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<title>1.2 What is an algorithm - Hello Algo</title>
<title>1.2 What Is an Algorithm - Hello Algo</title>
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<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
1.2 What is an algorithm
1.2 What Is an Algorithm
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<span class="md-ellipsis">
Before starting
Before Starting
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<span class="md-nav__icon md-icon"></span>
Before starting
Before Starting
</label>
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<span class="md-ellipsis">
0.1 About this book
0.1 About This Book
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<span class="md-ellipsis">
0.2 How to read
0.2 How to Use This Book
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<span class="md-ellipsis">
Chapter 1. Encounter with algorithms
Chapter 1. Encounter With Algorithms
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Chapter 1. Encounter with algorithms
Chapter 1. Encounter With Algorithms
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<span class="md-ellipsis">
1.1 Algorithms are everywhere
1.1 Algorithms Are Everywhere
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<span class="md-ellipsis">
1.2 What is an algorithm
1.2 What Is an Algorithm
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1.2 What is an algorithm
1.2 What Is an Algorithm
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<li class="md-nav__item">
<a href="#121-definition-of-an-algorithm" class="md-nav__link">
<a href="#121-algorithm-definition" class="md-nav__link">
<span class="md-ellipsis">
1.2.1 &nbsp; Definition of an algorithm
1.2.1 &nbsp; Algorithm Definition
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</li>
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1.2.2 &nbsp; Definition of a data structure
1.2.2 &nbsp; Data Structure Definition
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</li>
<li class="md-nav__item">
<a href="#123-relationship-between-data-structures-and-algorithms" class="md-nav__link">
<a href="#123-the-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; The Relationship Between Data Structures and Algorithms
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Chapter 2. Complexity analysis
Chapter 2. Complexity Analysis
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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 Evaluation
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<span class="md-ellipsis">
2.2 Iteration and recursion
2.2 Iteration and Recursion
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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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Chapter 3. Data structures
Chapter 3. Data Structures
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Chapter 3. Data structures
Chapter 3. Data Structures
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3.1 Classification of data structures
3.1 Classification of Data Structures
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<span class="md-ellipsis">
3.2 Basic data types
3.2 Basic Data Types
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3.3 Number encoding *
3.3 Number Encoding *
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<span class="md-ellipsis">
3.4 Character encoding *
3.4 Character Encoding *
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<span class="md-ellipsis">
Chapter 4. Array and linked list
Chapter 4. Array and Linked List
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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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Chapter 6. Hash table
Chapter 6. Hashing
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Chapter 6. Hash table
Chapter 6. Hashing
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6.1 Hash table
6.1 Hash Table
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<span class="md-ellipsis">
6.2 Hash collision
6.2 Hash Collision
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6.3 Hash algorithm
6.3 Hash Algorithm
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7.1 Binary tree
7.1 Binary Tree
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7.2 Binary tree traversal
7.2 Binary Tree Traversal
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7.3 Array Representation of tree
7.3 Array Representation of Tree
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7.4 Binary Search tree
7.4 Binary Search Tree
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7.5 AVL tree *
7.5 AVL Tree *
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8.2 Building a heap
8.2 Building a Heap
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8.3 Top-k problem
8.3 Top-K Problem
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<span class="md-ellipsis">
9.2 Basic graph operations
9.2 Basic Operations on Graphs
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<span class="md-ellipsis">
9.3 Graph traversal
9.3 Graph Traversal
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<span class="md-ellipsis">
10.1 Binary search
10.1 Binary Search
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10.2 Binary search insertion
10.2 Binary Search Insertion
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10.3 Binary search boundaries
10.3 Binary Search Edge Cases
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10.4 Hash Optimization Strategy
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<span class="md-ellipsis">
10.5 Search algorithms revisited
