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  • 1 Java basics
    1.1

    Classes, main & output

    Every Java program lives inside a class 类. It starts at a method 方法 named main. System.out.println(...) prints a line; System.out.print(...) prints with no new line.

    public class Main {
        public static void main(String[] args) {
            System.out.println("Hello, world!");
            System.out.println("I am learning Java.");
        }
    }
    
    • Java is compiled 编译: the compiler 编译器 checks the whole program, then it runs.
    • Every statement 语句 ends with a semicolon ;.
    Java programs live in a class and start at main
    Java programs live in a class and start at main
    Vocabulary
    English中文Pinyin
    class/klæs/类lèi
    method/ˈmeθəd/方法fāng fǎ
    compile/kəmˈpaɪl/编译biān yì
    compiler/kəmˈpaɪlə/编译器biān yì qì
    statement/ˈsteɪtmənt/语句yǔ jù
    1.2

    Variables & primitive types

    A variable 变量 must declare 声明 its type. Common primitive types 基本类型: int (whole number), double (decimal), boolean (true/false), char (one letter).

    public class Main {
        public static void main(String[] args) {
            int age = 17;
            double price = 9.99;
            boolean passed = true;
            System.out.println(age + " " + price + " " + passed);
        }
    }
    
    Vocabulary
    English中文Pinyin
    variable/ˈveərɪəbl/变量biàn liàng
    declare/dɪˈkleə/声明shēng míng
    primitive type/ˈprɪmɪtɪv taɪp/基本类型jī běn lèi xíng
    1.3

    Comments & style

    A comment 注释 is // (one line) or /* ... */ (a block). Indent the code inside braces { }. Class names start Capitalised; variables and methods use camelCase 驼峰命名 (lowercase first).

    public class Main {
        public static void main(String[] args) {
            // greet the user
            String firstName = "Mei";
            System.out.println("Hi, " + firstName);
        }
    }
    

    Common mistakes

    • Every statement ends with a semicolon ;.
    • main must be exactly public static void main(String[] args).
    • println adds a new line; print does not.
    Vocabulary
    English中文Pinyin
    comment/ˈkɒment/注释zhù shì
    camelCase/ˈkæml keɪs/驼峰命名tuó fēng mìng míng
  • 2 Operators & expressions
    2.1

    Arithmetic & assignment

    Java arithmetic 算术 uses + - * / and % (remainder). With two ints, / is integer division 整数除法 — it drops the decimal. +=, -=, and ++ are shortcuts.

    public class Main {
        public static void main(String[] args) {
            int a = 7, b = 2;
            System.out.println(a / b);    // 3 (integer division)
            System.out.println(a % b);    // 1
            double x = 7.0 / 2;           // 3.5 (one side is double)
            System.out.println(x);
        }
    }
    
    int/int truncates; involve a double for a real quotient
    int/int truncates; involve a double for a real quotient
    Vocabulary
    English中文Pinyin
    arithmetic/əˈrɪθmətɪk/算术suàn shù
    integer division/ˈɪntɪdʒə dɪˈvɪʒn/整数除法zhěng shù chú fǎ
    2.2

    Using objects: String, Math, wrappers

    Some values are objects 对象 with methods. String has .length(), .substring(), .toUpperCase(). Math has Math.max, Math.sqrt, Math.pow. Wrapper classes 包装类 (Integer, Double) wrap a primitive — e.g. Integer.parseInt("42").

    public class Main {
        public static void main(String[] args) {
            String s = "Hello";
            System.out.println(s.length());                  // 5
            System.out.println(s.toUpperCase());             // HELLO
            System.out.println(Math.max(3, 9));              // 9
            System.out.println(Integer.parseInt("42") + 1);  // 43
        }
    }
    

    Math.random() returns a random 随机 double from 0.0 up to (but not including) 1.0. Scale it and cast to get whole numbers — this is the AP idiom:

    public class Main {
        public static void main(String[] args) {
            // a random whole number from 1 to 6 (a dice roll)
            int roll = (int) (Math.random() * 6) + 1;
            System.out.println(roll >= 1 && roll <= 6);   // true
        }
    }
    
    • Integer.MAX_VALUE (2147483647) and Integer.MIN_VALUE are the limits of int; going past them wraps around (an overflow).
    • An object variable that points at no object holds null; calling a method on it throws a NullPointerException.
    Vocabulary
    English中文Pinyin
    object/ˈɒbdʒekt/对象duì xiàng
    wrapper class/ˈræpə klæs/包装类bāo zhuāng lèi
    random/ˈrændəm/随机suí jī
    2.3

