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<title>1.1 Algorithms are Everywhere - Hello Algo</title>
<title>1.1 Algorithms are everywhere - Hello Algo</title>
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<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
1.1 Algorithms are Everywhere
1.1 Algorithms are everywhere
</span>
</div>
@@ -201,7 +201,13 @@
<li class="md-select__item">
<a href="/" hreflang="zh" class="md-select__link">
中文
简体中文
</a>
</li>
<li class="md-select__item">
<a href="/zh-hant/" hreflang="zh-Hant" class="md-select__link">
繁體中文
</a>
</li>
@@ -393,7 +399,7 @@
<span class="md-ellipsis">
0.1 About This Book
0.1 About this book
</span>
@@ -414,7 +420,7 @@
<span class="md-ellipsis">
0.2 How to Read
0.2 How to read
</span>
@@ -493,7 +499,7 @@
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<span class="md-ellipsis">
Chapter 1. Introduction to Algorithms
Chapter 1. Introduction to algorithms
</span>
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<label class="md-nav__title" for="__nav_2">
<span class="md-nav__icon md-icon"></span>
Chapter 1. Introduction to Algorithms
Chapter 1. Introduction to algorithms
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
1.1 Algorithms are Everywhere
1.1 Algorithms are everywhere
</span>
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<span class="md-ellipsis">
1.2 What is an Algorithm
1.2 What is an algorithm
</span>
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<span class="md-ellipsis">
Chapter 2. Complexity Analysis
Chapter 2. Complexity analysis
</span>
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<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
Chapter 2. Complexity Analysis
Chapter 2. Complexity analysis
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
2.1 Algorithm Efficiency Assessment
2.1 Algorithm efficiency assessment
</span>
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<span class="md-ellipsis">
2.2 Iteration and Recursion
2.2 Iteration and recursion
</span>
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<span class="md-ellipsis">
2.3 Time Complexity
2.3 Time complexity
</span>
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<span class="md-ellipsis">
2.4 Space Complexity
2.4 Space complexity
</span>
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<span class="md-ellipsis">
Chapter 3. Data Structures
Chapter 3. Data structures
</span>
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Chapter 3. Data Structures
Chapter 3. Data structures
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
3.1 Classification of Data Structures
3.1 Classification of data structures
</span>
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<span class="md-ellipsis">
3.2 Fundamental Data Types
3.2 Fundamental data types
</span>
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<span class="md-ellipsis">
3.3 Number Encoding *
3.3 Number encoding *
</span>
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<span class="md-ellipsis">
3.4 Character Encoding *
3.4 Character encoding *
</span>
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<span class="md-ellipsis">
Chapter 4. Array and Linked List
Chapter 4. Array and linked list
</span>
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<label class="md-nav__title" for="__nav_5">
<span class="md-nav__icon md-icon"></span>
Chapter 4. Array and Linked List
Chapter 4. Array and linked list
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
4.2 Linked List
4.2 Linked list
</span>
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<span class="md-ellipsis">
4.4 Memory and Cache
4.4 Memory and cache
</span>
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<span class="md-ellipsis">
Chapter 5. Stack and Queue
Chapter 5. Stack and queue
</span>
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<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
Chapter 5. Stack and Queue
Chapter 5. Stack and queue
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
5.3 Double-ended Queue
5.3 Double-ended queue
</span>
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<span class="md-ellipsis">
Chapter 6. Hash Table
Chapter 6. Hash table
</span>
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Chapter 6. Hash Table
Chapter 6. Hash table
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
6.1 Hash Table
6.1 Hash table
</span>
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<span class="md-ellipsis">
6.2 Hash Collision
6.2 Hash collision
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<span class="md-ellipsis">
6.3 Hash Algorithm
6.3 Hash algorithm
</span>
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<!-- Page content -->
<h1 id="11-algorithms-are-everywhere">1.1 &nbsp; Algorithms are Everywhere<a class="headerlink" href="#11-algorithms-are-everywhere" title="Permanent link">&para;</a></h1>
<h1 id="11-algorithms-are-everywhere">1.1 &nbsp; Algorithms are everywhere<a class="headerlink" href="#11-algorithms-are-everywhere" title="Permanent link">&para;</a></h1>
<p>When we hear the word "algorithm," we naturally think of mathematics. However, many algorithms do not involve complex mathematics but rely more on basic logic, which can be seen everywhere in our daily lives.</p>
<p>Before formally discussing algorithms, there's an interesting fact worth sharing: <strong>you have already unconsciously learned many algorithms and have become accustomed to applying them in your daily life</strong>. Here, I will give a few specific examples to prove this point.</p>