10.5 Search Algorithms Revisited
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<span class="md-ellipsis">
11.1 Sorting algorithms
11.1 Sorting Algorithms
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<span class="md-ellipsis">
11.2 Selection sort
11.2 Selection Sort
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11.3 Bubble sort
11.3 Bubble Sort
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11.4 Insertion sort
11.4 Insertion Sort
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11.5 Quick sort
11.5 Quick Sort
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<span class="md-ellipsis">
11.6 Merge sort
11.6 Merge Sort
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<span class="md-ellipsis">
11.7 Heap sort
11.7 Heap Sort
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11.8 Bucket sort
11.8 Bucket Sort
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<span class="md-ellipsis">
11.9 Counting sort
11.9 Counting Sort
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<span class="md-ellipsis">
11.10 Radix sort
11.10 Radix Sort
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<span class="md-ellipsis">
Chapter 12. Divide and conquer
Chapter 12. Divide and Conquer
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Chapter 12. Divide and conquer
Chapter 12. Divide and Conquer
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12.1 Divide and conquer algorithms
12.1 Divide and Conquer Algorithms
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<span class="md-ellipsis">
12.2 Divide and conquer search strategy
12.2 Divide and Conquer Search Strategy
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<span class="md-ellipsis">
12.3 Building binary tree problem
12.3 Building a Binary Tree Problem
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<span class="md-ellipsis">
12.4 Tower of Hanoi Problem
12.4 Hanoi Tower Problem
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<span class="md-ellipsis">
13.1 Backtracking algorithms
13.1 Backtracking Algorithm
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<span class="md-ellipsis">
13.2 Permutation problem
13.2 Permutations Problem
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<span class="md-ellipsis">
13.3 Subset sum problem
13.3 Subset-Sum Problem
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<span class="md-ellipsis">
13.4 n queens problem
13.4 N-Queens Problem
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<span class="md-ellipsis">
Chapter 14. Dynamic programming
Chapter 14. Dynamic Programming
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Chapter 14. Dynamic programming
Chapter 14. Dynamic Programming
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<span class="md-ellipsis">
14.1 Introduction to dynamic programming
14.1 Introduction to Dynamic Programming
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<span class="md-ellipsis">
14.2 Characteristics of DP problems
14.2 Characteristics of Dynamic Programming Problems
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14.3 DP problem-solving approach
14.3 Dynamic Programming Problem-Solving Approach
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<span class="md-ellipsis">
14.4 0-1 Knapsack problem
14.4 0-1 Knapsack Problem
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<span class="md-ellipsis">
14.5 Unbounded knapsack problem
14.5 Unbounded Knapsack Problem
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<span class="md-ellipsis">
14.6 Edit distance problem
14.6 Edit Distance Problem
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<span class="md-ellipsis">
15.1 Greedy algorithms
15.1 Greedy Algorithm
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<span class="md-ellipsis">
15.2 Fractional knapsack problem
15.2 Fractional Knapsack Problem
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<span class="md-ellipsis">
15.3 Maximum capacity problem
15.3 Maximum Capacity Problem
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<span class="md-ellipsis">
15.4 Maximum product cutting problem
15.4 Maximum Product Cutting Problem
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<span class="md-ellipsis">
16.1 Installation
16.1 Programming Environment Installation
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<span class="md-ellipsis">
16.2 Contributing
16.2 Contributing Together
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16.3 Terminology
16.3 Terminology Table
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<a href="#121-algorithm-definition" class="md-nav__link">
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1.2.1 &nbsp; Definition of an algorithm
1.2.1 &nbsp; Algorithm Definition
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1.2.2 &nbsp; Definition of a data structure
1.2.2 &nbsp; Data Structure Definition
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1.2.3 &nbsp; Relationship between data structures and algorithms
1.2.3 &nbsp; The Relationship Between Data Structures and Algorithms
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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>
<p>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:</p>
<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-algorithm-definition">1.2.1 &nbsp; Algorithm Definition<a class="headerlink" href="#121-algorithm-definition" title="Permanent link">&para;</a></h2>
<p>An <u>algorithm</u> is a set of instructions or operational steps that solves 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>
<li>The problem is well-defined, with clear input and output definitions.</li>
