AP CSA Unit 4 | Arrays & Array Algorithms

1. Why Arrays Exist

Without arrays, a program that stores related data becomes messy fast.

Without an array

double angle0 = 15;
double angle1 = 20;
double angle2 = 25;
double angle3 = 30;

// What if we need 100 launch angles?

With an array

double[] angles = {15, 20, 25, 30};

System.out.println(angles[0]); // 15.0
System.out.println(angles[3]); // 30.0

Analogy: spreadsheet column. An array is like one column of related values. Each row has an index, and each index stores one value.

Index	Value
0	15
1	20
2	25
3	30

2. Array Creation and Initialization

Fixed Number of Lockers

This creates five slots. Each slot starts with the default value for its type.

int[] scores = new int[5];

scores[0] = 88;
scores[1] = 94;

Preloaded Lockers

This creates the array and fills it immediately.

int[] scores = {85, 92, 77, 100, 88};

Default Values

Type	Default
`int`	`0`
`double`	`0.0`
`boolean`	`false`
Object references	`null`

AP warning: If scores.length is 5, the valid indexes are 0 through 4. scores[5] causes an ArrayIndexOutOfBoundsException.

Check for understanding: What is the last valid index?

For any array named arr, the last valid index is arr.length - 1.

3. Traversing Arrays

Traversing means visiting each element in the array. Most AP array algorithms begin with a traversal.

Index-Based For Loop

for (int i = 0; i < scores.length; i++) {
    System.out.println(scores[i]);
}

This is the best choice when you need the index, need to modify elements, or need to compare neighboring elements.

Enhanced For Loop

for (int score : scores) {
    System.out.println(score);
}

This is the best choice when you only need to read each value.

Analogy: An index-based loop walks locker-to-locker using locker numbers. An enhanced for loop is like a tour guide handing you each item one at a time.

Important limitation: changing the enhanced-for variable does not change the array.

int[] scores = {80, 90, 100};

for (int score : scores) {
    score = 0;     // only changes the temporary variable
}

System.out.println(scores[0]); // still 80

4. Standard Array Algorithms

These are the core AP CSA array patterns. Students should recognize, trace, and write each one.

Sum

int total = 0;
for (int value : nums) {
    total += value;
}

Average

int total = 0;
for (int value : nums) {
    total += value;
}
double average = (double) total / nums.length;

Maximum

int max = nums[0];
for (int i = 1; i < nums.length; i++) {
    if (nums[i] > max) {
        max = nums[i];
    }
}

Analogy: mountain climbing. Keep the tallest mountain seen so far.

Minimum

int min = nums[0];
for (int i = 1; i < nums.length; i++) {
    if (nums[i] < min) {
        min = nums[i];
    }
}

Count Matching Values

int count = 0;
for (double time : times) {
    if (time < 12.0) {
        count++;
    }
}

Linear Search

public static boolean contains(int[] nums, int target) {
    for (int value : nums) {
        if (value == target) {
            return true;
        }
    }
    return false;
}

Analogy: looking through papers one at a time until the target is found.

5. Interactive IDE Examples

Paste these into the IDE, run them, and then change the data. The goal is not just to copy code. The goal is to predict how the output changes.

Example A: Average and Maximum

public class Main {
    public static void main(String[] args) {
        int[] scores = {85, 92, 77, 100, 88};

        int total = 0;
        int max = scores[0];

        for (int i = 0; i < scores.length; i++) {
            total += scores[i];
            if (scores[i] > max) {
                max = scores[i];
            }
        }

        double average = (double) total / scores.length;
        System.out.println("Average = " + average);
        System.out.println("Max = " + max);
    }
}

Example B: Projectile Data Analyzer

public class Main {
    public static void main(String[] args) {
        double[] angles = {15, 20, 25, 30, 35, 40, 45};
        double[] ranges = {18.4, 24.9, 29.8, 31.2, 30.7, 27.1, 22.8};

        int bestIndex = 0;
        double totalRange = 0;

        for (int i = 0; i < ranges.length; i++) {
            totalRange += ranges[i];
            if (ranges[i] > ranges[bestIndex]) {
                bestIndex = i;
            }
        }

        double averageRange = totalRange / ranges.length;
        System.out.println("Average range = " + averageRange);
        System.out.println("Best angle = " + angles[bestIndex]);
        System.out.println("Best range = " + ranges[bestIndex]);
    }
}

6. Object Arrays Preview

Arrays can store primitive values like int and double, but they can also store object references. This connects directly back to Unit 3.

Athlete[] team = new Athlete[3];

team[0] = new Athlete("Sarah", 11, 5.23);
team[1] = new Athlete("Emma", 12, 5.01);
team[2] = new Athlete("Maya", 10, 5.45);

System.out.println(team[0].getName());

Analogy: the array slots are parking spaces. Each space can hold a reference to an object. If a space is empty, it holds null.

7. AP Code Tracing Challenges

1. What is printed?

int[] nums = {3, 6, 9};
for (int i = 0; i < nums.length; i++) {
    System.out.print(nums[i] + " ");
}

Answer: 3 6 9

2. What is printed?

int[] nums = {2, 4, 6};
nums[1] = 8;
System.out.println(nums[1]);

Answer: 8

3. What is printed?

int[] nums = {1, 3, 5, 7};
int total = 0;
for (int n : nums) {
    total += n;
}
System.out.println(total);

Answer: 16

4. What is printed?

int[] nums = {4, 1, 9, 2};
int max = nums[0];
for (int i = 1; i < nums.length; i++) {
    if (nums[i] > max) {
        max = nums[i];
    }
}
System.out.println(max);

Answer: 9

5. What is printed?

int[] nums = {5, 10, 15};
for (int x : nums) {
    x = x + 100;
}
System.out.println(nums[0]);

Answer: 5. The enhanced-for variable x is a temporary copy of each value.