<p><strong>Example 1: Looking Up a Dictionary</strong>. In an English dictionary, words are listed alphabetically. Suppose we're searching for a word that starts with the letter <span class="arithmatex">\(r\)</span>. This is typically done in the following way:</p>
@@ -2033,8 +2039,8 @@
<li>Take out a card from the unordered section and insert it into the correct position in the ordered section; after this, the leftmost two cards are in order.</li>
<li>Continue to repeat step <code>2.</code> until all cards are in order.</li>
</ol>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/playing_cards_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Playing Cards Sorting Process" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></a></p>
<p align="center"> Figure 1-2 &nbsp; Playing Cards Sorting Process </p>
<p><a class="glightbox" href="../algorithms_are_everywhere.assets/playing_cards_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Playing cards sorting process" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></a></p>
<p align="center"> Figure 1-2 &nbsp; Playing cards sorting process </p>
<p>The above method of organizing playing cards is essentially the "Insertion Sort" algorithm, which is very efficient for small datasets. Many programming languages' sorting functions include the insertion sort.</p>
<p><strong>Example 3: Making Change</strong>. Suppose we buy goods worth <span class="arithmatex">\(69\)</span> yuan at a supermarket and give the cashier <span class="arithmatex">\(100\)</span> yuan, then the cashier needs to give us <span class="arithmatex">\(31\)</span> yuan in change. They would naturally complete the thought process as shown below.</p>
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<a
href="../"
class="md-footer__link md-footer__link--prev"
aria-label="Previous: Chapter 1. &amp;nbsp; Introduction to Algorithms"
aria-label="Previous: Chapter 1. &amp;nbsp; Introduction to algorithms"
rel="prev"
>
<div class="md-footer__button md-icon">
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Previous
</span>
<div class="md-ellipsis">
Chapter 1. &nbsp; Introduction to Algorithms
Chapter 1. &nbsp; Introduction to algorithms
</div>
</div>
</a>
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<a
href="../what_is_dsa/"
class="md-footer__link md-footer__link--next"
aria-label="Next: 1.2 What is an Algorithm"
aria-label="Next: 1.2 What is an algorithm"
rel="next"
>
<div class="md-footer__title">
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Next
</span>
<div class="md-ellipsis">
1.2 What is an Algorithm
1.2 What is an algorithm
</div>
</div>
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<nav class="md-footer__inner md-grid" aria-label="Footer" >
<a href="../" class="md-footer__link md-footer__link--prev" aria-label="Previous: Chapter 1. &amp;nbsp; Introduction to Algorithms">
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Previous
</span>
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Chapter 1. &nbsp; Introduction to Algorithms
Chapter 1. &nbsp; Introduction to algorithms
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</div>
</a>
<a href="../what_is_dsa/" class="md-footer__link md-footer__link--next" aria-label="Next: 1.2 What is an Algorithm">
<a href="../what_is_dsa/" class="md-footer__link md-footer__link--next" aria-label="Next: 1.2 What is an algorithm">
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Next
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1.2 What is an algorithm
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en/chapter_introduction/index.html
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<title>Chapter 1.   Introduction to Algorithms - Hello Algo</title>
<title>Chapter 1.   Introduction to algorithms - Hello Algo</title>
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<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
Chapter 1. &nbsp; Introduction to Algorithms
Chapter 1. &nbsp; Introduction to algorithms
</span>
</div>
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<li class="md-select__item">
<a href="/" hreflang="zh" class="md-select__link">
中文
简体中文
</a>
</li>
<li class="md-select__item">
<a href="/zh-hant/" hreflang="zh-Hant" class="md-select__link">
繁體中文
</a>
</li>
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<span class="md-ellipsis">
0.1 About This Book
0.1 About this book
</span>
@@ -414,7 +420,7 @@
<span class="md-ellipsis">
0.2 How to Read
0.2 How to read
</span>
@@ -493,7 +499,7 @@
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<span class="md-ellipsis">
Chapter 1. Introduction to Algorithms
Chapter 1. Introduction to algorithms
</span>
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<label class="md-nav__title" for="__nav_2">
<span class="md-nav__icon md-icon"></span>
Chapter 1. Introduction to Algorithms
Chapter 1. Introduction to algorithms
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
1.1 Algorithms are Everywhere
1.1 Algorithms are everywhere
</span>
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<span class="md-ellipsis">
1.2 What is an Algorithm
1.2 What is an algorithm
</span>
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<span class="md-ellipsis">
Chapter 2. Complexity Analysis
Chapter 2. Complexity analysis
</span>
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<label class="md-nav__title" for="__nav_3">
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Chapter 2. Complexity Analysis
