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Algorithm Design & Representation 算法设计与表示

Learning Objectives 学习目标

  • Design algorithms to solve problems using Pseudocode, Flowcharts, and Decision Tables.
  • Draw structured Nassi-Shneiderman (NS) diagrams representing sequential logic.
  • Formulate Decision Tables to map complex conditional business rules.
  • 设计算法，使用伪代码、流程图和决策表解决问题。
  • 绘制代表顺序逻辑的结构化 Nassi-Shneiderman (NS) 图。
  • 制定决策表来映射复杂的条件业务规则。
Bilingual Navigation:双语导航： Read and toggle languages using the globe button at the top. Test your understanding at the end of this page. 阅读并使用顶部的语言按钮切换中英文。在页面底部进行自我检测。

2 · Pseudocode Outline

Pseudocode is an informal, high-level description of an algorithm. It uses structured English-like keywords (such as BEGIN, INPUT, IF-THEN-ELSE, WHILE, and END) to focus on program logic without worrying about language-specific syntax. 伪代码是算法的一种非正式的高级描述。它使用类似于结构化英语的关键字（例如 BEGIN、INPUT、IF-THEN-ELSE、WHILE 和 END），让开发者能够专注于程序逻辑，而无需担心特定语言的语法。

Core Properties of Algorithms算法的核心属性

  • Definite:明确性： Each step must be clear and unambiguous.每一步都必须清晰且无歧义。
  • Finite:有限性： It must terminate after a finite number of steps.必须在有限的步骤后终止。
  • Effective:有效性： Operations must be feasible and simple to perform.操作必须是可行的且易于执行。

3 · Flowchart Standard Shapes

A flowchart is a graphical representation of the sequential steps of an algorithm or program logic. It uses standard geometric shapes connected by arrows (flowlines) to show the path of execution: 流程图是算法或程序逻辑的顺序步骤的图形表示。它使用由箭头（流程线）连接的标准几何形状来显示执行路径：

Shape形状 Name名称 Purpose & Description用途与说明 Example示例
Oval / 椭圆 Terminator终结符 Represents the Start or End point of an algorithm.代表算法的起点或终点。 Start / End
Rectangle / 矩形 Process处理 Represents arithmetic processes, calculations, or variables assignments.代表算术处理、计算或变量赋值。 total = price + tax
Parallelogram / 平行四边形 Input / Output输入/输出 Represents reading data from user or displaying text on console.代表读取用户数据或在控制台显示文本。 Input age / Display fee
Diamond / 菱形 Decision决策 Represents conditional branches with true/false (yes/no) output lines.代表具有真/假（是/否）输出线的条件分支。 Is age < 12?

4 · Decision Tables & NS Diagrams

When conditions grow complex, nested IF-THEN blocks become difficult to read. Two advanced tools simplify representation: 当条件变得复杂时，嵌套的 IF-THEN 块会变得难以阅读。两个先进的工具可以简化这种表示：

Decision Table决策表

A tabular layout mapping conditional rules to distinct logic actions. Excellent for business rules and verifying all test cases. 将条件规则映射到不同逻辑操作的表格布局。非常适合业务规则和验证所有测试用例。

Nassi-Shneiderman (NS)NS 盒图 (Nassi-Shneiderman)

Also known as a structogram. It uses nested boxes instead of shapes and flowlines to enforce structured programming patterns. 也被称为结构图。它使用嵌套框而不是形状和流程线来强制执行结构化编程模式。

Applied Case Study: Billing & Pricing Logic应用案例研究：账单与定价逻辑

Let's analyze three real-world logic systems designed for services and operations. We use these scenario parameters to formulate decision tables and pseudocodes. 让我们分析为服务和运营设计的三个实际逻辑系统。我们使用这些场景参数来制定决策表和伪代码。

Scenario Details场景详情

A theatre bills customers based on age bounds: age under 12 costs RM 12; senior citizen (age 60 and above) costs RM 15; others cost RM 25. 剧院根据年龄段收费：12 岁以下费用为 RM 12；老年人（60 岁及以上）费用为 RM 15；其他人费用为 RM 25。

Decision Table决策表

Conditions & Actions条件与操作 Rule 1 Rule 2 Rule 3
Age < 12 Yes No No
Age ≥ 60 No Yes No
Price = RM 12 X - -
Price = RM 15 - X -
Price = RM 25 - - X

