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Chapter 1. Introduction to Algorithms
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1.1 Algorithms are Everywhere
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1.2 What is an Algorithm
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1.2.1 Definition of an Algorithm
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1.2.2 Definition of a Data Structure
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Chapter 2. Complexity Analysis
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2.1 Algorithm Efficiency Assessment
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2.3 Time Complexity
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2.4 Space Complexity
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4.1 Array
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5.1 Stack
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< h1 id = "12-what-is-an-algorithm" > 1.2 What is an Algorithm< a class = "headerlink" href = "#12-what-is-an-algorithm" title = "Permanent link" > ¶ < / a > < / h1 >
< h2 id = "121-definition-of-an-algorithm" > 1.2.1 Definition of an Algorithm< a class = "headerlink" href = "#121-definition-of-an-algorithm" title = "Permanent link" > ¶ < / a > < / h2 >
< p > An "algorithm" is a set of instructions or steps to solve a specific problem within a finite amount of time. It has the following characteristics:< / p >
< ul >
< li > The problem is clearly defined, including unambiguous definitions of input and output.< / li >
< li > The algorithm is feasible, meaning it can be completed within a finite number of steps, time, and memory space.< / li >
< li > Each step has a definitive meaning. The output is consistently the same under the same inputs and conditions.< / li >
< / ul >
< h2 id = "122-definition-of-a-data-structure" > 1.2.2 Definition of a Data Structure< a class = "headerlink" href = "#122-definition-of-a-data-structure" title = "Permanent link" > ¶ < / a > < / h2 >
< p > A "data structure" is a way of organizing and storing data in a computer, with the following design goals:< / p >
< ul >
< li > Minimize space occupancy to save computer memory.< / li >
< li > Make data operations as fast as possible, covering data access, addition, deletion, updating, etc.< / li >
< li > Provide concise data representation and logical information to enable efficient algorithm execution.< / li >
< / ul >
< p > < strong > Designing data structures is a balancing act, often requiring trade-offs< / strong > . If you want to improve in one aspect, you often need to compromise in another. Here are two examples:< / p >
< ul >
< li > Compared to arrays, linked lists offer more convenience in data addition and deletion but sacrifice data access speed.< / li >
< li > Graphs, compared to linked lists, provide richer logical information but require more memory space.< / li >
< / ul >
< h2 id = "123-relationship-between-data-structures-and-algorithms" > 1.2.3 Relationship Between Data Structures and Algorithms< a class = "headerlink" href = "#123-relationship-between-data-structures-and-algorithms" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > As shown in the Figure 1-4 , data structures and algorithms are highly related and closely integrated, specifically in the following three aspects:< / p >
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< ul >
< li > Data structures are the foundation of algorithms. They provide structured data storage and methods for manipulating data for algorithms.< / li >
< li > 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.< / li >
< li > Algorithms can often be implemented based on different data structures, but their execution efficiency can vary greatly. Choosing the right data structure is key.< / li >
< / ul >
< p > < a class = "glightbox" href = "../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Relationship between data structures and algorithms" class = "animation-figure" src = "../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" / > < / a > < / p >
< p align = "center" > Figure 1-4 Relationship between data structures and algorithms < / p >
< p > Data structures and algorithms can be likened to a set of building blocks, as illustrated in the Figure 1-5 . 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.< / p >
< p > < a class = "glightbox" href = "../what_is_dsa.assets/assembling_blocks.jpg" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Assembling blocks" class = "animation-figure" src = "../what_is_dsa.assets/assembling_blocks.jpg" / > < / a > < / p >
< p align = "center" > Figure 1-5 Assembling blocks < / p >
< p > The detailed correspondence between the two is shown in the Table 1-1 .< / p >
< p align = "center" > Table 1-1 Comparing Data Structures and Algorithms to Building Blocks < / p >
< div class = "center-table" >
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< thead >
< tr >
< th > Data Structures and Algorithms< / th >
< th > Building Blocks< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > Input data< / td >
< td > Unassembled blocks< / td >
< / tr >
< tr >
< td > Data structure< / td >
< td > Organization of blocks, including shape, size, connections, etc< / td >
< / tr >
< tr >
< td > Algorithm< / td >
< td > A series of steps to assemble the blocks into the desired shape< / td >
< / tr >
< tr >
< td > Output data< / td >
< td > Completed Block model< / td >
< / tr >
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< p > 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.< / p >
< div class = "admonition tip" >
< p class = "admonition-title" > Conventional Abbreviation< / p >
< p > 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.< / p >
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