📚 Worked Examples for CCEA A-Level Computer Science | A-Level CCEA 计算机：典型例题详解
This article provides detailed, step-by-step solutions to typical exam-style questions for CCEA A-Level Computer Science. Each worked example targets a key topic from the specification, including data structures, algorithms, Boolean logic, SQL, object-oriented programming, floating-point representation, and more. The explanations are presented in a side-by-side bilingual format to reinforce understanding and examination technique.
本文针对 CCEA A-Level 计算机科学考试中的典型题型提供逐步详解。每个例题覆盖考纲核心主题，如数据结构、算法、布尔逻辑、SQL、面向对象编程、浮点表示等。通过中英双语对照讲解，帮助加深理解并掌握答题方法。
1. Stacks and Reverse Polish Notation | 栈与逆波兰表达式
Stacks play a fundamental role in evaluating expressions. A common CCEA question asks to convert an infix expression to Reverse Polish Notation (RPN) and then evaluate it using a stack. Below we work through the expression (3+4)*5-2.
栈在表达式求值中起着基础作用。CCEA考试常要求学生将中缀表达式转换为逆波兰表达式(RPN)，然后用栈求值。下面我们对表达式 (3+4)*5-2 进行转换与求值。
Conversion to RPN:
转换为逆波兰表达式：
| Action (English) | 操作 (中文) |
|---|---|
| Read '(' → push to operator stack. | 读取 '(' → 压入运算符栈。 |
| Read '3' → output '3'. | 读取 '3' → 输出 '3'。 |
| Read '+' → stack top is '(', push '+'. | 读取 '+' → 栈顶是 '('，压入 '+'。 |
| Read '4' → output '4'. | 读取 '4' → 输出 '4'。 |
| Read ')' → pop until '(': pop '+', output '+', discard '('. | 读取 ')' → 弹出直至 '('：弹出 '+'，输出 '+'，丢弃 '('。 |
| Read '*' → stack empty? push '*'. | 读取 '*' → 栈为空？压入 '*'。 |
| Read '5' → output '5'. | 读取 '5' → 输出 '5'。 |
| Read '-' → '*' has higher precedence, pop and output '*', then push '-'. | 读取 '-' → '*' 优先级高于 '-'，弹出并输出 '*'，然后压入 '-'。 |
| Read '2' → output '2'. | 读取 '2' → 输出 '2'。 |
| End: pop remaining operators → pop and output '-'. | 结束：弹出剩余运算符 → 弹出并输出 '-'。 |
The resulting RPN expression is: 3 4 + 5 * 2 -
得到的逆波兰表达式为：3 4 + 5 * 2 -
Evaluation using a stack:
使用栈求值：
| Step (English) | 步骤 (中文) |
|---|---|
| Read '3' → push 3. Stack: [3] | 读取 '3' → 压入 3。栈：[3] |
| Read '4' → push 4. Stack: [3,4] | 读取 '4' → 压入 4。栈：[3,4] |
| Read '+' → pop 4, pop 3, 3+4=7, push 7. Stack: [7] | 读取 '+' → 弹出 4 和 3，3+4=7，压入 7。栈：[7] |
| Read '5' → push 5. Stack: [7,5] | 读取 '5' → 压入 5。栈：[7,5] |
| Read '*' → pop 5, pop 7, 7*5=35, push 35. Stack: [35] | 读取 '*' → 弹出 5 和 7，7×5=35，压入 35。栈：[35] |
| Read '2' → push 2. Stack: [35,2] | 读取 '2' → 压入 2。栈：[35,2] |
| Read '-' → pop 2, pop 35, 35-2=33, push 33. Stack: [33] | 读取 '-' → 弹出 2 和 35，35-2=33，压入 33。栈：[33] |
Final result: 33.
最终结果：33。
2. Implementing Queues Using Arrays | 用数组实现队列
CCEA frequently examines circular queue implementation with an array, testing the tracking of front and rear pointers and handling overflow. Consider a queue of size 5 and the following operations: enqueue 10, enqueue 20, enqueue 30, dequeue, enqueue 40, enqueue 50, enqueue 60.
CCEA 常考用数组实现循环队列，测试队首、队尾指针的跟踪以及溢出处理。假设队列大小为5，执行操作：入队 10，入队 20，入队 30，出队，入队 40，入队 50，入队 60。
| Operation (English) | 操作 (中文) | Array State (front=0 initially) | 数组状态 (初始 front=0) |
|---|---|---|---|
| Enqueue 10 | 入队 10 |
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