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53 lines
3.7 KiB
Markdown
53 lines
3.7 KiB
Markdown
# What is an algorithm
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## Definition of an algorithm
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An <u>algorithm</u> is a set of instructions or steps to solve a specific problem within a finite amount of time. It has the following characteristics:
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- The problem is clearly defined, including unambiguous definitions of input and output.
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- The algorithm is feasible, meaning it can be completed within a finite number of steps, time, and memory space.
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- Each step has a definitive meaning. The output is consistently the same under the same inputs and conditions.
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## Definition of a data structure
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A <u>data structure</u> is a way of organizing and storing data in a computer, with the following design goals:
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- Minimize space occupancy to save computer memory.
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- Make data operations as fast as possible, covering data access, addition, deletion, updating, etc.
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- Provide concise data representation and logical information to enable efficient algorithm execution.
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**Designing data structures is a balancing act, often requiring trade-offs**. If you want to improve in one aspect, you often need to compromise in another. Here are two examples:
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- Compared to arrays, linked lists offer more convenience in data addition and deletion but sacrifice data access speed.
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- Graphs, compared to linked lists, provide richer logical information but require more memory space.
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## Relationship between data structures and algorithms
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As shown in the figure below, data structures and algorithms are highly related and closely integrated, specifically in the following three aspects:
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- Data structures are the foundation of algorithms. They provide structured data storage and methods for manipulating data for algorithms.
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- Algorithms are the stage where data structures come into play. The data structure alone only stores data information; it is through the application of algorithms that specific problems can be solved.
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- Algorithms can often be implemented based on different data structures, but their execution efficiency can vary greatly. Choosing the right data structure is key.
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Data structures and algorithms can be likened to a set of building blocks, as illustrated in the figure below. A building block set includes numerous pieces, accompanied by detailed assembly instructions. Following these instructions step by step allows us to construct an intricate block model.
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The detailed correspondence between the two is shown in the table below.
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<p align="center"> Table <id> Comparing data structures and algorithms to building blocks </p>
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| Data Structures and Algorithms | Building Blocks |
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| ------------------------------ | --------------------------------------------------------------- |
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| Input data | Unassembled blocks |
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| Data structure | Organization of blocks, including shape, size, connections, etc |
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| Algorithm | A series of steps to assemble the blocks into the desired shape |
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| Output data | Completed Block model |
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It's worth noting that data structures and algorithms are independent of programming languages. For this reason, this book is able to provide implementations in multiple programming languages.
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!!! tip "Conventional Abbreviation"
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In real-life discussions, we often refer to "Data Structures and Algorithms" simply as "Algorithms". For example, the well-known LeetCode algorithm problems actually test both data structure and algorithm knowledge.
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