    Casting & type conversion

    A cast 强制转换 changes a value's type. (int) drops the decimal; (double) avoids integer division when you need an exact result.

    public class Main {
        public static void main(String[] args) {
            double pi = 3.99;
            System.out.println((int) pi);            // 3
            int total = 7, n = 2;
            System.out.println((double) total / n);  // 3.5
        }
    }
    

    Common mistakes

    • Integer division: 5 / 2 is 2, not 2.5. Cast first: (double) 5 / 2.
    • Compare Strings (and other objects) with .equals(), not ==.
    • == on two objects tests whether they are the SAME object, not whether they look equal.
    Vocabulary
    English中文Pinyin
    cast/kæst/强制转换qiáng zhì zhuǎn huàn
  • 3 Booleans & selection
    3.1

    if / else

    if runs a block when a condition 条件 is true; else if and else add more cases. The condition goes in ( ), the block in { }.

    public class Main {
        public static void main(String[] args) {
            int score = 72;
            if (score >= 80) {
                System.out.println("A");
            } else if (score >= 60) {
                System.out.println("B");
            } else {
                System.out.println("fail");
            }
        }
    }
    
    if chooses the true branch; else the false branch
    if chooses the true branch; else the false branch
    Vocabulary
    English中文Pinyin
    condition/kənˈdɪʃn/条件tiáo jiàn
    3.2

    Logical operators & comparisons

    Compare with ==, !=, <, >, <=, >= — a comparison 比较 gives a boolean. Combine with && (and), || (or), ! (not) — the logical operators 逻辑运算符. For Strings, use .equals(...), not ==.

    public class Main {
        public static void main(String[] args) {
            int age = 16;
            boolean member = true;
            System.out.println(age >= 18 && member);   // false
            String a = "hi";
            System.out.println(a.equals("hi"));        // true
        }
    }
    
    Vocabulary
    English中文Pinyin
    comparison/kəmˈpærɪsn/比较bǐ jiào
    logical operator/ˈlɒdʒɪkl ˈɒpəreɪtə/逻辑运算符luó jí yùn suàn fú
    3.3

    switch

    switch chooses among many fixed values. Each case ends with break; default is the fallback.

    public class Main {
        public static void main(String[] args) {
            int day = 3;
            switch (day) {
                case 1: System.out.println("Mon"); break;
                case 3: System.out.println("Wed"); break;
                default: System.out.println("other");
            }
        }
    }
    

    Common mistakes

    • A condition must be a boolean; if (x = 5) does not compile (use ==).
    • Each switch case needs a break;, or control falls through to the next case.
    • && and || are the logical operators; & and | are bitwise.
  • 4 Loops
    4.1

    while loops

    A while loop repeats while a condition is true. Change something inside, or it loops forever.

    public class Main {
        public static void main(String[] args) {
            int n = 1;
            while (n <= 3) {
                System.out.println(n);
                n++;
            }
        }
    }
    
    while checks the condition before each pass of the body
    while checks the condition before each pass of the body
    4.2

    for loops

    A for loop packs the start, the condition, and the step into one line. Best when you know the count.

    public class Main {
        public static void main(String[] args) {
            for (int i = 0; i < 5; i++) {
                System.out.print(i + " ");
            }
            System.out.println();   // 0 1 2 3 4
        }
    }
    
    4.3

    Accumulation

    The accumulator 累加器 pattern: start a variable before the loop, then update it each turn.

    public class Main {
        public static void main(String[] args) {
            int total = 0;
            for (int i = 1; i <= 5; i++) {
                total += i;
            }
            System.out.println(total);   // 15
        }
    }
    
    Vocabulary
    English中文Pinyin
    accumulator/əˈkjuːmjʊleɪtə/累加器lěi jiā qì
    4.4

    Nested loops

    A loop inside a loop is a nested loop 嵌套循环. The inner loop runs fully on each turn of the outer one.

    public class Main {
        public static void main(String[] args) {
            for (int r = 0; r < 3; r++) {
                for (int c = 0; c < 3; c++) {
                    System.out.print("*");
                }
                System.out.println();
            }
        }
    }
    

