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Hello Algo
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0.2 How to Read
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Chapter 0. Preface
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Chapter 0. Preface
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0.1 About This Book
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0.2 How to Read
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0.2 How to Read
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0.2.1 Writing Conventions
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0.2.2 Efficient Learning via Animated Illustrations
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0.2.3 Deepen Understanding through Coding Practice
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0.2.4 Learning Together in Discussion
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0.2.5 Algorithm Learning Path
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0.3 Summary
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Chapter 1. Introduction to Algorithms
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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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1.3 Summary
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Chapter 2. Complexity Analysis
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Chapter 2. Complexity Analysis
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2.1 Algorithm Efficiency Assessment
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2.2 Iteration and Recursion
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2.3 Time Complexity
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2.4 Space Complexity
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2.5 Summary
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Chapter 3. Data Structures
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Chapter 3. Data Structures
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3.1 Classification of Data Structures
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3.2 Fundamental Data Types
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3.3 Number Encoding *
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3.4 Character Encoding *
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3.5 Summary
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Chapter 4. Array and Linked List
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Chapter 4. Array and Linked List
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4.1 Array
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4.2 Linked List
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4.3 List
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4.4 Memory and Cache
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4.5 Summary
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0.2.1 Writing Conventions
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0.2.2 Efficient Learning via Animated Illustrations
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0.2.3 Deepen Understanding through Coding Practice
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0.2.4 Learning Together in Discussion
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0.2.5 Algorithm Learning Path
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< p > For the best reading experience, it is recommended that you read through this section.< / p >
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< li > Chapters marked with '*' after the title are optional and contain relatively challenging content. If you are short on time, it is advisable to skip them.< / li >
< li > Key technical terms and their English equivalents are enclosed in < strong > Bold< / strong > + < em > italics< / em > brackets, for example, < strong > < em > array< / em > < / strong > . It's advisable to familiarize yourself with these for better comprehension of technical texts.< / li >
< li > Proprietary terms and words with specific meanings are indicated with “quotation marks” to avoid ambiguity.< / li >
< li > < strong > Bolded text< / strong > indicates key content or summary statements, which deserve special attention.< / li >
< li > When it comes to terms that are inconsistent between programming languages, this book follows Python, for example using < span class = "arithmatex" > \(\text{None}\)< / span > to mean "null".< / li >
< li > This book partially ignores the comment conventions for programming languages in exchange for a more compact layout of the content. The comments primarily consist of three types: title comments, content comments, and multi-line comments.< / li >
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< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "c1" > # Comments for explaining details< / span >
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< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "sd" > Multiline< / span >
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< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "sd" > " " " < / span >
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< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "cm" > * Multiline< / span >
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< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "sd" > /**< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / a > < span class = "sd" > * Multiline< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "sd" > * comments< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "sd" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* Header comments for labeling functions, classes, test samples, etc */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "cm" > * Multiline< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "cm" > * comments< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "cm" > */< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "c1" > // Header comments for labeling functions, classes, test samples, etc< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "c1" > // Comments for explaining details.< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "c1" > // Multiline< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "c1" > // comments< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h2 id = "022-efficient-learning-via-animated-illustrations" > 0.2.2 Efficient Learning via Animated Illustrations< a class = "headerlink" href = "#022-efficient-learning-via-animated-illustrations" title = "Permanent link" > ¶ < / a > < / h2 >
< p > Compared with text, videos and pictures have a higher density of information and are more structured, making them easier to understand. In this book, < strong > key and difficult concepts are mainly presented through animations and illustrations< / strong > , with text serving as explanations and supplements.< / p >
< p > When encountering content with animations or illustrations as shown in the Figure 0-2 , < strong > prioritize understanding the figure, with text as supplementary< / strong > , integrating both for a comprehensive understanding.< / p >