Chapter 2. Complexity analysis
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
2.1 Algorithm Efficiency Assessment
2.1 Algorithm efficiency assessment
</span>
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<span class="md-ellipsis">
2.2 Iteration and Recursion
2.2 Iteration and recursion
</span>
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<span class="md-ellipsis">
2.3 Time Complexity
2.3 Time complexity
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<span class="md-ellipsis">
2.4 Space Complexity
2.4 Space complexity
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<span class="md-ellipsis">
Chapter 3. Data Structures
Chapter 3. Data structures
</span>
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Chapter 3. Data Structures
Chapter 3. Data structures
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
3.1 Classification of Data Structures
3.1 Classification of data structures
</span>
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<span class="md-ellipsis">
3.2 Fundamental Data Types
3.2 Fundamental data types
</span>
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<span class="md-ellipsis">
3.3 Number Encoding *
3.3 Number encoding *
</span>
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<span class="md-ellipsis">
3.4 Character Encoding *
3.4 Character encoding *
</span>
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Chapter 4. Array and Linked List
Chapter 4. Array and linked list
</span>
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<label class="md-nav__title" for="__nav_5">
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Chapter 4. Array and Linked List
Chapter 4. Array and linked list
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
4.2 Linked List
4.2 Linked list
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4.4 Memory and Cache
4.4 Memory and cache
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<span class="md-ellipsis">
Chapter 5. Stack and Queue
Chapter 5. Stack and queue
</span>
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<label class="md-nav__title" for="__nav_6">
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Chapter 5. Stack and Queue
Chapter 5. Stack and queue
</label>
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5.3 Double-ended Queue
5.3 Double-ended queue
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Chapter 6. Hash Table
Chapter 6. Hash table
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6.1 Hash Table
6.1 Hash table
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6.2 Hash Collision
6.2 Hash collision
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6.3 Hash Algorithm
6.3 Hash algorithm
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<!-- Page content -->
<h1 id="chapter-1-introduction-to-algorithms">Chapter 1. &nbsp; Introduction to Algorithms<a class="headerlink" href="#chapter-1-introduction-to-algorithms" title="Permanent link">&para;</a></h1>
<p><a class="glightbox" href="../assets/covers/chapter_introduction.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="A first look at the algorithm" class="cover-image" src="../assets/covers/chapter_introduction.jpg" /></a></p>
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<div class="admonition abstract">
<p class="admonition-title">Abstract</p>
<p>A graceful maiden dances, intertwined with the data, her skirt swaying to the melody of algorithms.</p>
@@ -2012,8 +2018,8 @@
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<ul>
<li><a href="https://www.hello-algo.com/en/chapter_introduction/algorithms_are_everywhere/">1.1 &nbsp; Algorithms are Everywhere</a></li>
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<li><a href="https://www.hello-algo.com/en/chapter_introduction/summary/">1.3 &nbsp; Summary</a></li>
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0.1 About This Book
0.1 About this book
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0.2 How to Read
0.2 How to read
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Chapter 1. Introduction to Algorithms
Chapter 1. Introduction to algorithms
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1.1 Algorithms are Everywhere
1.1 Algorithms are everywhere
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1.2 What is an Algorithm
1.2 What is an algorithm
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2.2 Iteration and Recursion
2.2 Iteration and recursion
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2.3 Time Complexity
2.3 Time complexity
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3.1 Classification of Data Structures
3.1 Classification of data structures
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3.2 Fundamental Data Types
3.2 Fundamental data types
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3.3 Number Encoding *
3.3 Number encoding *
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3.4 Character Encoding *
3.4 Character encoding *
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4.2 Linked List
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4.4 Memory and Cache
4.4 Memory and cache
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Chapter 6. Hash table
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6.2 Hash Collision
6.2 Hash collision
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1.2 What is an Algorithm
1.2 What is an algorithm
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1.2 What is an Algorithm
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Chapter 2. Complexity Analysis
