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fix space issue

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Deming Chu 2024-05-24 18:51:09 +10:00
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en/docs/chapter_data_structure/summary.md
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# Summary
### Key review
- Data structures can be categorized from two perspectives: logical structure and physical structure. Logical structure describes the logical relationships between data, while physical structure describes how data is stored in memory.
- Frequently used logical structures include linear structures, trees, and networks. We usually divide data structures into 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 is running, data is stored in memory. Each memory space has a corresponding address, and the program accesses data through these addresses.
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**Q**: Why does a hash table contain both linear and non-linear data structures?
The underlying structure of a hash table is an array. To resolve hash collisions, we may use "chaining" (discussed in a later section, "Hash collision"): each bucket in the array points to a linked list, and it might be transformed into a tree (usually a red-black tree) when its length is larger than a certain threshold.
From a storage perspective, the underlying structure of a hash table is an array, where each bucket might contain a value, a linked list, or a tree. Therefore, hash tables may contain both linear data structures (arrays, linked lists) and non-linear data structures (trees).
**Q**: Is the length of the `char` type 1 byte?
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Observe that the sum of the original code and the complement code is $0010 + 1110 = 10000$, i.e., the complement code $1110$ is the "complement" of the original code $0010$ to $10000$. **This means that the above "first negate and then add 1" is equivalent to computing the complement to $10000$**.
So, what is the "complement" of $1110$ to $10000$? We can still compute it by "negating first and then adding 1":
$$
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In other words, the original code and the complement code are each other's "complement" to $10000$, so "original code to complement code" and "complement code to original code" can be implemented with the same operation (first negate and then add 1).
Of course, we can also use the inverse operation of "first negate and then add 1" to find the original code of the complement code $1110$, that is, "first subtract 1 and then negate":
$$