6. What is printed?

int[] nums = {2, 4, 6, 8};
for (int i = 0; i < nums.length; i++) {
    nums[i] += i;
}
System.out.println(nums[3]);

Answer: 11. The array becomes {2, 5, 8, 11}.

8. Common AP Array Mistakes

Off-by-One Error

// Wrong
for (int i = 0; i <= arr.length; i++) {
    System.out.println(arr[i]);
}

Use i < arr.length, not i <= arr.length.

Invalid Last Element

// Wrong
System.out.println(arr[arr.length]);

// Correct
System.out.println(arr[arr.length - 1]);

Enhanced For Modification Myth

// Does not change the array
for (int x : arr) {
    x = 0;
}

Use an index-based loop to modify elements.

Starting Max at 0

// Risky if all values are negative
int max = 0;

// Safer
int max = nums[0];

Debug this code

int[] ranges = {20, 25, 30};
for (int i = 0; i <= ranges.length; i++) {
    System.out.println(ranges[i]);
}

Bug: the loop goes one step too far. Change i <= ranges.length to i < ranges.length.

9. AP-Style Multiple Choice

1. Which expression accesses the last element of arr?

Answer: arr[arr.length - 1]

2. What is the output?

int[] a = {2, 4, 6};
System.out.println(a.length);

Answer: 3

3. Which loop can safely modify every element of an int[]?

Answer: an index-based for loop.

for (int i = 0; i < arr.length; i++) {
    arr[i] = arr[i] * 2;
}

4. What value should a failed search commonly return when searching for an index?

Answer: -1, because it is not a valid array index.

5. Why should max often start as nums[0] instead of 0?

If all values are negative, starting max at 0 gives an answer that is not even in the array.

10. AP-Style FRQ Practice

FRQ A: Average Range

Write a static method averageRange that accepts a double[] ranges and returns the average of all values.

public static double averageRange(double[] ranges)

Show sample solution

public static double averageRange(double[] ranges) {
    double total = 0;
    for (double r : ranges) {
        total += r;
    }
    return total / ranges.length;
}

FRQ B: Best Angle

Write a static method bestAngle that accepts parallel arrays angles and ranges. Return the angle that produced the greatest range.

public static double bestAngle(double[] angles, double[] ranges)

Show sample solution

public static double bestAngle(double[] angles, double[] ranges) {
    int bestIndex = 0;
    for (int i = 1; i < ranges.length; i++) {
        if (ranges[i] > ranges[bestIndex]) {
            bestIndex = i;
        }
    }
    return angles[bestIndex];
}

FRQ C: Count Under Threshold

Write a method that returns the number of race times below a target time.

public static int countUnder(double[] times, double target)

Show sample solution

public static int countUnder(double[] times, double target) {
    int count = 0;
    for (double t : times) {
        if (t < target) {
            count++;
        }
    }
    return count;
}

11. End-of-Unit Project: Physics Launch Analysis

Students will analyze launch-angle data using arrays and standard algorithms.

Required Data

double[] angles = {15, 20, 25, 30, 35, 40, 45};
double[] ranges = {18.4, 24.9, 29.8, 31.2, 30.7, 27.1, 22.8};

Required Methods

averageRange
maxRange
bestAngle
countAbove
printTable

Extension

Add a method that calculates theoretical range from launch speed and angle, stores the results in an array, then compares measured and theoretical values.

Starter Code

public class LaunchAnalysis {
    public static void main(String[] args) {
        double[] angles = {15, 20, 25, 30, 35, 40, 45};
        double[] ranges = {18.4, 24.9, 29.8, 31.2, 30.7, 27.1, 22.8};

        printTable(angles, ranges);
        System.out.println("Average range: " + averageRange(ranges));
        System.out.println("Best angle: " + bestAngle(angles, ranges));
    }

    public static void printTable(double[] angles, double[] ranges) {
        for (int i = 0; i < angles.length; i++) {
            System.out.println(angles[i] + " degrees: " + ranges[i] + " m");
        }
    }

    public static double averageRange(double[] ranges) {
        double total = 0;
        for (double r : ranges) {
            total += r;
        }
        return total / ranges.length;
    }

    public static double bestAngle(double[] angles, double[] ranges) {
        int bestIndex = 0;
        for (int i = 1; i < ranges.length; i++) {
            if (ranges[i] > ranges[bestIndex]) {
                bestIndex = i;
            }
        }
        return angles[bestIndex];
    }
}

Submission checklist: working code, at least three methods, correct array traversal, one written trace of a loop, and a short explanation of why arrays were useful.

Teacher Notes

Skill	Evidence
Array creation	Student can create arrays using both `new` and initializer lists.
Traversal	Student can choose between index-based and enhanced-for loops.
Algorithms	Student can write sum, average, max, count, and search algorithms.
Debugging	Student identifies off-by-one and invalid-index errors.
AP Readiness	Student can trace array loops and write short FRQ-style methods.