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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>
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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>
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<span class="md-ellipsis">
0.2 How to Read
0.2 How to read
</span>
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<span class="md-ellipsis">
Chapter 1. Introduction to Algorithms
Chapter 1. Introduction to algorithms
</span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="true">
<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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<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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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
<span class="md-ellipsis">
Chapter 3. Data Structures
Chapter 3. Data structures
</span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_4">
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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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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
<span class="md-ellipsis">
Chapter 4. Array and Linked List
Chapter 4. Array and linked list
</span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
<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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
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
</span>
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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>
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<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"
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Previous
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Chapter 1. &nbsp; Introduction to Algorithms
Chapter 1. &nbsp; Introduction to algorithms
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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"
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1.2 What is an algorithm
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Chapter 1. &nbsp; Introduction to Algorithms
Chapter 1. &nbsp; Introduction to algorithms
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