📚 A-Level Edexcel Programming: Algorithms, Data Structures and Core Techniques | A-Level Edexcel 编程：算法、数据结构与核心技巧
Programming is the heart of Edexcel A-Level Computer Science. This article revisits the essential constructs, data structures, algorithms, and problem-solving habits that appear across both examined and coursework components. Each section pairs a concise English explanation with its Chinese equivalent to support bilingual revision.
编程是 Edexcel A-Level 计算机科学的核心。本文重温考试和课程作业中都会出现的基本构造、数据结构、算法与问题解决习惯。每一节都将简明的英文解释与中文配对，以支持双语复习。
1. Computational Thinking and Problem Decomposition | 计算思维与问题分解
Computational thinking underpins all programming tasks in Edexcel A-Level Computer Science. It involves breaking a complex problem into smaller, manageable subproblems through decomposition, spotting patterns, generalising through abstraction, and designing step-by-step algorithms.
计算思维是 Edexcel A-Level 计算机科学所有编程任务的基础。它涉及通过问题分解将复杂问题拆分为更小、更易管理的子问题、识别模式、通过抽象进行概括，以及设计逐步执行的算法。
An algorithm is a finite sequence of well-defined instructions to solve a problem. It must be unambiguous, have clear inputs and outputs, and terminate for all valid inputs. Edexcel questions often ask you to trace or write algorithms in a pseudocode style.
算法是解决问题的一系列有限且明确的指令。它必须无歧义、具有清晰的输入输出，并对所有有效输入终止。Edexcel 考试题目常要求你以伪代码风格跟踪或编写算法。
2. Programming Constructs: Sequence, Selection, Iteration | 编程构造：顺序、选择、迭代
The three basic programming constructs are sequence, selection, and iteration. Sequence means statements are executed in order; selection uses IF…THEN…ELSE…ENDIF to make decisions; iteration repeats statements using FOR, WHILE, or REPEAT…UNTIL loops.
三种基本编程构造是顺序、选择和迭代。顺序指语句按顺序执行；选择使用 IF…THEN…ELSE…ENDIF 做决策；迭代使用 FOR、WHILE 或 REPEAT…UNTIL 循环重复语句。
- Sequence: total = x + y — 顺序：先加后赋值。
- Selection: IF score >= 90 THEN grade = “A” ELSE grade = “B” ENDIF — 选择：根据条件决定分支。
- Iteration: FOR i = 1 TO 10 … ENDFOR — 迭代：固定次数重复。
Understanding how to combine these constructs is fundamental. Nested selection and iteration allow you to solve more realistic problems such as validation checks, menu systems, and searching through data.
理解如何组合这些构造是基础。嵌套选择和迭代使你能够解决更实际的问题，例如验证检查、菜单系统和数据查找。
3. Built-in Data Types and Variables | 内置数据类型与变量
Variables must be declared and typed in many languages. Edexcel pseudocode uses INTEGER, REAL, BOOLEAN, CHAR, STRING, and DATE. Choosing the correct data type saves memory and prevents type errors.
在许多语言中，变量必须先声明并确定类型。Edexcel 伪代码使用 INTEGER、REAL、BOOLEAN、CHAR、STRING 和 DATE。选择正确的数据类型可节省内存并防止类型错误。
Constants are named values that cannot change at runtime. Type casting or conversion is often needed, for example converting a string “123” to integer 123 before arithmetic.
常量是在运行时不能更改的命名值。类型转换通常是必需的，例如在执行算术之前将字符串 “123” 转换为整数 123。
4. Subprograms: Procedures and Functions | 子程序：过程与函数
Procedures and functions allow modular programming. A procedure performs a task and does not return a value, while a function returns a value. Parameters can be passed by value or by reference depending on the language and the effect required.
过程和函数允许模块化编程。过程执行任务且不返回值，而函数返回一个值。参数可以根据语言和所需效果按值或按引用传递。
Using subprograms avoids repeated code, improves readability, and makes testing easier. In Edexcel pseudocode, a function is called within an expression, whereas a procedure is called as a standalone statement.
使用子程序可避免重复代码、提高可读性并简化测试。在 Edexcel 伪代码中，函数在表达式中调用，而过程作为独立语句调用。
5. Arrays and Lists | 数组与列表
Arrays are fixed-size or dynamic collections of elements of the same type, accessed by an index, usually starting at 0 or 1. Lists, especially in Python, are dynamic and can hold mixed types.
数组是固定大小或动态的、相同类型元素的集合，通过索引访问，索引通常从 0 或 1 开始。列表（尤其是 Python 中的列表）是动态的，并且可以保存混合类型。
A two-dimensional array can represent a table or matrix, for example grid[3][4]. Edexcel questions often require populating a 2D array and iterating through rows and columns.
二维数组可以表示表格或矩阵，例如 grid[3][4]。Edexcel 题目常要求填充二维数组并遍历行和列。
6. Stacks and Queues | 栈与队列
A stack is a Last In, First Out (LIFO) data structure. Common operations are push, pop, and peek/top. A queue is First In, First Out (FIFO), with enqueue, dequeue, and front. These structures are used in recursion, backtracking, scheduling, and buffering.