    Common mistakes

    • for (int i = 0; i < n; i++) runs n times (0 to n - 1); using <= runs one extra.
    • Do not put a semicolon right after for (...) or while (...) — it makes an empty loop.
    • Declare the counter in the for header so its scope ends with the loop.
    Vocabulary
    English中文Pinyin
    nested loop/ˈnestɪd luːp/嵌套循环qiàn tào xún huán
  • 5 Strings
    5.1

    String methods

    A String 字符串 is text. Useful methods: .length(), .charAt(i), .substring(a, b), .indexOf(x), .toUpperCase(), .equals(...). Strings are immutable 不可变 — each method returns a new String.

    public class Main {
        public static void main(String[] args) {
            String s = "Python";
            System.out.println(s.length());          // 6
            System.out.println(s.charAt(0));         // P
            System.out.println(s.substring(0, 3));   // Pyt
            System.out.println(s.toUpperCase());     // PYTHON
        }
    }
    

    The methods you will use every day:

    Method Meaning Example → result
    .length() how many characters "Hi".length() → 2
    .charAt(i) one character "Hi".charAt(0) → H
    .substring(a, b) part, stops before b "Python".substring(0, 3) → Pyt
    .substring(a) from a to the end "Python".substring(3) → hon
    .indexOf(x) first position, -1 if absent "banana".indexOf("na") → 2
    .equals(s) same text? "hi".equals("hi") → true
    .compareTo(s) order: negative / 0 / positive "apple".compareTo("banana") → negative

    compareTo puts Strings in dictionary order — the AP exam uses it for sorting questions:

    public class Main {
        public static void main(String[] args) {
            String a = "apple", b = "banana";
            System.out.println(a.compareTo(b) < 0);    // true (apple comes first)
            System.out.println(a.compareTo("apple"));  // 0 (equal)
        }
    }
    
    Key String methods: length, charAt, substring, equals
    Key String methods: length, charAt, substring, equals
    Vocabulary
    English中文Pinyin
    String/strɪŋ/字符串zì fú chuàn
    immutable/ɪˈmjuːtəbl/不可变bù kě biàn
    5.2

    Building & traversing strings

    Join strings with + (concatenation 拼接). Visit each character with a loop and .charAt(i).

    public class Main {
        public static void main(String[] args) {
            String word = "banana";
            int count = 0;
            for (int i = 0; i < word.length(); i++) {
                if (word.charAt(i) == 'a') count++;
            }
            System.out.println(count);   // 3
        }
    }
    

    When you build a long String in a loop, StringBuilder is much faster: append the pieces, then call .toString() once.

    public class Main {
        public static void main(String[] args) {
            StringBuilder sb = new StringBuilder();
            for (int i = 1; i <= 5; i++) {
                sb.append(i).append(" ");
            }
            System.out.println(sb.toString().trim());   // 1 2 3 4 5
        }
    }
    

    Common mistakes

    • Strings are immutable: s.toUpperCase() returns a new String, so store the result.
    • Read a character with s.charAt(i); the length is s.length() (a method, with ()).
    • Building a String with += in a big loop is slow; use a StringBuilder.
    Vocabulary
    English中文Pinyin
    concatenation/kənˌkætəˈneɪʃn/拼接pīn jiē
  • 6 Arrays
    6.1

    1-D arrays

    An array 数组 holds a fixed number of values of one type. Index from 0, and get the size with .length.

    public class Main {
        public static void main(String[] args) {
            int[] scores = {88, 71, 95};
            System.out.println(scores[0]);       // 88
            System.out.println(scores.length);   // 3
            scores[1] = 100;
            System.out.println(scores[1]);       // 100
        }
    }
    
    A primitive holds its value; an array variable holds a reference to the array object
    A primitive holds its value; an array variable holds a reference to the array object
    Vocabulary
    English中文Pinyin
    array/əˈreɪ/数组shù zǔ
    6.2

    Array algorithms

    Walk the array with a loop to find a max, a total, a count, or to search 查找. A for-each loop (for (int x : a)) reads each value in turn.

    public class Main {
        public static void main(String[] args) {
            int[] a = {3, 9, 2, 7};
            int max = a[0], total = 0;
            for (int x : a) {
                if (x > max) max = x;
                total += x;
            }
            System.out.println(max + " " + total);   // 9 21
        }
    }
    
    Vocabulary
    English中文Pinyin
    search/sɜːtʃ/查找chá zhǎo
    6.3

    2-D arrays

    A 2-D array 二维数组 is a grid 网格 of rows and columns: grid[row][col].

