2.8 For Loops

For loops provide a compact way to write iteration when you know how many times you want to repeat. They combine initialization, condition checking, and updating into a single header line, making the loop's control logic clear and organized. This structure makes for loops ideal for counting, array processing, and any situation where you need a specific number of iterations.

What distinguishes for loops from while loops is their built-in organization. All the loop control logic sits in one place at the top, reducing the chance of forgetting to update your counter or misplacing initialization code. This design makes for loops the preferred choice for most iteration tasks in Java programming.

• Major concepts: For loop structure (initialization, condition, update), loop control variables, equivalent while loop conversion
• Why this matters for AP: Essential for array processing, appears in most FRQs involving data structures
• Common pitfalls: Off-by-one errors, wrong increment direction, scope confusion with loop variables
• Key vocabulary: Initialization, condition, update, loop control variable, iteration
• Prereqs: While loops, understanding of variable scope, boolean expressions

Key Concepts

The Three-Part Structure

Every for loop has three parts in its header: initialization, condition, and update. This structure keeps everything organized and visible at the top of the loop.

for (initialization; condition; update) {
    // Loop body
}

The initialization runs once before the loop starts. The condition is checked before each iteration. The update runs after each iteration of the loop body.

How for Loops Execute

Here's the step-by-step process that happens with every for loop:

1. Run the initialization statement (only once)

2. Check the condition - if false, skip the entire loop

3. If true, execute the loop body

4. Run the update statement

5. Go back to step 2

This execution order is crucial to understand, especially when debugging or tracing through code.

Loop Control Variables

The variable in the initialization is typically your loop control variable. It's what determines when the loop stops running. You can declare it right in the for loop header, which limits its scope to just that loop.

for (int i = 0; i < 5; i++) {
    System.out.println("i is: " + i);
}
// i is not accessible here - out of scope

Converting Between for and while Loops

Any for loop can be rewritten as a while loop, and vice versa. Understanding this helps you choose the right loop for each situation.

// For loop version
for (int i = 1; i <= 10; i++) {
    System.out.println(i);
}

// Equivalent while loop
int i = 1;          // initialization
while (i <= 10) {   // condition
    System.out.println(i);
    i++;            // update
}

Code Examples

Basic Counting Pattern

public class CountingExample {
    public static void main(String[] args) {
        // Count from 0 to 4
        for (int i = 0; i < 5; i++) {
            System.out.println("Iteration: " + i);
        }

        // Count from 1 to 5
        for (int count = 1; count <= 5; count++) {
            System.out.println("Count: " + count);
        }

        // Count backwards from 10 to 1
        for (int countdown = 10; countdown >= 1; countdown--) {
            System.out.println("T-minus " + countdown);
        }
    }
}

Processing Arrays

public class ArrayProcessing {
    public static void main(String[] args) {
        int[] numbers = {10, 20, 30, 40, 50};

        // Print all elements
        for (int i = 0; i < numbers.length; i++) {
            System.out.println("Element " + i + ": " + numbers[i]);
        }

        // Calculate sum
        int sum = 0;
        for (int i = 0; i < numbers.length; i++) {
            sum += numbers[i];
        }
        System.out.println("Sum: " + sum);

        // Find maximum value
        int max = numbers[0];  // Start with first element
        for (int i = 1; i < numbers.length; i++) {  // Start from index 1
            if (numbers[i] > max) {
                max = numbers[i];
            }
        }
        System.out.println("Maximum: " + max);
    }
}

Nested for Loops

public class NestedLoopExample {
    public static void main(String[] args) {
        // Print a multiplication table
        System.out.println("Multiplication Table (1-5):");

        for (int row = 1; row <= 5; row++) {
            for (int col = 1; col <= 5; col++) {
                int product = row * col;
                System.out.print(product + "\t");  // Tab for spacing
            }
            System.out.println();  // New line after each row
        }
    }
}

String Processing

public class StringProcessing {
    public static void main(String[] args) {
        String word = "programming";

        // Print each character with its index
        for (int i = 0; i < word.length(); i++) {
            char ch = word.charAt(i);
            System.out.println("Index " + i + ": " + ch);
        }

        // Count vowels
        int vowelCount = 0;
        for (int i = 0; i < word.length(); i++) {
            char ch = word.charAt(i);
            if (ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u') {
                vowelCount++;
            }
        }
        System.out.println("Vowels found: " + vowelCount);
    }
}

Skip Patterns

public class SkipPatterns {
    public static void main(String[] args) {
        // Print even numbers from 0 to 20
        for (int i = 0; i <= 20; i += 2) {
            System.out.print(i + " ");
        }
        System.out.println();

        // Print every third number
        for (int i = 3; i <= 30; i += 3) {
            System.out.print(i + " ");
        }
        System.out.println();

        // Process only even indices of an array
        int[] data = {10, 15, 20, 25, 30, 35, 40, 45};
        for (int i = 0; i < data.length; i += 2) {
            System.out.println("Even index " + i + ": " + data[i]);
        }
    }
}

Common Errors and Debugging

Off-by-One Errors

This is the most common mistake with for loops. You either run one iteration too many or too few.

