspectives: logical structure and physical structure. Logical structure describes the logical relationships between data elements, while physical structure describes how data is stored in computer memory.
- Common logical structures include linear, tree, and network structures. We typically classify data structures as linear (arrays, linked lists, stacks, queues) and non-linear (trees, graphs, heaps) based on their logical structure. The implementation of hash tables may involve both linear and non-linear data structures.
- Common logical structures include linear, tree-like, and network structures. We typically classify data structures as linear (arrays, linked lists, stacks, queues) and non-linear (trees, graphs, heaps) based on their logical structure. The implementation of hash tables may involve both linear and non-linear data structures.
- When a program runs, data is stored in computer memory. Each memory space has a corresponding memory address, and the program accesses data through these memory addresses.
- Physical structures are primarily divided into contiguous space storage (arrays) and dispersed space storage (linked lists). All data structures are implemented using arrays, linked lists, or a combination of both.
- Basic data types in computers include integers `byte`, `short`, `int`, `long`, floating-point numbers `float`, `double`, characters `char`, and booleans `bool`. Their value ranges depend on the size of space they occupy and their representation method.
- Sign-magnitude, 1's complement, and 2's complement are three methods for encoding numbers in computers, and they can be converted into each other. The most significant bit of sign-magnitude is the sign bit, and the remaining bits represent the value of the number.
- Integers are stored in computers in 2's complement form. Under 2's complement representation, computers can treat the addition of positive and negative numbers uniformly, without needing to design special hardware circuits for subtraction, and there is no ambiguity of positive and negative zero.
- The encoding of floating-point numbers consists of 1 sign bit, 8 exponent bits, and 23 fraction bits. Due to the exponent bits, the range of floating-point numbers is much larger than that of integers, at the cost of sacrificing precision.
- ASCII is the earliest English character set, with a length of 1 byte, containing a total of 127 characters. GBK is a commonly used Chinese character set, containing over 20,000 Chinese characters. Unicode is committed to providing a complete character set standard, collecting characters from various languages around the world, thereby solving the garbled text problem caused by inconsistent character encoding methods.
- UTF-8 is the most popular Unicode encoding method, with excellent universality. It is a variable-length encoding method with good scalability, effectively improving storage space efficiency. UTF-16 and UTF-32 are fixed-length encoding methods. When encoding Chinese characters, UTF-16 occupies less space than UTF-8. Programming languages such as Java and C# use UTF-16 encoding by default.
- ASCII is the earliest English character set, with a length of 1 byte, containing a total of 128 characters. GBK is a commonly used Chinese character set, containing over 20,000 Chinese characters. Unicode is committed to providing a complete character set standard, collecting characters from various languages around the world, thereby solving the garbled text problem caused by inconsistent character encoding methods.
- UTF-8 is the most popular Unicode encoding method and has excellent compatibility. It is a variable-length encoding method with good scalability, effectively improving storage space efficiency. UTF-16 and UTF-32 are common Unicode encoding methods. When encoding Chinese characters, UTF-16 occupies less space than UTF-8. Programming languages such as Java and C# use UTF-16 encoding by default.
### 2.   Q & A
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**Q**: When constructing a stack (queue), its size is not specified. Why are they "static data structures"?
In high-level programming languages, we do not need to manually specify the initial capacity of a stack (queue); this work is automatically completed within the class. For example, the initial capacity of Java's `ArrayList` is typically 10. Additionally, the expansion operation is also automatically implemented. See the subsequent "List" section for details.
In high-level programming languages, we do not need to manually specify the initial capacity of a stack (queue); the class handles this automatically. For example, the initial capacity of Java's `ArrayList` is typically 10. Additionally, the expansion operation is also automatically implemented. See the subsequent "List" section for details.
**Q**: The method of converting sign-magnitude to 2's complement is "first negate then add 1". So converting 2's complement to sign-magnitude should be the inverse operation "first subtract 1 then negate". However, 2's complement can also be converted to sign-magnitude through "first negate then add 1". Why is this?