<li>It is feasible and can be completed within a finite number of steps, time, and memory space.</li>
<li>Each step has a definite meaning, and under the same input and operating conditions, the output is always the same.</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>
<p>A <u>data structure</u> is a way of organizing and storing data in a computer, with the following design goals:</p>
<h2 id="122-data-structure-definition">1.2.2 &nbsp; Data Structure Definition<a class="headerlink" href="#122-data-structure-definition" title="Permanent link">&para;</a></h2>
<p>A <u>data structure</u> is a way of organizing and storing data, covering the data content, relationships between data, and methods for data operations. It has the following design objectives.</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>
<li>Occupy as little space as possible to save computer memory.</li>
<li>Data operations should be as fast as possible, covering data access, addition, deletion, update, etc.</li>
<li>Provide a concise data representation and logical information so that algorithms can run efficiently.</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>
<p><strong>Data structure design is a process full of trade-offs</strong>. If we want to achieve improvements in one aspect, we often need to make compromises in another aspect. 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>Compared with linked lists, graphs provide richer logical information but require more memory space.</li>
<li>Compared to arrays, linked lists are more convenient for data addition and deletion operations but sacrifice data access speed.</li>
<li>Compared to linked lists, graphs provide richer logical information but require larger 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>
<p>As shown in Figure 1-4, data structures and algorithms are highly related and closely integrated, specifically in the following three aspects:</p>
<h2 id="123-the-relationship-between-data-structures-and-algorithms">1.2.3 &nbsp; The Relationship Between Data Structures and Algorithms<a class="headerlink" href="#123-the-relationship-between-data-structures-and-algorithms" title="Permanent link">&para;</a></h2>
<p>As shown in Figure 1-4, data structures and algorithms are highly related and tightly coupled, specifically manifested 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>
<li>Algorithms inject vitality into data structures. 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>
<li>Data structures are the foundation of algorithms. Data structures provide algorithms with structured storage of data and methods for operating on data.</li>
<li>Algorithms breathe life into data structures. Data structures themselves only store data information; combined with algorithms, they can solve specific problems.</li>
<li>Algorithms can usually be implemented based on different data structures, but execution efficiency may vary greatly. Choosing the appropriate 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 &nbsp; Relationship between data structures and algorithms </p>
<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="The 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 &nbsp; The relationship between data structures and algorithms </p>
<p>Data structures and algorithms can be likened to a set of building blocks, as illustrated in 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>Data structures and algorithms are like assembling building blocks as shown in Figure 1-5. A set of building blocks, in addition to containing many parts, also comes with detailed assembly instructions. By following the instructions step by step, we can assemble an exquisite building block model.</p>
<p><a class="glightbox" href="../what_is_dsa.assets/assembling_blocks.png" 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.png" /></a></p>
<p align="center"> Figure 1-5 &nbsp; Assembling blocks </p>
<p>The detailed correspondence between the two is shown in 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 assembling building blocks </p>
<div class="center-table">
<table>
<thead>
<tr>
<th>Data Structures and Algorithms</th>
<th>Building Blocks</th>
<th>Data structures and algorithms</th>
<th>Assembling building blocks</th>
</tr>
</thead>
<tbody>
<tr>
<td>Input data</td>
<td>Unassembled blocks</td>
<td>Unassembled building blocks</td>
</tr>
<tr>
<td>Data structure</td>
<td>Organization of blocks, including shape, size, connections, etc</td>
<td>Organization form of building blocks, including shape, size, connection method, etc.</td>
</tr>
<tr>
<td>Algorithm</td>
<td>A series of steps to assemble the blocks into the desired shape</td>
<td>A series of operational steps to assemble the blocks into the target form</td>
</tr>
<tr>
<td>Output data</td>
<td>Completed Block model</td>
<td>Building block model</td>
</tr>
</tbody>
</table>
</div>
<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>
<p>It is worth noting that data structures and algorithms are independent of programming languages. For this reason, this book is able to provide implementations based on 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 questions actually test knowledge of both data structures and algorithms.</p>
<p class="admonition-title">Conventional abbreviation</p>
<p>In actual discussions, we usually abbreviate "data structures and algorithms" as "algorithms". For example, the well-known LeetCode algorithm problems actually examine knowledge of both data structures and algorithms.</p>
</div>
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