Chapter 2. Complexity analysis
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2.1 Algorithm Efficiency Assessment
2.1 Algorithm efficiency assessment
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2.2 Iteration and Recursion
2.2 Iteration and recursion
</span>
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2.3 Time Complexity
2.3 Time complexity
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2.4 Space Complexity
2.4 Space complexity
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Chapter 3. Data Structures
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3.1 Classification of Data Structures
3.1 Classification of data structures
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3.2 Fundamental Data Types
3.2 Fundamental data types
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3.3 Number Encoding *
3.3 Number encoding *
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3.4 Character Encoding *
3.4 Character encoding *
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Chapter 4. Array and Linked List
Chapter 4. Array and linked list
</span>
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Chapter 4. Array and Linked List
Chapter 4. Array and linked list
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4.2 Linked List
4.2 Linked list
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4.4 Memory and Cache
4.4 Memory and cache
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Chapter 5. Stack and Queue
Chapter 5. Stack and queue
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Chapter 5. Stack and Queue
Chapter 5. Stack and queue
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5.3 Double-ended Queue
5.3 Double-ended queue
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<span class="md-ellipsis">
Chapter 6. Hash Table
Chapter 6. Hash table
</span>
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Chapter 6. Hash Table
Chapter 6. Hash table
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<span class="md-ellipsis">
6.1 Hash Table
6.1 Hash table
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6.2 Hash Collision
6.2 Hash collision
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6.3 Hash Algorithm
6.3 Hash algorithm
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<a href="#121-definition-of-an-algorithm" class="md-nav__link">
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1.2.1 &nbsp; Definition of an Algorithm
1.2.1 &nbsp; Definition of an algorithm
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</a>
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<a href="#122-definition-of-a-data-structure" class="md-nav__link">
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1.2.2 &nbsp; Definition of a Data Structure
1.2.2 &nbsp; Definition of a data structure
</span>
</a>
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<a href="#123-relationship-between-data-structures-and-algorithms" class="md-nav__link">
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1.2.3 &nbsp; Relationship Between Data Structures and Algorithms
1.2.3 &nbsp; Relationship between data structures and algorithms
</span>
</a>
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<!-- Page content -->
<h1 id="12-what-is-an-algorithm">1.2 &nbsp; What is an Algorithm<a class="headerlink" href="#12-what-is-an-algorithm" title="Permanent link">&para;</a></h1>
<h2 id="121-definition-of-an-algorithm">1.2.1 &nbsp; Definition of an Algorithm<a class="headerlink" href="#121-definition-of-an-algorithm" title="Permanent link">&para;</a></h2>
<h1 id="12-what-is-an-algorithm">1.2 &nbsp; What is an algorithm<a class="headerlink" href="#12-what-is-an-algorithm" title="Permanent link">&para;</a></h1>
<h2 id="121-definition-of-an-algorithm">1.2.1 &nbsp; Definition of an algorithm<a class="headerlink" href="#121-definition-of-an-algorithm" title="Permanent link">&para;</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 &nbsp; Definition of a Data Structure<a class="headerlink" href="#122-definition-of-a-data-structure" title="Permanent link">&para;</a></h2>
<h2 id="122-definition-of-a-data-structure">1.2.2 &nbsp; Definition of a data structure<a class="headerlink" href="#122-definition-of-a-data-structure" title="Permanent link">&para;</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>
@@ -2108,7 +2114,7 @@
<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 &nbsp; Relationship Between Data Structures and Algorithms<a class="headerlink" href="#123-relationship-between-data-structures-and-algorithms" title="Permanent link">&para;</a></h2>
<h2 id="123-relationship-between-data-structures-and-algorithms">1.2.3 &nbsp; Relationship between data structures and algorithms<a class="headerlink" href="#123-relationship-between-data-structures-and-algorithms" title="Permanent link">&para;</a></h2>
<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>
<ul>
<li>Data structures are the foundation of algorithms. They provide structured data storage and methods for manipulating data for algorithms.</li>
@@ -2123,7 +2129,7 @@
<p align="center"> Figure 1-5 &nbsp; Assembling blocks </p>
<p>The detailed correspondence between the two is shown in the Table 1-1 .</p>
<p align="center"> Table 1-1 &nbsp; Comparing Data Structures and Algorithms to Building Blocks </p>
<p align="center"> Table 1-1 &nbsp; Comparing data structures and algorithms to building blocks </p>
<div class="center-table">
<table>
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