< p > < a class = "glightbox" href = "../../index.assets/animation.gif" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Animated Illustration Example" class = "animation-figure" src = "../../index.assets/animation.gif" / > < / a > < / p >
< p align = "center" > Figure 0-2 Animated Illustration Example < / p >
< h2 id = "023-deepen-understanding-through-coding-practice" > 0.2.3 Deepen Understanding through Coding Practice< a class = "headerlink" href = "#023-deepen-understanding-through-coding-practice" title = "Permanent link" > ¶ < / a > < / h2 >
< p > The source code of this book is hosted on the < a href = "https://github.com/krahets/hello-algo" > GitHub Repository< / a > . As shown in the Figure 0-3 , < strong > the source code comes with test examples and can be executed with just a single click< / strong > .< / p >
< p > If time permits, < strong > it's recommended to type out the code yourself< / strong > . If pressed for time, at least read and run all the codes.< / p >
< p > Compared to just reading code, writing code often yields more learning. < strong > Learning by doing is the real way to learn.< / strong > < / p >
< p > < a class = "glightbox" href = "../../index.assets/running_code.gif" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Running Code Example" class = "animation-figure" src = "../../index.assets/running_code.gif" / > < / a > < / p >
< p align = "center" > Figure 0-3 Running Code Example < / p >
< p > Setting up to run the code involves three main steps.< / p >
< p > < strong > Step 1: Install a local programming environment< / strong > . Follow the < a href = "https://www.hello-algo.com/chapter_appendix/installation/" > tutorial< / a > in the appendix for installation, or skip this step if already installed.< / p >
< p > < strong > Step 2: Clone or download the code repository< / strong > . Visit the < a href = "https://github.com/krahets/hello-algo" > GitHub Repository< / a > .< / p >
< p > If < a href = "https://git-scm.com/downloads" > Git< / a > is installed, use the following command to clone the repository:< / p >
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-12-1" name = "__codelineno-12-1" href = "#__codelineno-12-1" > < / a > git< span class = "w" > < / span > clone< span class = "w" > < / span > https://github.com/krahets/hello-algo.git
< / code > < / pre > < / div >
< p > Alternatively, you can also click the "Download ZIP" button at the location shown in the Figure 0-4 to directly download the code as a compressed ZIP file. Then, you can simply extract it locally.< / p >
< p > < a class = "glightbox" href = "../suggestions.assets/download_code.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Cloning Repository and Downloading Code" class = "animation-figure" src = "../suggestions.assets/download_code.png" / > < / a > < / p >
< p align = "center" > Figure 0-4 Cloning Repository and Downloading Code < / p >
< p > < strong > Step 3: Run the source code< / strong > . As shown in the Figure 0-5 , for the code block labeled with the file name at the top, we can find the corresponding source code file in the < code > codes< / code > folder of the repository. These files can be executed with a single click, which will help you save unnecessary debugging time and allow you to focus on learning.< / p >
< p > < a class = "glightbox" href = "../suggestions.assets/code_md_to_repo.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Code Block and Corresponding Source Code File" class = "animation-figure" src = "../suggestions.assets/code_md_to_repo.png" / > < / a > < / p >
< p align = "center" > Figure 0-5 Code Block and Corresponding Source Code File < / p >
< h2 id = "024-learning-together-in-discussion" > 0.2.4 Learning Together in Discussion< a class = "headerlink" href = "#024-learning-together-in-discussion" title = "Permanent link" > ¶ < / a > < / h2 >
< p > While reading this book, please don't skip over the points that you didn't learn. < strong > Feel free to post your questions in the comment section< / strong > . We will be happy to answer them and can usually respond within two days.< / p >
< p > As illustrated in the Figure 0-6 , each chapter features a comment section at the bottom. I encourage you to pay attention to these comments. They not only expose you to others' encountered problems, aiding in identifying knowledge gaps and sparking deeper contemplation, but also invite you to generously contribute by answering fellow readers' inquiries, sharing insights, and fostering mutual improvement.< / p >
< p > < a class = "glightbox" href = "../../index.assets/comment.gif" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Comment Section Example" class = "animation-figure" src = "../../index.assets/comment.gif" / > < / a > < / p >
< p align = "center" > Figure 0-6 Comment Section Example < / p >
< h2 id = "025-algorithm-learning-path" > 0.2.5 Algorithm Learning Path< a class = "headerlink" href = "#025-algorithm-learning-path" title = "Permanent link" > ¶ < / a > < / h2 >
< p > Overall, the journey of mastering data structures and algorithms can be divided into three stages:< / p >
< ol >
< li > < strong > Stage 1: Introduction to algorithms< / strong > . We need to familiarize ourselves with the characteristics and usage of various data structures and learn about the principles, processes, uses, and efficiency of different algorithms.< / li >
< li > < strong > Stage 2: Practicing algorithm problems< / strong > . It is recommended to start from popular problems, such as < a href = "https://leetcode.cn/studyplan/coding-interviews/" > Sword for Offer< / a > and < a href = "https://leetcode.cn/studyplan/top-100- liked/" > LeetCode Hot 100< / a > , and accumulate at least 100 questions to familiarize yourself with mainstream algorithmic problems. Forgetfulness can be a challenge when you start practicing, but rest assured that this is normal. We can follow the "Ebbinghaus Forgetting Curve" to review the questions, and usually after 3~5 rounds of repetitions, we will be able to memorize them.< / li >
< li > < strong > Stage 3: Building the knowledge system< / strong > . In terms of learning, we can read algorithm column articles, solution frameworks, and algorithm textbooks to continuously enrich the knowledge system. In terms of practicing, we can try advanced strategies, such as categorizing by topic, multiple solutions for a single problem, and one solution for multiple problems, etc. Insights on these strategies can be found in various communities.< / li >
< / ol >
< p > As shown in the Figure 0-7 , this book mainly covers “Stage 1,” aiming to help you more efficiently embark on Stages 2 and 3.< / p >
< p > < a class = "glightbox" href = "../suggestions.assets/learning_route.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "Algorithm Learning Path" class = "animation-figure" src = "../suggestions.assets/learning_route.png" / > < / a > < / p >
< p align = "center" > Figure 0-7 Algorithm Learning Path < / p >
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