Selection & Iteration
Algorithms

Master the building blocks of programming: conditional logic and loop structures that power every Java application.

AP Computer Science A

What Is an Algorithm?

An algorithm is a finite, step-by-step procedure for solving a problem or performing a computation. In Java, algorithms are built from three fundamental control structures: sequence, selection, and iteration.

Sequence

Statements execute one after another, top to bottom.

Selection

Choose which statements to execute based on a condition.

Iteration

Repeat statements while a condition remains true.

Selection: Branching Logic

Selection statements let your program make decisions. Java evaluates a boolean expression and executes different code blocks depending on whether the result is true or false.

Iteration: Loop Structures

Iteration repeats a block of code while a condition holds true. Java provides three main loop constructs, each suited to different situations.

while loop

Tests condition before each iteration. May execute zero times if condition is initially false.

for loop

Combines init, condition, and update in one line. Ideal when the number of iterations is known.

for-each loop

Iterates over every element of an array or collection. Cannot modify index or skip elements.

The while Loop Pattern

int count = 0;
while (count < 5) {
    System.out.println(count);
    count++;
}

The for Loop Pattern

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

1

Init: int i = 0 : executed once before the loop starts.

2

Test: \(i < \text{arr.length}\) : checked before every iteration.

3

Update: i++ : executed after the loop body each time.

Core Rule: Nesting Selection Inside Iteration

The real power emerges when you combine selection and iteration. A loop traverses data, and an if statement inside the loop filters, counts, or transforms each element conditionally.

// Count positive numbers in an array
int count = 0;
for (int num : arr) {
    if (num > 0) {
        count++;
    }
}
System.out.println("Positives: " + count);

while vs for: When to Use Each

	while loop	for loop
Iterations known?	Not necessarily	Usually known
Init / Update	Separate statements	Built into header
Use case	Sentinel values, user input	Array traversal, counting
Off-by-one risk	Higher (manual update)	Lower (compact header)
Infinite loop risk	Higher (forget update)	Lower

How to Implement an Algorithm

1

Identify the task: What are you computing? (Sum, max, count, search, filter?)

2

Choose data structure: Array, ArrayList, or single variables?

3

Pick the loop type: Use for when count is known, while for sentinel-controlled, for-each for read-only traversal.

4

Add selection inside: Use if / else if / else to handle conditions on each element.

5

Trace and test: Manually trace through 2-3 iterations to verify correctness and edge cases.

Example 1: Find the Maximum

Given an array of integers, find and return the largest value.

public static int findMax(int[] arr) {
    int max = arr[0];
    for (int i = 1; i < arr.length; i++) {
        if (arr[i] > max) {
            max = arr[i];
        }
    }
    return max;
}

Key insight: Initialize max to the first element (not 0 or Integer.MIN_VALUE unnecessarily). Then iterate starting at index 1, comparing each element with selection.

Example 2: The Accumulator Pattern

Compute the average of all even numbers in an array.

int sum = 0, count = 0;
for (int num : arr) {
    if (num % 2 == 0) {
        sum += num;
        count++;
    }
}
double avg = (double) sum / count;

Two accumulators work together: sum tracks the running total, count tracks how many qualify. The selection inside the loop filters for even numbers using the modulo operator. Important: Before dividing, always check if count is greater than 0 to avoid a division-by-zero error!

Example 3: Nested Iteration

Check if an array contains any duplicate values using nested loops.

public static boolean hasDuplicates(int[] arr) {
    for (int i = 0; i < arr.length; i++) {
        for (int j = i + 1; j < arr.length; j++) {
            if (arr[i] == arr[j]) {
                return true;
            }
        }
    }
    return false;
}

Example 4: String Traversal

Count the number of vowels in a given String.

public static int countVowels(String s) {
    int count = 0;
    String vowels = "aeiouAEIOU";
    for (int i = 0; i < s.length(); i++) {
        if (vowels.indexOf(s.charAt(i)) != -1) {
            count++;
        }
    }
    return count;
}

Strings are traversed using .charAt(i) inside a for loop (you cannot use for-each on a String). The selection checks membership using indexOf.