Common cause: Using wrong comparison operators or bounds.

Example scenario:

int[] array = {1, 2, 3, 4, 5};
// Want to print all elements
for (int i = 0; i < array.length; i++) {  // Correct
    System.out.println(array[i]);
}

// Common mistakes:
for (int i = 1; i < array.length; i++) {  // Skips first element
    System.out.println(array[i]);
}

for (int i = 0; i <= array.length; i++) {  // Goes beyond array bounds
    System.out.println(array[i]);  // ArrayIndexOutOfBoundsException
}

How to fix: Always double-check your starting value, ending condition, and increment. For arrays, use i < array.length to access all elements.

Debugging tip: Test your loop bounds with a small array and trace through each iteration.

Wrong Update Direction

Sometimes you update the loop variable in the wrong direction, creating infinite loops or unexpected behavior.

Common cause: Using ++ when you should use -- or vice versa.

Example scenario:

// Want to count down from 10 to 1
for (int i = 10; i >= 1; i++) {  // Bug: i++ instead of i--
    System.out.println(i);

}
// This creates an infinite loop because i keeps getting bigger

How to fix: Make sure your update moves the variable toward your stopping condition.

Scope Confusion

Variables declared in the for loop header are only available inside that loop.

Common cause: Trying to use the loop variable after the loop ends.

Example scenario:

for (int i = 0; i < 10; i++) {
    // i is available here
}
System.out.println(i);  // Error: i is not in scope

How to fix: Declare the variable before the loop if you need it afterward, or use a different approach.

int i;
for (i = 0; i < 10; i++) {
    // i is available here
}
System.out.println("Final i: " + i);  // Now i is accessible

Practice Problems

Problem 1: Sum of Squares

Write a method that calculates the sum of squares from 1 to n:

public static int sumOfSquares(int n) {
    // Calculate 1² + 2² + 3² + ... + n²
    // Your code here
}

Solution:

public static int sumOfSquares(int n) {
    int sum = 0;
    for (int i = 1; i <= n; i++) {
        sum += i * i;  // Add i squared to sum
    }
    return sum;
}

Example: sumOfSquares(3) returns 1 + 4 + 9 = 14

Problem 2: Reverse String

Write a method that reverses a string using a for loop:

public static String reverseString(String str) {
    // Your code here - use a for loop

}

Solution:

public static String reverseString(String str) {
    String reversed = "";
    for (int i = str.length() - 1; i >= 0; i--) {
        reversed += str.charAt(i);
    }
    return reversed;
}

Key insight: Start from the last index and work backward to the first index.

Problem 3: Find All Factors

Write a method that prints all factors of a given number:

public static void printFactors(int number) {
    // Print all numbers that divide evenly into number
    // Your code here
}

Solution:

public static void printFactors(int number) {
    System.out.println("Factors of " + number + ":");
    for (int i = 1; i <= number; i++) {
        if (number % i == 0) {  // i divides evenly into number
            System.out.print(i + " ");
        }
    }
    System.out.println();
}

Example: printFactors(12) prints "1 2 3 4 6 12"

Problem 4: Pattern Printing

Write a method that prints a triangle pattern:

public static void printTriangle(int height) {
    // Print a triangle like:
    // *
    // **
    // ***
    // ****
}

Solution:

public static void printTriangle(int height) {
    for (int row = 1; row <= height; row++) {
        for (int star = 1; star <= row; star++) {
            System.out.print("*");
        }
        System.out.println();  // New line after each row
    }
}

Key insight: Use nested loops - outer loop for rows, inner loop for stars in each row.

AP Exam Connections

For loops are essential for array processing and appear frequently on AP Computer Science A exams.

Multiple Choice Patterns

You'll often see questions that ask you to trace through for loops and determine the final value of variables or the output produced. Pay careful attention to the initialization, condition, and update parts. Common trap answers involve off-by-one errors or incorrect loop bounds.

FRQ Applications

FRQ 1 (Methods and Control Structures): For loops are perfect for methods that need to repeat a specific number of times or process a sequence of values.

FRQ 2 (Class Design): When implementing classes that work with arrays or collections, for loops help process the data efficiently.

FRQ 3 (Array/ArrayList): This is where for loops shine - traversing arrays to search, sort, or modify elements. Almost every array algorithm uses for loops.

FRQ 4 (2D Array): Nested for loops are essential for processing 2D arrays, whether you're traversing row-major or column-major order.

Quick Test-Taking Tips

When tracing for loops, write down the values of the loop variable at each iteration. Don't try to calculate everything in your head. Remember that the update happens after the loop body executes, not before.

For array problems, always check that your loop bounds match the array size. Using i < array.length accesses indices 0 through array.length - 1, which covers all elements exactly once.

If you see nested for loops, trace through the inner loop completely for each iteration of the outer loop. The inner loop runs to completion before the outer loop advances to its next iteration.