    public class Main {
        public static void main(String[] args) {
            int[][] grid = {{1, 2, 3}, {4, 5, 6}};
            System.out.println(grid[1][2]);   // 6
            for (int[] row : grid) {
                for (int v : row) System.out.print(v + " ");
            }
            System.out.println();             // 1 2 3 4 5 6
        }
    }
    

    Common mistakes

    • An array's size is a.length (no brackets, no ()), and it is fixed when created.
    • Valid indexes are 0 to a.length - 1; a[a.length] throws ArrayIndexOutOfBoundsException.
    • A new int[5] is filled with zeros, not left empty.
    Vocabulary
    English中文Pinyin
    2-D array/tuː diː əˈreɪ/二维数组èr wéi shù zǔ
    grid/ɡrɪd/网格wǎng gé
  • 7 ArrayList
    7.1

    ArrayList basics

    An ArrayList is a resizable 可变大小 list — it grows and shrinks as you add or remove items. It stores objects, so use a wrapper 包装类 type like Integer (not int). The <Integer> part is a generic 泛型 type. Key methods: .add(x), .get(i), .set(i, x), .size(), .remove(i).

    import java.util.ArrayList;
    
    public class Main {
        public static void main(String[] args) {
            ArrayList<Integer> nums = new ArrayList<Integer>();
            nums.add(10);
            nums.add(20);
            nums.add(30);
            System.out.println(nums.size());   // 3
            System.out.println(nums.get(1));   // 20
            nums.set(0, 99);
            System.out.println(nums);          // [99, 20, 30]
        }
    }
    
    ArrayList: add, get, size on a resizable list
    ArrayList: add, get, size on a resizable list
    Vocabulary
    English中文Pinyin
    resizable/rɪˈsaɪzəbl/可变大小kě biàn dà xiǎo
    wrapper/ˈræpə/包装类bāo zhuāng lèi
    generic/dʒəˈnerɪk/泛型fàn xíng
    7.2

    ArrayList algorithms & the remove bug

    .remove(i) shifts 移动 every later element one place left. If you remove while counting i up, you skip the next element. Fix: loop backwards, or don't increment i after a remove.

    import java.util.ArrayList;
    
    public class Main {
        public static void main(String[] args) {
            ArrayList<Integer> nums = new ArrayList<Integer>();
            for (int n : new int[]{4, 7, 4, 9, 4}) nums.add(n);
            // Remove every 4 — loop backwards so removals don't skip items.
            for (int i = nums.size() - 1; i >= 0; i--) {
                if (nums.get(i) == 4) nums.remove(i);
            }
            System.out.println(nums);   // [7, 9]
        }
    }
    

    Common mistakes

    • ArrayList uses .size(), .get(i) and .add(...) — not the [] you use on arrays.
    • Removing items while looping forward by index skips the next item (the remove bug). Loop backwards, or use an iterator.
    • Store objects, not primitives: use ArrayList<Integer>, and Java auto-boxes int values.
    Vocabulary
    English中文Pinyin
    shift/ʃɪft/移动yí dòng
  • 8 Writing classes
    8.1

    Fields, constructor & methods

    A class 类 is a blueprint for objects. Its fields 字段 store data, its constructor 构造方法 sets up a new object, and its methods 方法 are the actions. this.name means "this object's name". Create an object with new.

    public class Main {
        public static void main(String[] args) {
            Dog d = new Dog("Rex", 3);
            System.out.println(d.describe());   // Rex is 3 years old
            d.haveBirthday();
            System.out.println(d.describe());   // Rex is 4 years old
        }
    }
    
    class Dog {
        private String name;
        private int age;
    
        public Dog(String name, int age) {   // constructor
            this.name = name;
            this.age = age;
        }
    
        public String describe() {
            return name + " is " + age + " years old";
        }
    
        public void haveBirthday() {
            age++;
        }
    }
    

    A static member belongs to the class itself, not to any one object. Call a static method on the class name — like Math.max — and a static field is shared by every object:

    public class Main {
        public static void main(String[] args) {
            System.out.println(Counter.made());   // 0
            new Counter();
            new Counter();
            System.out.println(Counter.made());   // 2
        }
    }
    
    class Counter {
        private static int count = 0;      // shared by ALL Counter objects
    
        public Counter() { count++; }
    
        public static int made() {         // called on the class: Counter.made()
            return count;
        }
    }
    