栈是一种后进先出（LIFO）数据结构。常见操作是 push、pop 和 peek/top。队列是先进先出（FIFO）的，具有 enqueue、dequeue 和 front。这些结构用于递归、回溯、调度和缓冲。
| Structure | Order | Common Operations |
|---|---|---|
| Stack | LIFO | push, pop, peek |
| Queue | FIFO | enqueue, dequeue, front |
7. Searching and Sorting Algorithms | 查找与排序算法
Linear search checks each element in turn, with O(n) in the worst case. Binary search requires a sorted list and repeatedly halves the search interval, giving O(log n) time. Understanding this trade-off is essential for Edexcel.
线性查找逐个检查每个元素，最坏情况为 O(n)。二分查找要求列表有序，并反复将查找区间减半，时间复杂度为 O(log n)。理解这种权衡对 Edexcel 至关重要。
Sorting algorithms include bubble sort, insertion sort, and merge sort. Bubble sort is simple but O(n²); merge sort is more efficient at O(n log n) and is stable.
排序算法包括冒泡排序、插入排序和归并排序。冒泡排序简单但为 O(n²)；归并排序更高效，为 O(n log n) 且是稳定的。
Binary search: O(log n) | Linear search: O(n) | Merge sort: O(n log n)
8. Algorithm Efficiency and Big O Notation | 算法效率与大 O 表示法
Big O notation describes the upper bound of an algorithm’s running time or space usage as the input size n grows. Common complexities are O(1), O(log n), O(n), O(n log n), O(n²), O(2ⁿ).
大 O 表示法描述随着输入规模 n 增长，算法运行时间或空间使用的上限。常见复杂度为 O(1)、O(log n)、O(n)、O(n log n)、O(n²)、O(2ⁿ)。
When choosing an algorithm, consider the worst-case and average-case behaviour. For large data sets, an O(n log n) algorithm is usually much faster than an O(n²) algorithm.
选择算法时，要考虑最坏情况和平均情况行为。对于大数据集，O(n log n) 算法通常比 O(n²) 算法快得多。
9. Recursion | 递归
Recursion occurs when a subroutine calls itself. A recursive solution must have a base case to stop and a recursive case that reduces the problem size. Classic examples are factorial, Fibonacci, and tree traversals.
递归发生在子程序调用自身时。递归解决方案必须有一个停止条件（基准情形）和一个减小问题规模的递归情形。经典例子包括阶乘、斐波那契和树遍历。
Recursion can be elegant but uses call stack memory; each call creates a stack frame. Infinite recursion leads to stack overflow. Edexcel pupils should be able to trace recursive calls step by step.
递归可以很优雅，但会使用调用栈内存；每次调用都会创建一个栈帧。无限递归会导致栈溢出。Edexcel 学生应能够逐步跟踪递归调用。
FUNCTION factorial(n) IF n <= 1 THEN RETURN 1 ELSE RETURN n * factorial(n-1)
10. Object-Oriented Programming Fundamentals | 面向对象编程基础
Object-oriented programming (OOP) organises code into classes and objects. A class is a blueprint; an object is an instance. Key principles are encapsulation, inheritance, polymorphism, and abstraction.
面向对象编程（OOP）将代码组织为类和对象。类是蓝图；对象是实例。关键原则是封装、继承、多态和抽象。
Edexcel may ask about attributes, methods, constructors, and access modifiers like private and public. Encapsulation protects data by exposing only necessary methods.
Edexcel 可能考察属性、方法、构造函数以及私有和公共等访问修饰符。封装通过仅暴露必要方法来保护数据。
11. File Handling and Exception Handling | 文件处理与异常处理
Programs often read from and write to files. Common operations are open, read, write, append, and close. Text files are sequential; binary files can be random access.
程序经常读写文件。常见操作是打开、读取、写入、追加和关闭。文本文件是顺序的；二进制文件可以随机访问。
Exception handling uses TRY…EXCEPT…FINALLY to manage runtime errors such as file not found or division by zero. It prevents the program from crashing and allows graceful recovery.
异常处理使用 TRY…EXCEPT…FINALLY 来管理运行时错误，如文件未找到或除零错误。它可以防止程序崩溃并允许优雅恢复。
12. Testing and Debugging | 测试与调试
Testing ensures that a program meets its specification. Types include unit testing, integration testing, system testing, and acceptance testing. Test data should include normal, boundary, and erroneous cases.
测试确保程序符合其规格。类型包括单元测试、集成测试、系统测试和验收测试。测试数据应包括正常、边界和错误情况。
Debugging is the process of finding and fixing defects. Techniques include dry running, trace tables, breakpoints, and print statements. Edexcel questions often provide a faulty algorithm and ask you to identify the error.
调试是查找和修复缺陷的过程。技术包括干运行、跟踪表、断点和打印语句。Edexcel 题目常提供一个有错误的算法并要求你找出错误。
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