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<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback">
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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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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#1-q-a" class="md-nav__link">
<a href="#1-key-review" class="md-nav__link">
<span class="md-ellipsis">
1. &nbsp; Q &amp; A
1. &nbsp; Key Review
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#2-q-a" class="md-nav__link">
<span class="md-ellipsis">
2. &nbsp; Q &amp; A
</span>
</a>
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<span class="md-ellipsis">
Chapter 2. Complexity analysis
Chapter 2. Complexity Analysis
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<span class="md-nav__icon md-icon"></span>
Chapter 2. Complexity analysis
Chapter 2. Complexity Analysis
</label>
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
Chapter 3. Data structures
Chapter 3. Data Structures
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<span class="md-nav__icon md-icon"></span>
Chapter 3. Data structures
Chapter 3. Data Structures
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
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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<span class="md-ellipsis">
4.2 Linked list
4.2 Linked List
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<span class="md-ellipsis">
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
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Chapter 5. Stack and queue
Chapter 5. Stack and Queue
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<span class="md-ellipsis">
5.3 Double-ended queue
5.3 Double-Ended Queue
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<span class="md-ellipsis">
Chapter 6. Hash table
Chapter 6. Hashing
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Chapter 6. Hash table
Chapter 6. Hashing
</label>
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
6.3 Hash algorithm
6.3 Hash Algorithm
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<span class="md-ellipsis">
7.1 Binary tree
7.1 Binary Tree
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<span class="md-ellipsis">
7.2 Binary tree traversal
7.2 Binary Tree Traversal
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<span class="md-ellipsis">
7.3 Array Representation of tree
7.3 Array Representation of Tree
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<span class="md-ellipsis">
7.4 Binary Search tree
7.4 Binary Search Tree
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<span class="md-ellipsis">
7.5 AVL tree *
7.5 AVL Tree *
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<span class="md-ellipsis">
8.2 Building a heap
8.2 Building a Heap
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
10.2 Binary search insertion
10.2 Binary Search Insertion
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<span class="md-ellipsis">
10.3 Binary search boundaries
10.3 Binary Search Edge Cases
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<span class="md-ellipsis">
10.4 Hashing optimization strategies
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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<span class="md-ellipsis">
11.3 Bubble sort
11.3 Bubble Sort
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<span class="md-ellipsis">
11.4 Insertion sort
11.4 Insertion Sort
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
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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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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<span class="md-ellipsis">
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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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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<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
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<a href="#1-q-a" class="md-nav__link">
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1. &nbsp; Q &amp; A
1. &nbsp; Key Review
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<a href="#2-q-a" class="md-nav__link">
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2. &nbsp; Q &amp; A
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<!-- Page content -->
<h1 id="13-summary">1.3 &nbsp; Summary<a class="headerlink" href="#13-summary" title="Permanent link">&para;</a></h1>
<h3 id="1-key-review">1. &nbsp; Key Review<a class="headerlink" href="#1-key-review" title="Permanent link">&para;</a></h3>
<ul>
<li>Algorithms are ubiquitous in daily life and are not as inaccessible and complex as they might seem. In fact, we have already unconsciously learned many algorithms to solve various problems in life.</li>
<li>The principle of looking up a word in a dictionary is consistent with the binary search algorithm. The binary search algorithm embodies the important algorithmic concept of divide and conquer.</li>
<li>The process of organizing playing cards is very similar to the insertion sort algorithm. The insertion sort algorithm is suitable for sorting small datasets.</li>
<li>The steps of making change in currency essentially follow the greedy algorithm, where each step involves making the best possible choice at the moment.</li>
<li>An algorithm is a set of step-by-step instructions for solving a specific problem within a finite time, while a data structure defines how data is organized and stored in a computer.</li>
<li>Data structures and algorithms are closely linked. Data structures are the foundation of algorithms, and algorithms are the stage to utilize the functions of data structures.</li>