    Fields store state; constructor builds; methods act
    Fields store state; constructor builds; methods act
    Vocabulary
    English中文Pinyin
    class/klæs/类lèi
    field/fiːld/字段zì duàn
    constructor/kənˈstrʌktə/构造方法gòu zào fāng fǎ
    method/ˈmeθəd/方法fāng fǎ
    8.2

    Encapsulation

    Encapsulation 封装 means hiding data behind methods. Mark fields private so outside code can't touch them directly; expose an accessor 访问方法 (getter) to read, and a method to change them safely. The method can guard the data — here a deposit must be positive.

    public class Main {
        public static void main(String[] args) {
            Account a = new Account(100);
            a.deposit(50);
            a.deposit(-999);                       // rejected by the guard
            System.out.println(a.getBalance());    // 150
        }
    }
    
    class Account {
        private int balance;                       // hidden from outside
    
        public Account(int start) {
            balance = start;
        }
    
        public void deposit(int amount) {
            if (amount > 0) balance += amount;     // guard keeps balance valid
        }
    
        public int getBalance() {                  // accessor (getter)
            return balance;
        }
    }
    

    Common mistakes

    • A constructor has the class name and no return type (not even void).
    • Use this.field to tell a field apart from a parameter with the same name.
    • Make fields private and reach them through getter/setter methods (encapsulation).
    Vocabulary
    English中文Pinyin
    encapsulation/ɪnˌkæpsjʊˈleɪʃn/封装fēng zhuāng
    accessor/əkˈsesə/访问方法fǎng wèn fāng fǎ
  • 9 Inheritance & polymorphism
    9.1

    Inheritance

    Inheritance 继承 lets a subclass 子类 reuse a superclass 父类. Write class Cat extends Animal and Cat gets Animal's fields and methods for free. Call the parent constructor with super(...).

    public class Main {
        public static void main(String[] args) {
            Cat c = new Cat("Milo");
            c.eat();      // Milo is eating  (inherited from Animal)
            c.speak();    // Meow            (Cat's own method)
        }
    }
    
    class Animal {
        protected String name;
        public Animal(String name) { this.name = name; }
        public void eat() { System.out.println(name + " is eating"); }
    }
    
    class Cat extends Animal {
        public Cat(String name) { super(name); }     // call Animal's constructor
        public void speak() { System.out.println("Meow"); }
    }
    
    Cat and Dog extend Animal: they inherit its members and add their own
    Cat and Dog extend Animal: they inherit its members and add their own
    Vocabulary
    English中文Pinyin
    inheritance/ɪnˈherɪtəns/继承jì chéng
    subclass/ˈsʌbklæs/子类zi lèi
    superclass/ˈsuːpəklæs/父类fù lèi
    9.2

    Polymorphism & toString

    A subclass can override 重写 a method to replace the parent's version. Polymorphism 多态 means a Shape variable can hold any subtype, and Java picks the right toString at run time. System.out.println(obj) automatically calls obj.toString().

    public class Main {
        public static void main(String[] args) {
            Shape[] shapes = { new Circle(2), new Square(3) };
            for (Shape s : shapes) {
                System.out.println(s);          // each calls its own toString
            }
        }
    }
    
    class Shape {
        public String toString() { return "a shape"; }
    }
    
    class Circle extends Shape {
        private int r;
        public Circle(int r) { this.r = r; }
        public String toString() { return "Circle r=" + r; }     // override
    }
    
    class Square extends Shape {
        private int side;
        public Square(int side) { this.side = side; }
        public String toString() { return "Square side=" + side; }   // override
    }
    

    Common mistakes

    • An overriding method must match the signature exactly; add @Override so the compiler catches slips.
    • super(...) must be the first line of a subclass constructor.
    • A subclass object IS-A superclass object, but not the other way round.
    Vocabulary
    English中文Pinyin
    override/ˌəʊvəˈraɪd/重写chóng xiě
    polymorphism/ˈpɒlɪmɔːfɪzəm/多态duō tài
  • 10 Recursion
    10.1

    Recursion

    Recursion 递归 is a method that calls itself. Every recursion needs a base case 基准情形 (when to stop) and a recursive call 递归调用 that moves toward it. Without a base case it never stops and crashes with a stack overflow.

