Writing and Amending Algorithms | 编写和修改算法

📚 Writing and Amending Algorithms | 编写和修改算法

In the Cambridge IGCSE Computer Science syllabus, writing and amending algorithms is one of the most important skills you will be tested on. An algorithm is a precise, step-by-step set of instructions used to solve a problem, and examiners expect you to design clear algorithms, follow them using trace tables, and modify them correctly when requirements change.

在剑桥 IGCSE 计算机科学课程中，编写和修改算法是你最需要掌握的核心技能之一。算法是解决问题的一组精确、逐步执行的指令；考官期望你能够设计出清晰的算法，使用跟踪表逐行检查算法，并在需求变化时正确修改算法。

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1. What Is an Algorithm | 什么是算法

An algorithm is a finite sequence of well-defined, unambiguous steps that, when followed correctly, transforms an input into an output and solves a specific problem. In computer science, algorithms can be expressed in three main ways: pseudocode, flowcharts, and program code written in a high-level language.

算法是有限的一系列定义清晰、没有歧义的步骤；按照这些步骤正确执行，就能把输入转换为输出，从而解决具体问题。在计算机科学中，算法通常用三种方式表示：伪代码、流程图，以及用高级语言编写的程序代码。

For an algorithm to be considered valid, it must have three key characteristics: it must terminate after a finite number of steps, each instruction must be clear and unambiguous, and it must be general enough to handle a whole class of similar problems rather than just one single case.

一个算法要想有效，必须具备三个关键特征：必须在有限步骤后终止；每一条指令都必须清晰且没有歧义；必须具有一定的通用性，能够处理一类相似问题，而不仅仅针对某一个具体例子。

For example, the steps “pick up the phone, unlock it, open the calculator app, enter 2 + 3, press equals” form an algorithm for adding two numbers on a phone. In the IGCSE exam, you will normally be asked to write algorithms using either pseudocode or flowchart symbols, so you must be fluent in both.

例如，“拿起手机、解锁、打开计算器应用、输入 2 + 3、按等号”这一系列步骤就是手机上计算两个数字之和的算法。在 IGCSE 考试中，你通常需要用伪代码或流程图符号来写算法，因此你必须熟练掌握这两种表示方式。

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2. The Three Basic Constructs | 三种基本结构

A well-written algorithm is built from just three basic constructs: sequence, selection, and iteration. All structured algorithms, no matter how complex, are combinations of these three building blocks. Examiners will check that your algorithms use these constructs correctly.

一个编写良好的算法只由三种基本结构组成：顺序、选择和循环。无论多复杂的算法，本质上都是这三种基本结构的组合。考官会检查你编写的算法是否正确使用了这些结构。

• Sequence | 顺序：

  Instructions are executed one after another in the order they appear. For example, entering your name, then entering your age, then displaying a greeting.

  指令按照其出现的顺序逐条执行。例如：先输入姓名，再输入年龄，最后显示问候语。

• Selection | 选择：

  The algorithm chooses between two or more alternative paths depending on a condition. Selection is implemented with IF statements or CASE statements.

  算法根据条件在两条或多条可选路径中选择一条执行。选择结构通过 IF 语句或 CASE 语句实现。

• Iteration | 循环：

  A block of statements is repeated either a fixed number of times (count-controlled using a FOR loop) or until a condition is met (condition-controlled using WHILE or REPEAT loops).

  一组语句被重复执行：要么重复固定次数（使用 FOR 循环，即计数控制循环），要么一直重复到某个条件成立为止（使用 WHILE 或 REPEAT 循环，即条件控制循环）。

You should be able to spot which construct is being used in any algorithm you read, and you should deliberately choose the correct construct when writing your own. A common exam mistake is using a FOR loop when the number of repetitions is unknown — in that case a WHILE loop is more appropriate.

你应该能从任何给定的算法中辨认出使用了哪种结构，并且在编写自己的算法时有意识地选择合适的结构。考试中常见的错误是：在重复次数未知的情况下使用 FOR 循环，而这时使用 WHILE 循环才更合适。

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3. Writing Pseudocode | 编写伪代码

Pseudocode is a simple, human-readable way of writing an algorithm without worrying about the exact syntax of a programming language. Cambridge IGCSE uses its own standard pseudocode conventions, and using them correctly will earn you marks even if you do not know a real programming language.

伪代码是一种简单、便于人类阅读的算法描述方式，不需要关心某种编程语言的具体语法。剑桥 IGCSE 使用自己规定的标准伪代码约定；即使你不会任何一种真实编程语言，只要按照这些约定书写，就能得分。

The table below summarises the key pseudocode constructs you must know for the exam.

下表总结了你在考试中必须掌握的关键伪代码结构。

Construct | 结构	Pseudocode Example | 伪代码示例
Input | 输入	INPUT Number
Output | 输出	OUTPUT “Hello”
Assignment | 赋值	Total ← 0
Selection | 选择	IF x > 5 THEN … ELSE … ENDIF
Count-controlled loop | 计数循环	FOR count ← 1 TO 10 … NEXT count
Condition-controlled loop | 条件循环	WHILE x > 0 … ENDWHILE
Repeat until | 重复直到	REPEAT … UNTIL x = 0

Notice that assignment uses the left arrow symbol, written as “←“. When you read the line Total ← Total + 1, it means “take the current value of Total, add 1 to it, and store the result back into Total”. This is different from a mathematical equation, and examiners expect you to understand this distinction.