<li>We can compare data structures and algorithms to assembling building blocks. The blocks represent data, the shape and connection method of the blocks represent data structures, and the steps of assembling the blocks correspond to algorithms.</li>
<li>Algorithms are ubiquitous in daily life and are not distant, esoteric knowledge. In fact, we have already learned many algorithms unconsciously and use them to solve problems big and small in life.</li>
<li>The principle of looking up a dictionary is consistent with the binary search algorithm. Binary search embodies the important algorithmic idea of divide and conquer.</li>
<li>The process of organizing playing cards is very similar to the insertion sort algorithm. Insertion sort is suitable for sorting small datasets.</li>
<li>The steps of making change are essentially a greedy algorithm, where the best choice is made at each step based on the current situation.</li>
<li>An algorithm is a set of instructions or operational steps that solves a specific problem within a finite amount of time, while a data structure is the way computers organize and store data.</li>
<li>Data structures and algorithms are closely connected. Data structures are the foundation of algorithms, and algorithms breathe life into data structures.</li>
<li>We can compare data structures and algorithms to assembling building blocks. The blocks represent data, the shape and connection method of the blocks represent the data structure, and the steps to assemble the blocks correspond to the algorithm.</li>
</ul>
<h3 id="1-q-a">1. &nbsp; Q &amp; A<a class="headerlink" href="#1-q-a" title="Permanent link">&para;</a></h3>
<p><strong>Q</strong>：As a programmer, I’ve rarely needed to implement algorithms manually in my daily work. Most commonly used algorithms are already built into programming languages and libraries, ready to use. Does this suggest that the problems we encounter in our work haven’t yet reached the level of complexity that demands custom algorithm design?</p>
<p>If specific work skills are like the "moves" in martial arts, then fundamental subjects are more like "internal strength".</p>
<p>I believe the significance of learning algorithms (and other fundamental subjects) isn’t necessarily to implement them from scratch at work, but to enable more professional decision-making and problem-solving based on a solid understanding of the concepts. This, in turn, raises the overall quality of our work. For example, every programming language provides a built-in sorting function:</p>
<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
<p><strong>Q</strong>: As a programmer, I have never used algorithms to solve problems in my daily work. Common algorithms are already encapsulated by programming languages and can be used directly. Does this mean that the problems in our work have not yet reached the level where algorithms are needed?</p>
<p>If we compare specific work skills to "techniques" in martial arts, then fundamental subjects should be more like "internal skills".</p>
<p>I believe the significance of learning algorithms (and other fundamental subjects) is not to implement them from scratch at work, but rather to be able to make professional reactions and judgments when solving problems based on the knowledge learned, thereby improving the overall quality of work. Here is a simple example. Every programming language has a built-in sorting function:</p>
<ul>
<li>If we have not learned data structures and algorithms, then given any data, we might just give it to this sorting function. It runs smoothly, has good performance, and seems to have no problems.</li>
<li>However, if we’ve studied algorithms, we understand that the time complexity of a built-in sorting function is typically <span class="arithmatex">\(O(n \log n)\)</span>. Moreover, if the data consists of integers with a fixed number of digits (such as student IDs), we can apply a more efficient approach like radix sort, reducing the time complexity to O(nk) , where k is the number of digits. When handling large volumes of data, the time saved can turn into significant value — lowering costs, improving user experience, and enhancing system performance.</li>
<li>If we have not studied data structures and algorithms, we might simply feed any given data to this sorting function. It runs smoothly with good performance, and there doesn't seem to be any problem.</li>
<li>But if we have studied algorithms, we would know that the time complexity of the built-in sorting function is <span class="arithmatex">\(O(n \log n)\)</span>. However, if the given data consists of integers with a fixed number of digits (such as student IDs), we can use the more efficient "radix sort", reducing the time complexity to <span class="arithmatex">\(O(nk)\)</span>, where <span class="arithmatex">\(k\)</span> is the number of digits. When the data volume is very large, the saved running time can create significant value (reduced costs, improved experience, etc.).</li>
</ul>
<p>In engineering, many problems are difficult to solve optimally; most are addressed with ‘near-optimal’ solutions. The difficulty of a problem depends not only on its inherent complexity but also on the knowledge and experience of the person tackling it. The deeper one’s expertise and experience, the more thorough the analysis, and the more elegantly the problem can be solved.</p>
<p>In the field of engineering, a large number of problems are difficult to reach optimal solutions, and many problems are only solved "approximately". The difficulty of a problem depends on one hand on the nature of the problem itself, and on the other hand on the knowledge reserve of the person observing the problem. The more complete a person's knowledge and the more experience they have, the deeper their analysis of the problem will be, and the more elegantly the problem can be solved.</p>
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