Sentinel-Controlled Loops

A sentinel value is a special input that signals the loop to stop. This pattern uses a while loop because the number of iterations is unknown in advance.

Scanner sc = new Scanner(System.in);
int total = 0;
int input = sc.nextInt();

while (input != -1) {  // -1 is the sentinel
    total += input;
    input = sc.nextInt();
}

Common Mistakes

✕ Infinite Loop

Forgetting to update the loop variable inside a while loop causes it to run forever.

✕ Off-by-One

Using \(\le\) instead of \(<\) with arr.length causes an ArrayIndexOutOfBoundsException.

✕ Misplaced Selection

Placing an if statement outside the loop when it should be inside, causing it to check only the last element.

✕ Using == on Strings

Comparing Strings with \(==\) checks reference equality, not content. Use .equals() instead.

✕ Modifying During For-Each

The loop variable is a copy. Reassigning it (e.g., num = 0) won't change the original array. For objects, you can still modify the object's state via its methods.

Algorithm Patterns Summary

Pattern	Loop Type	Selection	Example
Find max/min	for	if (comparison)	Largest value
Count/filter	for-each	if (test)	Count evens
Accumulate	for-each	if (qualify)	Sum positives
Search	for / while	if (match)	Find index
Sentinel input	while	if (validate)	Read until -1
Duplicate check	nested for	if (\(==\))	Any repeats?

Question 1 of 5

Consider the following code segment:

int x = 0;
for (int i = 1; i <= 4; i++) {
    if (i % 2 == 0) {
        x += i;
    }
}
System.out.println(x);

▼ Tap to read code

What is printed when this code segment is executed?

The loop runs for \( i = 1, 2, 3, 4 \). Only even values of \(i\) pass the selection: \( 2 + 4 = 6 \).

Question 2 of 5

Which loop type is most appropriate when the number of iterations is not known before the loop begins?

A while loop is ideal for sentinel-controlled or input-driven situations where the iteration count is unknown. A for loop is preferred when the count is known; for-each traverses a fixed collection.

Question 3 of 5

Consider the following code segment:

int[] arr = {3, 7, 2, 9, 5};
int result = arr[0];
for (int k = 1; k < arr.length; k++) {
    if (arr[k] < result) {
        result = arr[k];
    }
}
System.out.println(result);

▼ Tap to read code

What value is printed?

The algorithm finds the minimum value. It initializes \(result\) to 3, then compares: \( 7 > 3 \) (no change), \( 2 < 3 \) (result becomes 2), \( 9 > 2 \) (no), \( 5 > 2 \) (no). Final answer: 2.

Question 4 of 5

Consider the following code segment:

int n = 5;
int count = 0;
while (n > 1) {
    if (n % 2 == 0) {
        n = n / 2;
    } else {
        n = 3 * n + 1;
    }
    count++;
}
System.out.println(count);

▼ Tap to read code

What value of count is printed?

Trace: \( n=5 \) (odd) → \(16\), \( \text{count}=1 \). \( n=16 \) (even) → \(8\), \( \text{count}=2 \). \( n=8 \) → \(4\), \( \text{count}=3 \). \( n=4 \) → \(2\), \( \text{count}=4 \). \( n=2 \) → \(1\), \( \text{count}=5 \). Loop exits because \(n=1\) is not \(> 1\). Answer: 5.

Question 5 of 5

What is the main risk of placing the loop variable update inside an if statement within a while loop?

If the update statement (e.g., i++) is inside an if block, and the condition is never true, the loop variable never changes and the while condition stays true forever, creating an infinite loop.

Selection & IterationAlgorithms

What Is an Algorithm?

Selection: Branching Logic

Iteration: Loop Structures

The while Loop Pattern

The for Loop Pattern

Core Rule: Nesting Selection Inside Iteration

while vs for: When to Use Each

How to Implement an Algorithm

Example 1: Find the Maximum

Example 2: The Accumulator Pattern

Example 3: Nested Iteration

Example 4: String Traversal

Sentinel-Controlled Loops

Common Mistakes

Algorithm Patterns Summary

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Selection & Iteration
Algorithms