    The call stack for factorial(3): each call waits, then returns in reverse order
    The call stack for factorial(3): each call waits, then returns in reverse order
    public class Main {
        public static void main(String[] args) {
            System.out.println(factorial(5));   // 120
        }
    
        public static int factorial(int n) {
            if (n <= 1) return 1;            // base case
            return n * factorial(n - 1);     // recursive call: n * (n-1)!
        }
    }
    

    Trace it: factorial(5) waits for factorial(4), which waits for factorial(3)… down to factorial(1) returning 1. Then the answers multiply back up: 1 → 2 → 6 → 24 → 120.

    Recursion also works on Strings — peel off one character each call:

    public class Main {
        public static void main(String[] args) {
            System.out.println(reverse("PYTHON"));   // NOHTYP
        }
    
        static String reverse(String s) {
            if (s.length() <= 1) return s;               // base case
            return reverse(s.substring(1)) + s.charAt(0);
        }
    }
    

    Merge sort 归并排序 is the recursive sort on the AP exam: split the array in half, sort each half recursively, then merge 合并 the two sorted halves. It runs in O(n log n) — far faster than the O(n²) sorts on big arrays.

    import java.util.Arrays;
    
    public class Main {
        public static void main(String[] args) {
            int[] a = {5, 2, 9, 1, 7, 3};
            mergeSort(a, 0, a.length - 1);
            System.out.println(Arrays.toString(a));   // [1, 2, 3, 5, 7, 9]
        }
    
        static void mergeSort(int[] a, int lo, int hi) {
            if (lo >= hi) return;                 // base case: one element
            int mid = (lo + hi) / 2;
            mergeSort(a, lo, mid);                // sort the left half
            mergeSort(a, mid + 1, hi);            // sort the right half
            merge(a, lo, mid, hi);                // merge the two halves
        }
    
        static void merge(int[] a, int lo, int mid, int hi) {
            int[] tmp = new int[hi - lo + 1];
            int i = lo, j = mid + 1, k = 0;
            while (i <= mid && j <= hi) {
                if (a[i] <= a[j]) tmp[k++] = a[i++];
                else              tmp[k++] = a[j++];
            }
            while (i <= mid) tmp[k++] = a[i++];
            while (j <= hi)  tmp[k++] = a[j++];
            for (k = 0; k < tmp.length; k++) a[lo + k] = tmp[k];
        }
    }
    

    Common mistakes

    • Recursion needs a base case, or it throws StackOverflowError.
    • Each recursive call must move CLOSER to the base case.
    • Trace a small example by hand to check the recursion returns the right value.
    • In merge sort, the merge step does the real work; the recursion only splits the array.
    Vocabulary
    English中文Pinyin
    recursion/rɪˈkɜːʃn/递归dì guī
    base case/beɪs keɪs/基准情形jī zhǔn qíng xíng
    recursive call/rɪˈkɜːsɪv kɔːl/递归调用dì guī diào yòng
    merge sort/mɜːdʒ sɔːt/归并排序guī bìng pái xù
    merge/mɜːdʒ/合并hé bìng
  • 11 Searching & sorting
    11.1

    Linear & binary search

    Linear search 线性查找 checks every element — works on any array. Binary search 二分查找 is much faster but needs a sorted 已排序 array: it looks at the middle, then throws away half each step. Both return the index, or -1 if not found.

    public class Main {
        public static void main(String[] args) {
            int[] a = {2, 5, 8, 12, 16, 23};      // sorted, so binary search works
            System.out.println(linear(a, 12));    // 3
            System.out.println(binary(a, 12));    // 3
            System.out.println(binary(a, 9));     // -1 (not found)
        }
    
        static int linear(int[] a, int target) {
            for (int i = 0; i < a.length; i++)
                if (a[i] == target) return i;
            return -1;
        }
    
        static int binary(int[] a, int target) {
            int lo = 0, hi = a.length - 1;
            while (lo <= hi) {
                int mid = (lo + hi) / 2;
                if (a[mid] == target) return mid;
                else if (a[mid] < target) lo = mid + 1;
                else hi = mid - 1;
            }
            return -1;
        }
    }
    
    Binary search halves the range each step, so a sorted array is searched in O(log n)
    Binary search halves the range each step, so a sorted array is searched in O(log n)
    Vocabulary
    English中文Pinyin
    linear search/ˈlɪnɪə sɜːtʃ/线性查找xiàn xìng chá zhǎo
    binary search/ˈbaɪnəri sɜːtʃ/二分查找èr fēn chá zhǎo
    sorted/ˈsɔːtɪd/已排序yǐ pái xù
    11.2

