2.1 Algorithms with Selection and Repetition

1. The three building blocks

An algorithm is a step-by-step process that solves a problem or completes a task. Every algorithm, from a recipe to a video game, is built from three building blocks: sequencing, selection and repetition 2.1.A.1.

Building block	What it does	Everyday example	Java tool (later in Unit 2)
Sequencing	Runs steps one after another, in order	Put on socks, then shoes	Statements in order
Selection	Makes a decision, then picks which steps run	If it is raining, take an umbrella	if, if-else
Repetition	Repeats steps until a goal is reached	Keep stirring until the sugar dissolves	while, for

Algorithms get selection through decision making and repetition through looping 2.1.A.2. Here is an everyday algorithm, written in plain language, that uses all three:

1. Take the cap off the bottle. (sequencing)
2. If the bottle is dirty, rinse it. (selection)
3. Hold the bottle under the fountain until it is full. (repetition)
4. Put the cap back on. (sequencing)

2. Selection: a true or false decision

Selection happens when the way an algorithm continues depends on a true or false decision 2.1.A.3. The question must have exactly two possible answers. “Is the temperature above 25 degrees?” works. “What is the temperature?” does not, because its answer is a number, not true or false.

Decision	If true	If false
Is the temperature above 25?	Wear shorts	Wear jeans

The same decision in Java (you will learn the if statement in Topic 2.3):

int temperature = 31;
if (temperature > 25) {
    System.out.println("Wear shorts");
} else {
    System.out.println("Wear jeans");
}

Output:

Wear shorts

Watch out: only one of the two paths runs. The program never prints both lines.

3. Repetition: repeat until the desired outcome

In repetition, the same process runs again and again, and it stops once the result you want has been reached 2.1.A.4. In plain language: “Water the plant one cup at a time until the soil moisture reaches 50.”

int moisture = 20;
int cups = 0;
while (moisture < 50) {
    moisture += 15;
    cups++;
}
System.out.println("Cups of water: " + cups);

Output:

Cups of water: 2

Trace it. Each row is one check of the decision “is moisture still below 50?”

Check	moisture < 50?	moisture after the step	cups
1	20 < 50 is true	35	1
2	35 < 50 is true	50	2
3	50 < 50 is false	(stop)	2

Watch out: the repeated step must move toward the desired outcome. If the plant never got any water, the moisture would stay at 20 and the process would never end.

4. Order changes the outcome

Where you place each step of sequencing, selection and repetition helps decide what the algorithm produces, so changing the order can change the result 2.1.A.5. Look at two versions of a game rule. A player has 90 points, earns 15 bonus points, and levels up at 100 points.

Version A checks first, then adds the bonus:

int points = 90;
if (points >= 100) {
    System.out.println("Level up!");
}
points += 15;
System.out.println("Points: " + points);

Output:

Points: 105

Version B adds the bonus first, then checks:

int points = 90;
points += 15;
if (points >= 100) {
    System.out.println("Level up!");
}
System.out.println("Points: " + points);

Output:

Level up!
Points: 105

Same steps, same final points, different behavior. In Version A the decision saw the old value (90), so the player never leveled up.

5. From written steps to code

Writing the algorithm in plain language first helps you choose the right building blocks. Problem: a student saves 12 dollars each week for headphones that cost 50 dollars. How many weeks does it take, and how much extra money is left?

1. Set saved to 0 and weeks to 0.
2. Repeat until saved is at least 50: add 12 to saved and add 1 to weeks.
3. Print the number of weeks.
4. If saved is more than 50, print the extra money.

Each numbered step becomes code:

int saved = 0;
int weeks = 0;
while (saved < 50) {
    saved += 12;
    weeks++;
}
System.out.println("Weeks: " + weeks);
if (saved > 50) {
    System.out.println("Extra: " + (saved - 50));
}

Output:

Weeks: 5
Extra: 10

Notice the translation: “repeat until saved is at least 50” becomes “keep looping while saved is less than 50”. The loop continues while the opposite of the goal is true.