Algorithms with
Selection & Repetition

Master the building blocks of program logic: if/else decisions, loop structures, and how to combine them to solve problems algorithmically.

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. Every Java program you write encodes an algorithm: a precise sequence of instructions the computer follows.

Algorithms gain their power from two key control structures: selection (choosing different paths) and repetition (looping until a condition is met).

Selection: Making Decisions

Selection statements let your program choose between paths based on a Boolean condition. In Java, the primary selection constructs are if, if/else, and if/else if/else.

Repetition: Looping Structures

Repetition statements execute a block of code multiple times as long as a Boolean condition holds. Java provides three loop types, each suited to different scenarios.

while Loop

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

for Loop

Compact syntax: init, condition, update in one line. Ideal when the number of iterations is known.

for-each Loop

Iterates over every element in an array or collection. No index variable needed: read-only traversal.

Core Rule: Boolean Expressions

Every selection and loop in Java is controlled by a Boolean expression: an expression that evaluates to true or false. Understanding these is the key to controlling program flow.

1

Relational operators: ==, !=, <, >, <=, >= compare two values and return a boolean.

2

Logical operators: && (AND), || (OR), ! (NOT) combine or negate Boolean values.

3

Short-circuit evaluation: Java evaluates && and || left to right and stops as soon as the result is determined.

Example: x > 0 && x < 100 is true only when x is between 1 and 99 inclusive. If x > 0 is false, the second part is never evaluated.

Anatomy of if / else if / else

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

Key insight: Order matters. If we checked score >= 70 first, a score of 95 would incorrectly get "C" instead of "A".

Anatomy of while and for Loops

while loop

int i = 0;
while (i < 5) {
  System.out.print(i);
  i++;
}
// 01234

for loop

for (int i = 0; i < 5; i++) {
  System.out.print(i);
}

// 01234

Key Distinction: Choosing the Right Loop

	while	for	for-each
Iterations known?	Not necessarily	Usually yes	All elements
Condition tested	Before each pass	Before each pass	Automatic
Index access?	Yes (manual)	Yes (built-in)	No
Can modify array?	Yes	Yes	Not safely
Best for	Sentinel loops, input	Counting, indexed ops	Read-only traversal

How to Write an Algorithm

1

Identify the problem. What input do you have? What output do you need?

2

Determine if selection is needed. Does the logic branch based on a condition? Use if/else.

3

Determine if repetition is needed. Does a block of code repeat? Choose while, for, or for-each.

4

Trace through edge cases. What happens with \(n = 0\)? Empty arrays? Negative values?

5

Verify termination. Every loop must have a condition that eventually becomes false, or the program will loop forever.

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];       // assume first is max
    for (int i = 1; i < arr.length; i++) {
        if (arr[i] > max) {  // selection inside loop
            max = arr[i];
        }
    }
    return max;
}

Example 2: Count Even Numbers

public static int countEvens(int[] arr) {
    int count = 0;
    for (int val : arr) {     // for-each loop
        if (val % 2 == 0) { // selection
            count++;
        }
    }
    return count;
}

Trace with arr = {3, 8, 5, 12, 7}:

val	val % 2 == 0?	count
3	false	0
8	true	1
5	false	1
12	true	2
7	false	2

Example 3: Classify Temperatures

Print a label for each temperature in an array: cold, warm, or hot.

for (int temp : temps) {
    if (temp < 50) {
        System.out.println(temp + " Cold");
    } else if (temp < 80) {
        System.out.println(temp + " Warm");
    } else {
        System.out.println(temp + " Hot");
    }
}

For temps = {30, 65, 90}, the output is: 30 Cold, 65 Warm, 90 Hot.

The Sentinel Loop Pattern

A sentinel loop repeats until a special value (the sentinel) is encountered. This is the classic use case for a while loop because the number of iterations is unknown.

Scanner in = new Scanner(System.in);
int sum = 0;
int val = in.nextInt();

while (val != -1) {  // -1 is the sentinel
    sum += val;
    val = in.nextInt();
}
System.out.println("Sum: " + sum);

Visualizing Loop + Selection

Common Mistakes to Avoid

Infinite Loop

Forgetting to update the loop variable (e.g., missing i++) causes the condition to remain true forever.

Off-by-One Error

Using <= instead of < (or vice versa) causes the loop to execute one too many or one too few times.

== with Strings

Using == to compare Strings checks reference equality, not content. Always use .equals().

Dangling else

An else binds to the nearest if. Without braces, the structure may not match your intent.

Unreachable Code

Placing conditions in the wrong order (e.g., checking >= 70 before >= 90) makes later branches unreachable.

Summary: Selection vs. Repetition

	Selection	Repetition
Purpose	Choose a path	Repeat a block
Keywords	if, else if, else	while, for, for-each
Executes body	At most once per branch	Zero or more times
Controlled by	Boolean expression	Boolean expression
Nesting	Can contain loops	Can contain if/else
AP focus	Multi-way branching	Array traversal, accumulation

Question 1 of 5

Consider the following code segment:

int x = 7;
if (x > 10) {
  System.out.print("A");
} else if (x > 5) {
  System.out.print("B");
} else {
  System.out.print("C");
}

▼ Tap to read passage

What is printed when this code executes?

Since \( x = 7 \), the first condition x > 10 is false. The second condition x > 5 is true, so "B" is printed. The else branch is skipped.

Question 2 of 5

Consider the following code segment:

int sum = 0;
for (int i = 1; i <= 4; i++) {
sum += i;
}
System.out.print(sum);

▼ Tap to read passage

What value is printed?

The loop runs for \( i = 1, 2, 3, 4 \). The sum is \( 1 + 2 + 3 + 4 = 10 \). If the condition were i <= 5, the answer would be 15.

Question 3 of 5

Which loop is most appropriate when you need to traverse an array without modifying it and you do not need the index?

The for-each loop is designed for read-only traversal when you don't need the index. It's cleaner and less error-prone than a for or while loop in this scenario.

Question 4 of 5

Consider the following code segment:

int k = 0;
while (k < 10) {
System.out.print(k + " ");
}

▼ Tap to read passage

What happens when this code executes?

The variable k is never incremented inside the loop body, so the condition k < 10 remains true forever. This is a classic infinite loop error: always ensure the loop variable is updated.

Question 5 of 5

Consider the following code segment:

int[] arr = {5, 12, 3, 8, 1};
int count = 0;
for (int val : arr) {
  if (val > 4) {
    count++;
  }
}
System.out.print(count);

▼ Tap to read passage

What value is printed?

The values greater than 4 are 5, 12, and 8 (three values). The values 3 and 1 fail the condition. So \( \text{count} = 3 \).

Algorithms withSelection & Repetition

What Is an Algorithm?

Selection: Making Decisions

Repetition: Looping Structures

Core Rule: Boolean Expressions

Anatomy of if / else if / else

Anatomy of while and for Loops

Key Distinction: Choosing the Right Loop

How to Write an Algorithm

Example 1: Find the Maximum

Example 2: Count Even Numbers

Example 3: Classify Temperatures

The Sentinel Loop Pattern

Visualizing Loop + Selection

Common Mistakes to Avoid

Summary: Selection vs. Repetition

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Algorithms with
Selection & Repetition