Algorithms with Selection and Repetition

含选择与重复的算法

Algorithms are built from three fundamental blocks:

算法（algorithm）由三个基本结构构成：

Boolean Expressions

布尔表达式

Relational Operators

关系运算符（relational operator）

int a = 10;
boolean result = (a >= 5);  // true// true

if Statements

if 语句

Selection statements alter the sequential flow of execution based on a Boolean condition.

选择语句根据布尔条件改变顺序执行的流程。

One-Way Selection (if)

单分支选择（if）

if (score >= 90) {
    System.out.println("Excellent!");
}
// Body runs ONLY if condition is true// 仅当条件为 true 时循环体才执行

Two-Way Selection (if-else)

双分支选择（if-else）

if (age >= 18) {
    System.out.println("Adult");
} else {
    System.out.println("Minor");
}

Nested if Statements

嵌套 if（nested if）语句

An if inside another if. The inner condition is only checked if the outer condition is true.

一个 if 嵌套在另一个 if 中。只有外层条件为 true 时，才会检查内层条件。

if-else-if (Multiway Selection)

if-else-if（多分支选择）

if (grade >= 90) {
    letter = "A";
} else if (grade >= 80) {
    letter = "B";
} else if (grade >= 70) {
    letter = "C";
} else {
    letter = "F";
}

Compound Boolean Expressions

复合布尔表达式

Logical Operators

逻辑运算符（logical operator）

Precedence: ! → && → ||

优先级（precedence）： ! → && → ||

int age = 20;
boolean hasID = true;
if (age >= 18 && hasID) {
    System.out.println("Entry allowed");
}

String s = null;

// Wrong order: s.length() runs first, throws NullPointerException
if (s.length() > 0 && s != null) { ... }

// Correct order: null check first, short-circuit skips s.length()
if (s != null && s.length() > 0) { ... }

String s = null;

// 顺序错误：先执行 s.length()，抛出 NullPointerException
if (s.length() > 0 && s != null) { ... }

// 顺序正确：先判空，短路会跳过 s.length()
if (s != null && s.length() > 0) { ... }

Comparing Boolean Expressions

比较布尔表达式

De Morgan's Law

德摩根定律（De Morgan's Laws）

Comparing Objects

比较对象

String a = new String("Hi");
String b = new String("Hi");
a == b        // false, different objects// false，不同对象
a.equals(b)  // true , same content// true，内容相同

// Original
passed && onTime

// Negated (apply De Morgan: flip && to ||, negate each side)
!passed || !onTime

// 原式
passed && onTime

// 取反（用德摩根：&& 翻成 ||，每一项取反）
!passed || !onTime

while Loops

while 循环（while loop）

Iteration repeats code zero or more times while a condition is true.

循环（loop / iteration）会在条件为真时重复执行代码零次或多次。

int count = 1;
while (count <= 5) {
    System.out.print(count + " ");
    count++;
}
// Output: 1 2 3 4 5// 输出：1 2 3 4 5

int n = 20;
int count = 0;
while (n > 1) {
    n /= 2;
    count++;
}
// What is count?

int n = 20;
int count = 0;
while (n > 1) {
    n /= 2;
    count++;
}
// count 等于多少？

for Loops

for 循环（for loop）

A for loop packs initialization, condition, and update into one header.

一个 for 循环把初始化、条件和更新打包在同一个头部里。

for (int i = 0; i < 5; i++) {
    System.out.print(i + " ");
}
// Output: 0 1 2 3 4// 输出：0 1 2 3 4

// Equivalent while loop:// 等价的 while 循环：
int i = 0;
while (i < 5) {
    System.out.print(i + " ");
    i++;
}

for (int i = 0; i < 5; i++) {
    // body runs with i = 0, 1, 2, 3, 4
}
// after the loop, i = 5  (but only if i was declared OUTSIDE the for header)

for (int i = 0; i < 5; i++) {
    // 循环体在 i = 0, 1, 2, 3, 4 下执行
}
// 循环结束后，i = 5（仅当 i 在 for 头部之外声明时可见）

Implementing Selection and Iteration Algorithms

实现选择与循环算法

The AP exam expects you to recognize and implement these standard algorithms:

AP 考试要求你能识别并实现下列标准算法（algorithm）：

1. Divisibility Check

1. 整除性检查

if (num % 3 == 0) {
    System.out.println(num + " is divisible by 3");
}

2. Extract Digits

2. 提取数位

int n = 4827;
while (n > 0) {
    int digit = n % 10;  // last digit: 7, 2, 8, 4// 末位：7, 2, 8, 4
    n /= 10;
}

3. Count (Frequency)

3. 计数（频次）

int count = 0;
for (int i = 1; i <= 100; i++) {
    if (i % 7 == 0) count++;
}

4. Min / Max

4. 最小值 / 最大值

int max = Integer.MIN_VALUE;
// As you process values:// 处理每个值时：
if (val > max) max = val;

5. Sum / Average

5. 求和 / 平均

int sum = 0;
for (int i = 1; i <= n; i++) {
    sum += i;
}
double avg = (double) sum / n;

Implementing String Algorithms

实现字符串算法

Standard string algorithms you should know:

你应当掌握的标准字符串算法（algorithm）：

Traverse & Check Substrings

遍历并检查子串

String str = "hello world";
int vowels = 0;
for (int i = 0; i < str.length(); i++) {
    String ch = str.substring(i, i + 1);
    if ("aeiou".indexOf(ch) >= 0) {
        vowels++;
    }
}

Reverse a String

反转字符串

String original = "java";
String reversed = "";
for (int i = original.length() - 1; i >= 0; i--) {
    reversed += original.substring(i, i + 1);
}
// reversed = "avaj"// reversed = "avaj"

Nested Iteration

嵌套循环（nested loop）

A loop inside another loop. The inner loop completes all its iterations for each single iteration of the outer loop.

循环里再套循环。外层每跑一次，内层都要把它的所有迭代跑完。

for (int row = 1; row <= 3; row++) {
    for (int col = 1; col <= 4; col++) {
        System.out.print("* ");
    }
    System.out.println();
}
// Output:
// * * * *
// * * * *
// * * * *// 输出：
// * * * *
// * * * *
// * * * *

for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= i; j++) {
        System.out.print("*");
    }
    System.out.println();
}

*
**
***
****

for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= i; j++) {
        System.out.print("*");
    }
    System.out.println();
}

*
**
***
****

Informal Run-Time Analysis

非形式化运行时分析

A statement execution count is the number of times a statement runs. You determine this by tracing the loop.

语句执行次数指一条语句被执行的次数。通过追踪循环来确定它。

// How many times does the inner print execute?// 内层 print 共执行多少次？
for (int i = 0; i < 5; i++) {          // 5 times// 5 次
    for (int j = 0; j < 3; j++) {      // 3 times each// 每次 3 次
        System.out.print("X");       // 5 × 3 = 15 times// 5 × 3 = 15 次
    }
}

Unit 2 MCQ Patterns That Show Up Every Year

单元 2 每年都考的选择题套路

Unit 2 is the most-tested unit on the AP CSA MCQ section. Most questions fall into a handful of recurring shapes. Recognising the shape first lets you trace less and answer faster.

单元 2 是 AP CSA 选择题中考得最多的单元。大多数题都落在几种固定的套路里。先认出套路，就能少追踪、快出答案。

Flashcards, Click to Flip

闪卡，点击翻面

Unit 2, Practice Quiz

单元 2 练习小测

AP-Style Practice Problems

AP 风格练习题