📚 IGCSE CCEA Computer Science Algorithms: Key Exam Points | IGCSE CCEA 计算机：算法 考点精讲
Algorithms form the very foundation of computer science, providing step-by-step procedures to solve problems and process data. In the CCEA IGCSE Computer Science specification, the topic of algorithms is a core area that tests not only your understanding of how algorithms work but also your ability to design, interpret, and evaluate them. This revision guide will walk you through the key concepts, from basic definitions and representations to classic searching and sorting algorithms, ensuring you are fully prepared for your examinations.
算法是计算机科学的基石，它提供了解决问题的逐步过程和处理数据的方法。在 CCEA IGCSE 计算机科学大纲中，算法专题是核心内容，不仅考察你对算法工作原理的理解，还测试你设计、解释和评估算法的能力。本复习指南将带你梳理关键概念，从基本定义和表示方法到经典搜索和排序算法，确保你为考试做好充分准备。
1. What is an Algorithm? | 什么是算法？
An algorithm is a precise, step-by-step set of instructions designed to perform a specific task or solve a problem. Algorithms must be unambiguous, finite, and effective. In everyday life, a recipe for baking a cake is an algorithm – it provides an ordered sequence of steps that, if followed exactly, produces the desired result. In computing, algorithms handle activities like calculating a student’s average grade, finding the shortest route on a map, or encrypting data.
算法是一组精确、逐步的指令，用于执行特定任务或解决问题。算法必须明确、有限且有效。在日常生活中，烤蛋糕的食谱就是一个算法——它提供了一系列有序的步骤，严格按照步骤操作就会得到想要的结果。在计算领域，算法用于处理诸如计算学生平均成绩、在地图上寻找最短路线或加密数据等活动。
CCEA exam questions often ask you to identify characteristics of a good algorithm: inputs (data given to the algorithm), outputs (the result produced), definiteness (each step is clear and unambiguous), finiteness (the algorithm must terminate after a finite number of steps), and effectiveness (each step is basic enough to be carried out in practice).
CCEA 考试常会要求你识别良好算法的特征：输入（提供给算法的数据）、输出（产生的结果）、确定性（每一步清晰明确）、有限性（算法在有限步后必须终止）和有效性（每一步足够基本，可以实际执行）。
2. Representing Algorithms – Flowcharts | 算法表示 – 流程图
Flowcharts are a visual way to represent algorithms using standard symbols. The main symbols you need to know for CCEA are: an oval for Start/End, a parallelogram for Input/Output, a rectangle for Process, a diamond for Decision (yes/no), and arrows to show the flow of control. Flowcharts make it easy to trace the logic of an algorithm before coding.
流程图是一种使用标准符号可视化表示算法的方式。CCEA 需要掌握的主要符号有：椭圆代表开始/结束，平行四边形代表输入/输出，矩形代表处理过程，菱形代表判断（是/否），箭头表示控制流。流程图便于在编码前追踪算法逻辑。
| Symbol | Name | Purpose |
|---|---|---|
| Oval | Terminator | Start or end of the algorithm |
| Parallelogram | Input/Output | Data entry or display |
| Rectangle | Process | A calculation or assignment |
| Diamond | Decision | A yes/no or true/false branch |
| Arrow | Flow line | Shows direction of steps |
Always ensure that every flowchart has exactly one start and at least one end. Make sure decision boxes have exactly two flow lines leaving them, usually labeled ‘Yes’ and ‘No’.
始终确保每个流程图只有一个开始和至少一个结束。确保判断框有两个流向线离开，通常标记为 ‘是’ 和 ‘否’。
3. Pseudocode Essentials | 伪代码基础
Pseudocode is a simplified, language-independent way of writing algorithms that closely resembles structured English. CCEA expects you to be able to read, write, and trace pseudocode. Common constructs include variables, assignment (using ← or =), conditional statements (IF…THEN…ELSE…ENDIF), and loops (FOR…TO…NEXT, WHILE…DO…ENDWHILE).
伪代码是一种简化的、独立于编程语言的算法书写方式，类似结构化的英语。CCEA 要求你能够阅读、编写和追踪伪代码。常用结构包括变量、赋值（使用 ← 或 =）、条件语句（IF…THEN…ELSE…ENDIF）以及循环（FOR…TO…NEXT、WHILE…DO…ENDWHILE）。
INPUT num1, num2, num3
max ← num1
IF num2 > max THEN
max ← num2
ENDIF
IF num3 > max THEN
max ← num3
ENDIF
OUTPUT max
Notice the use of indentation to show structure. In exam questions, you may be asked to produce pseudocode for a given task, so practice writing solutions for simple problems like finding the largest of three numbers or summing a series.
