diff --git a/en/docs/chapter_introduction/algorithms_are_everywhere.md b/en/docs/chapter_introduction/algorithms_are_everywhere.md index a4b7638e2..de9e87664 100644 --- a/en/docs/chapter_introduction/algorithms_are_everywhere.md +++ b/en/docs/chapter_introduction/algorithms_are_everywhere.md @@ -25,17 +25,17 @@ Before formally discussing algorithms, there's an interesting fact worth sharing === "<5>" ![Binary Search in Dictionary Step 5](algorithms_are_everywhere.assets/binary_search_dictionary_step5.png) -This essential skill for elementary students, looking up a dictionary, is actually the famous "Binary Search" algorithm. From a data structure perspective, we can consider the dictionary as a sorted "array"; from an algorithmic perspective, the series of actions taken to look up a word in the dictionary can be viewed as "Binary Search." +Looking up a dictionary, a must-have skill for primary school students, is actually the famous "binary search" algorithm. From the perspective of data structure, we can regard the dictionary as a sorted "array"; from the perspective of algorithm, we can regard the above series of dictionary lookup operations as "binary search." **Example 2: Organizing Playing Cards**. When playing cards, we need to arrange the cards in our hand in ascending order, as shown in the following process. 1. Divide the playing cards into "ordered" and "unordered" sections, assuming initially the leftmost card is already in order. 2. 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. -3. Continue to repeat step `2.` until all cards are in order. +3. Repeat step `2` until all cards are in order. ![Playing cards sorting process](algorithms_are_everywhere.assets/playing_cards_sorting.png) -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. +The above method of organizing playing cards is essentially the "Insertion Sort" algorithm, which is very efficient for small datasets. Insertion sort is included in the sorting functions of many programming languages. **Example 3: Making Change**. Suppose we buy goods worth $69$ yuan at a supermarket and give the cashier $100$ yuan, then the cashier needs to give us $31$ yuan in change. They would naturally complete the thought process as shown in the figure below. @@ -49,8 +49,8 @@ The above method of organizing playing cards is essentially the "Insertion Sort" In the above steps, we make the best choice at each step (using the largest denomination possible), ultimately resulting in a feasible change-making plan. From the perspective of data structures and algorithms, this method is essentially a "Greedy" algorithm. -From cooking a meal to interstellar travel, almost all problem-solving involves algorithms. The advent of computers allows us to store data structures in memory and write code to call the CPU and GPU to execute algorithms. In this way, we can transfer real-life problems to computers, solving various complex issues more efficiently. +From cooking a meal to interstellar travel, almost all problem-solving involves algorithms. The advent of computers allows us to store data structures in memory and write code to call the CPU and GPU to execute algorithms. In this way, we can transfer real-life problems to computers and solve various complex issues in a more efficient way. !!! tip - If concepts such as data structures, algorithms, arrays, and binary search still seem somewhat obscure, I encourage you to continue reading. This book will gently guide you into the realm of understanding data structures and algorithms. + If concepts such as data structures, algorithms, arrays, and binary search still seem somewhat obscure, I encourage you to read on. This book will guide you step by step into the world of data structures and algorithms. diff --git a/en/docs/chapter_introduction/summary.md b/en/docs/chapter_introduction/summary.md index acfa2d4a5..0b40864cb 100644 --- a/en/docs/chapter_introduction/summary.md +++ b/en/docs/chapter_introduction/summary.md @@ -4,6 +4,19 @@ - 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. - The process of organizing playing cards is very similar to the insertion sort algorithm. The insertion sort algorithm is suitable for sorting small datasets. - The steps of making change in currency essentially follow the greedy algorithm, where each step involves making the best possible choice at the moment. -- An algorithm is a set of instructions or steps used to solve a specific problem within a finite amount of time, while a data structure is the way data is organized and stored in a computer. +- 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. - 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. -- We can liken data structures and algorithms to 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. +- 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. + +### Q & A + +**Q**：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? + +If specific work skills are like the "moves" in martial arts, then fundamental subjects are more like "internal strength". + +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: + +- 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. +- However, if we’ve studied algorithms, we understand that the time complexity of a built-in sorting function is typically $O(n \log n)$. 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. + +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. diff --git a/en/docs/chapter_introduction/what_is_dsa.md b/en/docs/chapter_introduction/what_is_dsa.md index 93aad451d..264e93e13 100644 --- a/en/docs/chapter_introduction/what_is_dsa.md +++ b/en/docs/chapter_introduction/what_is_dsa.md @@ -19,14 +19,14 @@ A data structure is a way of organizing and storing data in a computer, w **Designing data structures is a balancing act, often requiring trade-offs**. If you want to improve in one aspect, you often need to compromise in another. Here are two examples: - Compared to arrays, linked lists offer more convenience in data addition and deletion but sacrifice data access speed. -- Graphs, compared to linked lists, provide richer logical information but require more memory space. +- Compared with linked lists, graphs provide richer logical information but require more memory space. ## Relationship between data structures and algorithms As shown in the figure below, data structures and algorithms are highly related and closely integrated, specifically in the following three aspects: - Data structures are the foundation of algorithms. They provide structured data storage and methods for manipulating data for algorithms. -- Algorithms are the stage where data structures come into play. The data structure alone only stores data information; it is through the application of algorithms that specific problems can be solved. +- 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. - Algorithms can often be implemented based on different data structures, but their execution efficiency can vary greatly. Choosing the right data structure is key. ![Relationship between data structures and algorithms](what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png) @@ -50,4 +50,4 @@ It's worth noting that data structures and algorithms are independent of program !!! tip "Conventional Abbreviation" - In real-life discussions, we often refer to "Data Structures and Algorithms" simply as "Algorithms". For example, the well-known LeetCode algorithm problems actually test both data structure and algorithm knowledge. + 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.