What is a Trace Table?

A trace table is a technique used to trace the changes in variables and the states of inputs/outputs when dry running an algorithm. It helps us comprehend an algorithm in depth and spot mistakes.

Trace Table for Sequence

In sequence structures, statements execute one after another in order.

Trace Table for Loops

Loops require tracking the loop variable and iterations.

Trace Table for Selection

Selection structures require tracking which branch executes.

什麼是追蹤表？

追蹤表是一種技術，用於在演練算法時追蹤變量的變化和輸入/輸出的狀態。它幫助我們深入理解算法並發現錯誤。

順序結構的追蹤表

在順序結構中，語句按順序一個接一個地執行。

循環結構的追蹤表

循環需要追蹤循環變量和迭代次數。

選擇結構的追蹤表

選擇結構需要追蹤執行哪個分支。

Introduction to Data Structures

A data structure is a way of organizing and storing data so that it can be accessed and modified efficiently. Arrays are one of the most fundamental data structures in programming.

What is an Array?

An array is a collection of data items of the same type stored in consecutive memory locations. Each item can be accessed using an index number.

Array vs Individual Variables

Instead of declaring multiple individual variables:

We can use an array:

Strings as Character Arrays

A string is formed by a series of characters. Characters in a string can be stored in an array.

數據結構簡介

數據結構是組織和存儲數據的方式，以便能夠有效地訪問和修改數據。陣列是編程中最基本的數據結構之一。

什麼是陣列？

陣列是相同類型的數據項的集合，存儲在連續的內存位置中。每個項目都可以使用索引號訪問。

陣列與單個變量

與其聲明多個單獨的變量：

我們可以使用陣列：

字串作為字符陣列

字串由一系列字符組成。字串中的字符可以存儲在陣列中。

Loading Arrays with Data

Loading data into an array using a loop:

Printing Array Contents

Displaying all elements in an array:

Finding Maximum Value

Algorithm to find the largest value in an array:

Finding Minimum Value

Algorithm to find the smallest value in an array:

Checking if Array is Sorted

Algorithm to check if an array is in ascending order:

將數據載入陣列

使用循環將數據載入陣列：

打印陣列內容

顯示陣列中的所有元素：

查找最大值

查找陣列中最大值的算法：

查找最小值

查找陣列中最小值的算法：

檢查陣列是否已排序

檢查陣列是否按升序排列的算法：

Adding Items to Arrays

To add an item to the end of an array:

To insert an item at a specific position:

Deleting Items from Arrays

To delete an item at a specific position:

Flag Variables

A flag variable is a boolean variable used to indicate whether a certain condition has been met. It's commonly used in search algorithms.

向陣列添加項目

將項目添加到陣列末尾：

在特定位置插入項目：

從陣列中刪除項目

刪除特定位置的項目：

標誌變量

標誌變量是一個布爾變量，用於指示是否滿足某個條件。它通常用於搜索算法中。

What is Linear Search?

Linear search (also called sequential search) is a method for finding a target value within an array. It checks each element in sequence until the target is found or all elements have been checked.

Basic Linear Search

Search for an item and report if it exists:

Linear Search with Location

Search for an item and return its position:

Optimized Linear Search

Stop searching once the item is found:

Linear Search in Sorted Arrays

If the array is sorted, we can stop when we pass the target value:

什麼是線性搜索？

線性搜索（也稱為順序搜索）是在陣列中查找目標值的方法。它按順序檢查每個元素，直到找到目標或檢查完所有元素。

基本線性搜索

搜索項目並報告是否存在：

帶位置的線性搜索

搜索項目並返回其位置：

優化的線性搜索

一旦找到項目就停止搜索：

已排序陣列中的線性搜索

如果陣列已排序，當超過目標值時可以停止：

What is Modularity?

Modularity is the practice of breaking down a complex problem into smaller, manageable parts (modules). Each module performs a specific task and can be developed, tested, and maintained independently.

Benefits of Modular Design

• Easier to understand: Smaller modules are easier to comprehend than one large program
• Reusability: Modules can be reused in different parts of the program or in other programs
• Easier debugging: Errors can be isolated to specific modules
• Team collaboration: Different team members can work on different modules simultaneously
• Maintainability: Changes can be made to one module without affecting others

Example: Student Grade System

Instead of writing one large algorithm, we can break it into modules:

Logic Error Detection

Modular design helps identify and fix logic errors:

• Test each module independently with sample data
• Use trace tables to verify module correctness
• Check module inputs and outputs match specifications
• Verify module interactions work as expected
• Use debugging tools to step through module execution

什麼是模塊化？

模塊化是將複雜問題分解為較小、可管理的部分（模塊）的做法。每個模塊執行特定任務，可以獨立開發、測試和維護。

模塊化設計的好處

• 更容易理解：較小的模塊比一個大程序更容易理解
• 可重用性：模塊可以在程序的不同部分或其他程序中重用
• 更容易調試：錯誤可以隔離到特定模塊
• 團隊協作：不同團隊成員可以同時處理不同模塊
• 可維護性：可以對一個模塊進行更改而不影響其他模塊

示例：學生成績系統

與其編寫一個大算法，我們可以將其分解為模塊：

邏輯錯誤檢測

模塊化設計有助於識別和修復邏輯錯誤：

• 使用樣本數據獨立測試每個模塊
• 使用追蹤表驗證模塊正確性
• 檢查模塊輸入和輸出是否符合規範
• 驗證模塊交互是否按預期工作
• 使用調試工具逐步執行模塊