    Selection & insertion sort

    Selection sort 选择排序 repeatedly finds the smallest remaining value and swaps it to the front. Insertion sort 插入排序 takes each value and slides it back into its place among the already-sorted values.

    import java.util.Arrays;
    
    public class Main {
        public static void main(String[] args) {
            int[] a = {5, 2, 9, 1, 7};
            for (int i = 0; i < a.length - 1; i++) {
                int min = i;
                for (int j = i + 1; j < a.length; j++)
                    if (a[j] < a[min]) min = j;
                int t = a[min]; a[min] = a[i]; a[i] = t;   // swap into place
            }
            System.out.println(Arrays.toString(a));   // [1, 2, 5, 7, 9]
        }
    }
    
    import java.util.Arrays;
    
    public class Main {
        public static void main(String[] args) {
            int[] a = {5, 2, 9, 1, 7};
            for (int i = 1; i < a.length; i++) {
                int key = a[i], j = i - 1;
                while (j >= 0 && a[j] > key) {    // shift bigger values right
                    a[j + 1] = a[j];
                    j--;
                }
                a[j + 1] = key;                  // drop key into the gap
            }
            System.out.println(Arrays.toString(a));   // [1, 2, 5, 7, 9]
        }
    }
    

    How the speeds compare:

    Algorithm Time
    linear search O(n)
    binary search O(log n), sorted arrays only
    selection / insertion sort O(n²)
    merge sort (topic 10) O(n log n)

    Common mistakes

    • Binary search only works on a sorted array.
    • Linear search is O(n); binary search is O(log n) but needs the sort first.
    • Selection and insertion sort are O(n²) — clear to learn, slow on big data.
    Vocabulary
    English中文Pinyin
    selection sort/sɪˈlekʃn sɔːt/选择排序xuǎn zé pái xù
    insertion sort/ɪnˈsɜːʃn sɔːt/插入排序chā rù pái xù
  • 12 Files & the FRQ
    12.1

    Text files with Scanner

    A Scanner reads text one line at a time. For a real file you write new Scanner(new File("scores.txt")); here we wrap a String so the example runs anywhere. Use .split(" ") to split 拆分 a line into parts and Integer.parseInt(...) to parse 解析 a number from text.

    import java.util.Scanner;
    
    public class Main {
        public static void main(String[] args) {
            // Real file:  Scanner in = new Scanner(new File("scores.txt"));
            String data = "Alice 80\nBob 95\nCara 72";
            Scanner in = new Scanner(data);
            int total = 0, count = 0;
            while (in.hasNextLine()) {
                String line = in.nextLine();
                String[] parts = line.split(" ");      // break the line on the space
                total += Integer.parseInt(parts[1]);
                count++;
            }
            System.out.println("average = " + (total / count));   // average = 82
        }
    }
    
    Scanner reads lines while hasNextLine is true
    Scanner reads lines while hasNextLine is true
    Vocabulary
    English中文Pinyin
    parse/pɑːs/解析jiě xī
    split/splɪt/拆分chāi fēn
    12.2

    The AP FRQ question types

    The AP CS A exam has four free-response 自由作答 questions, each a fixed shape:

    • Q1 — Methods & control: write methods to a given spec; loops, if, String/Math.
    • Q2 — Class design: write a full class (fields, constructor, methods) from a description.
    • Q3 — Array / ArrayList: process a 1-D array or ArrayList (search, count, build a new list).
    • Q4 — 2-D array: traverse a grid by row and column.

    The skill is always the same: read the spec, write the method exactly as described, return the right type.

    public class Main {
        public static void main(String[] args) {
            // Q1 style: implement a method to a spec, then it is tested.
            System.out.println(countEven(new int[]{4, 7, 10, 3, 6}));   // 3
        }
    
        /** Returns how many values in arr are even. */
        public static int countEven(int[] arr) {
            int count = 0;
            for (int x : arr)
                if (x % 2 == 0) count++;
            return count;
        }
    }
    

    Common mistakes

    • nextInt() leaves the newline behind, so a following nextLine() reads an empty line — read it away first.
    • Check hasNext() before reading, to avoid running off the end of the file.
    • In the FRQ, read the method header carefully: match the return type and parameters exactly.
    Vocabulary
    English中文Pinyin
    free-response/friː rɪˈspɒns/自由作答zì yóu zuò dá

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