Pseudocode伪代码

BEGIN
  DISPLAY "Enter customer age:"
  INPUT age
  IF age < 12 THEN
    price = 12
  ELSE IF age >= 60 THEN
    price = 15
  ELSE
    price = 25
  END IF
  DISPLAY "Ticket price is RM " + price
END

Scenario Details场景详情

Parking fees: duration under 2 hours costs RM 3; duration between 2 and 8 hours (inclusive) costs RM 10; duration over 8 hours costs RM 20. 停车费：2小时以下收费 RM 3；2至8小时（含）收费 RM 10；8小时以上收费 RM 20。

Decision Table决策表

Conditions & Actions条件与操作 Rule 1 Rule 2 Rule 3
Duration < 2 hours Yes No No
Duration ≥ 2 and ≤ 8 hours No Yes No
Fee = RM 3 X - -
Fee = RM 10 - X -
Fee = RM 20 - - X

Pseudocode伪代码

BEGIN
  DISPLAY "Enter parking hours:"
  INPUT duration
  IF duration < 2 THEN
    fee = 3
  ELSE IF duration >= 2 AND duration <= 8 THEN
    fee = 10
  ELSE
    fee = 20
  END IF
  DISPLAY "Parking fee is RM " + fee
END

Scenario Details场景详情

Vehicle rental rate calculation: standard daily rate is RM 120. If renting more than 7 days, daily rate is discounted to RM 100. 车辆租金计算：标准每日费用为 RM 120。如果租赁天数超过 7 天，每日费用折扣为 RM 100。

Decision Table决策表

Conditions & Actions条件与操作 Rule 1 (Long Rental) Rule 2 (Standard Rental)
Rental Days > 7 Yes No
Set Daily Rate = RM 100 X -
Set Daily Rate = RM 120 - X

Pseudocode伪代码

BEGIN
  DISPLAY "Enter rental days:"
  INPUT days
  IF days > 7 THEN
    rate = 100
  ELSE
    rate = 120
  END IF
  totalCost = days * rate
  DISPLAY "Total cost is RM " + totalCost
END

Interactive Worked Logic Exercises交互式计算逻辑习题

Problem 1: Summing Odd Integers习题 1：奇数整数求和

Task: Read exactly 10 integers from user, sum up all odd integers, and print the total.任务：读取用户输入的 10 个整数，计算所有奇数的和，并输出总数。

💡 Hint / 提示

Use a counter-controlled loop (1 to 10). Within the loop, apply modulo checking (num % 2 != 0) to identify odd values.使用计数控制的循环（1到10）。在循环体内，使用取模判断（num % 2 != 0）来识别奇数值。

✅ Show Logic / 显示逻辑 
BEGIN
  sum = 0
  counter = 0
  WHILE counter < 10 DO
    INPUT num
    IF num % 2 != 0 THEN
      sum = sum + num
    END IF
    counter = counter + 1
  END WHILE
  DISPLAY "Sum of odd numbers: " + sum
END

Problem 2: Summing Positive Even Integers习题 2：正偶数求和

Task: Read exactly 15 integers from user, calculate the sum of all positive even integers (value > 0 and divisible by 2).任务：读取用户输入的 15 个整数，计算所有正偶数（值大于0且能被2整除）的和，并输出结果。

💡 Hint / 提示

Combine relational operator checking (num > 0) and modulo operator checking (num % 2 == 0) inside the loop.在循环体内结合关系运算符判断（num > 0）和取模运算符判断（num % 2 == 0）。

✅ Show Logic / 显示逻辑 
BEGIN
  sum = 0
  counter = 0
  WHILE counter < 15 DO
    INPUT num
    IF num > 0 AND num % 2 == 0 THEN
      sum = sum + num
    END IF
    counter = counter + 1
  END WHILE
  DISPLAY "Sum of positive even numbers: " + sum
END

Check Your Understanding自我检测

Q1. Which flowchart shape represents input or output operations?哪个流程图形状代表输入或输出操作？

Q2. Which algorithmic representation tool is also called a structogram?哪种算法表示工具也被称为结构图 (structogram)？

Q3. What is a key property of an algorithm stating each step must be clear and unambiguous?算法的哪个关键属性指出了每一步都必须清晰且无歧义？

Q4. In a decision table, rules evaluate output results based on combinations of:在决策表中，规则根据什么的组合来评估输出结果？