注意使用缩进来显示结构。在考试中，你可能需要针对给定任务编写伪代码，所以要练习为简单问题编写解决方案，比如找出三个数中的最大值或求一系列数的和。
4. Sequence, Selection, and Iteration | 顺序、选择与迭代
All algorithms are built from three fundamental control structures: sequence, selection, and iteration. Sequence means instructions are executed one after the other in the order they are written. Selection, typically implemented with IF statements, allows the algorithm to choose between different paths based on a condition. Iteration (loops) enables a block of code to be repeated either a set number of times or until a condition is met.
所有算法都由三种基本控制结构组成：顺序、选择和迭代。顺序意味着指令按照书写顺序依次执行。选择通常用 IF 语句实现，允许算法根据条件在不同路径之间进行选择。迭代（循环）使一个代码块可以被重复执行，要么固定次数，要么直到条件满足为止。
CCEA exams frequently ask you to identify these structures within a given algorithm or flowchart. For example, a series of rectangular boxes without branches demonstrates sequence; a diamond shape introduces selection; a loop back to an earlier step shows iteration.
CCEA 考试经常要求你在给定的算法或流程图中识别这些结构。例如，一系列没有分支的矩形框展示顺序；菱形引入选择；返回前一步骤的循环显示迭代。
5. Linear Search Algorithm | 线性搜索算法
Linear search (also called sequential search) is the simplest searching algorithm. It works by checking each element of a list one by one from the beginning until the target value is found or the end of the list is reached. The algorithm does not require the data to be sorted. For a list of n items, in the worst case it makes n comparisons, resulting in a time complexity often described as O(n).
线性搜索（也称顺序搜索）是最简单的搜索算法。它的工作原理是从头开始逐个检查列表中的每个元素，直到找到目标值或到达列表末尾。该算法不要求数据有序。对于一个有 n 个元素的列表，最坏情况下需要进行 n 次比较，时间复杂度通常描述为 O(n)。
INPUT list, target
found ← false
index ← 0
WHILE index < LENGTH(list) AND found = false DO
IF list[index] = target THEN
found ← true
OUTPUT “Found at index “, index
ELSE
index ← index + 1
ENDIF
ENDWHILE
IF found = false THEN
OUTPUT “Not found”
ENDIF
This algorithm is straightforward and easy to implement, but it can be slow for large datasets. The examination might ask you to trace a linear search or complete a flowchart for it.
该算法简单直接且易于实现，但对大型数据集可能较慢。考试可能会要求你跟踪线性搜索过程或完成其流程图。
6. Binary Search Algorithm | 二分搜索算法
Binary search is a much faster algorithm, but it requires the list to be sorted beforehand. It works by repeatedly dividing the search interval in half. The algorithm compares the target value with the middle element; if they are equal, the search is complete. If the target is less than the middle element, it searches the lower half; otherwise, it searches the upper half. This halves the problem size each time, giving a time complexity of O(log n).
二分搜索是一种快得多的算法，但它需要列表预先排序。它通过反复将搜索区间分成两半来工作。算法将目标值与中间元素比较；如果相等，搜索完成。如果目标值小于中间元素，则搜索下半部分；否则搜索上半部分。每次都将问题规模减半，时间复杂度为 O(log n)。
INPUT list (sorted), target
low ← 0
high ← LENGTH(list) – 1
found ← false
WHILE low ≤ high AND found = false DO
mid ← (low + high) DIV 2
IF list[mid] = target THEN
found ← true
OUTPUT “Found at index “, mid
ELSE IF list[mid] < target THEN
low ← mid + 1
ELSE
high ← mid – 1
ENDIF
ENDWHILE
IF found = false THEN
OUTPUT “Not found”
ENDIF
Be careful with integer division (DIV) when calculating the midpoint in pseudocode. CCEA may ask you to trace the steps of a binary search on a small dataset, illustrating how the interval shrinks. Also, you might need to explain why binary search cannot be used on unsorted data.
在伪代码中计算中点时要小心整数除法（DIV）。CCEA 可能要求你在小数据集上跟踪二分搜索的步骤，说明区间如何缩小。此外，你可能需要解释为什么二分搜索不能用于无序数据。
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