请注意，赋值使用左箭头符号 “←“。当你读到 Total ← Total + 1 这一行时，意思是“取出 Total 当前的值，加 1，再把结果存回 Total”。这不同于数学中的等式，考官期望你理解这一区别。

When writing an IF statement, you must remember to close it with ENDIF. For multi-way selection, you can use CASE: CASE Age OF 1: … 2: … OTHERWISE: … ENDCASE. Always keep the keywords in uppercase and make sure every structure that opens also closes.

编写 IF 语句时，必须记得用 ENDIF 结束。对于多分支选择，可以使用 CASE 语句：CASE Age OF 1: … 2: … OTHERWISE: … ENDCASE。关键字一律大写，并且确保每个开始的结构都有对应的结束。

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4. Flowchart Symbols | 流程图符号

A flowchart is a graphical way of representing an algorithm. Each type of step is drawn with a different shape, and arrows connect the shapes to show the order in which steps are carried out. In the exam, you may be asked to draw a flowchart or to interpret one that has been given to you.

流程图是用图形表示算法的方式。每一步都用不同的形状绘制，箭头连接各个形状，表示步骤执行的先后顺序。在考试中，你可能会被要求画出流程图，或者解释一个已经给出的流程图。

Symbol | 符号	Shape | 形状	Meaning | 含义
Start / Stop | 开始 / 结束	Rounded rectangle | 圆角矩形	Marks the beginning or end of the algorithm
Input / Output | 输入 / 输出	Parallelogram | 平行四边形	Represents reading data or displaying results
Process | 处理	Rectangle | 矩形	A calculation or assignment such as Total ← Total + 1
Decision | 判断	Diamond | 菱形	A yes/no question that chooses one of two branches
Flow line | 流向线	Arrow | 箭头	Shows the direction of flow between steps

A decision symbol must always have exactly one entry point and two exit paths, usually labelled “Yes” and “No”. When drawing a flowchart, ensure the flow lines do not cross if possible, and label decisions clearly with conditions such as Number > 0?. Keep your flowchart neat because examiners reward clearly readable diagrams.

判断符号必须有且只有一个入口和两条出口路径，通常标为”Yes”和”No”。画流程图时，尽量让流向线不交叉，并且用清晰的条件标注判断，例如 Number > 0?。保持流程图整洁，因为考官会奖励清晰可读的图表。

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5. Writing an Algorithm Step by Step | 一步一步编写算法

When you are asked to write an algorithm, do not panic. A systematic approach will help you produce a correct and complete answer. First, read the problem statement carefully and identify exactly what the inputs, outputs, and processing requirements are.

当你被要求编写算法时，不要慌张。按系统化的步骤进行，就能写出正确完整的答案。首先仔细阅读题目，明确输入是什么、输出是什么、需要处理哪些数据。

Second, decompose the problem into smaller parts. For example, a program that finds the average of ten test scores can be broken into three tasks: read the scores, add them together, and divide by ten. Solving each sub-task separately makes the whole algorithm easier to write.

第二，把问题分解成若干较小的部分。例如，计算十个考试分数平均值的程序可以分解为三个任务：读取分数、把所有分数相加、再除以十。分别解决每个子任务，会让整个算法更容易编写。

Third, choose the right constructs. Use a FOR loop when the number of repetitions is known in advance, a WHILE loop when the algorithm must keep going until a condition becomes false, and a REPEAT…UNTIL loop when the body must run at least once. Use IF or CASE whenever a decision must be made.

第三，选择正确的结构。当重复次数预先已知时使用 FOR 循环；当算法必须一直执行直到某个条件变为假时使用 WHILE 循环；当循环体至少要执行一次时使用 REPEAT…UNTIL 循环；当需要做决定时使用 IF 或 CASE 语句。

Finally, present your algorithm clearly. In an exam, write your pseudocode starting on a fresh page, indent each nested structure to show which block belongs to which statement, and use meaningful variable names such as Total, Count, and Highest rather than single letters like X and Y.

最后，清楚地呈现算法。考试时，从新的一页开始写伪代码，用缩进表示嵌套结构之间的所属关系，并为变量取有意义的名字，例如 Total、Count、Highest，而不是用 X、Y 等单个字母。

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6. Trace Tables | 跟踪表

A trace table is a table used to record the state of all variables and outputs each time a statement in the algorithm is executed. By completing a trace table, you can follow the logic of an algorithm step by step and check whether it produces the expected output. Trace tables are also a powerful tool for finding logic errors.

跟踪表是一种表格，用于在算法每次执行语句时记录所有变量和输出的状态。通过填写跟踪表，你可以逐行跟踪算法的逻辑，检查它是否产生预期输出。跟踪表也是查找逻辑错误的强大工具。

Every column of a trace table is headed with the name of a variable, with one extra column for output. Below is an example trace table for this simple algorithm, which finds the largest number from a list by comparing each new value with the current maximum.

跟踪表的每一列都以变量名作为表头，另外附加一列表示输出。下面是一个简单算法的跟踪表示例，该算法通过将每个新值与当前最大值进行比较，找出一组数中的最大数。

INPUT N
largest ← 0
FOR count ← 1 TO N
    INPUT number
    IF number > largest THEN
        largest ← number
    ENDIF
NEXT count
OUTPUT largest

Suppose the data entered is N = 4 and the numbers are 5, 3, 8, 2. The trace table would develop as follows, where we read across one row each time the loop body is executed.

假设输入 N = 4，数字依次是 5、3、8、2。跟踪表会像下面这样逐步填充，每次执行循环体时读取一行。

count | 变量 count	number | 变量 number	largest | 变量 largest	Output | 输出
1	5	5
2	3	5
3	8	8
4	2	8	8

Notice that when the condition number > largestPublished by TutorHao | IGCSE Science Revision Series | aleveler.com

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