AP® Computer Science Principles · Big Idea 3 · Topic 3.3

Algorithms and Sequencing

An algorithm is a precise, ordered sequence of steps that solves a problem, built from three building blocks: sequencing, selection, and iteration. Change the order and you often change or break the result.

Sequencing just means doing steps in a specific order, one after another. It sounds obvious, but order is the whole game: the same steps run in a different order can produce a different answer or stop working altogether. That is because most steps depend on the state left behind by the steps before them. A step that halves total only makes sense once total already holds a meaningful number. Swap it earlier and the rest of the algorithm is now working with the wrong value.

Every algorithm, no matter how complex, is built from three ingredients: sequencing (steps in order), selection (branching with if/else based on a condition), and iteration (repeating steps with a loop). Combine them and you can express any process a computer can carry out. The same algorithm can be written three ways without changing its meaning: as natural language ('set total to 0, add the first number, add the second number, divide by 2'), as a flowchart (boxes and arrows showing the order and any branches or loops), or as pseudocode (structured, code-like lines that are not tied to any real programming language). All three describe the identical sequence of steps.

This matters because an algorithm is the idea, not the implementation. A program is one specific expression of an algorithm, written in a real language like Python or Java, that a computer can actually run. The same algorithm can become many different programs, and a badly sequenced algorithm will produce a buggy program no matter how carefully it is coded, which is why the next step in the course is learning to trace and test these sequences carefully.

Key terms

Algorithm
A precise, ordered sequence of steps that solves a problem or completes a task.
Sequencing
Carrying out steps one after another in a specific, meaningful order.
Selection
Branching behavior where a condition decides which of two or more paths an algorithm takes.
Iteration
Repeating one or more steps, usually until a condition is met.
Pseudocode
Structured, code-like writing that expresses an algorithm's steps without following a specific programming language's syntax.

Watch it explained

  1. How it worksHow do sequencing, selection, and iteration combine to build any algorithm at all?
  2. How it worksWalk me through one algorithm expressed as natural language, as a flowchart, and as pseudocode.
  3. Worked exampleTrace the sequence that sets total to 0, adds 8, adds 12, and then halves total.
  4. Common mistakeWhy isn't an algorithm the same thing as a program?

Check yourself

Your turn1 of 2
An algorithm sets total to 0, then adds 35, then adds 33, then halves the result. What value does total end with?

End of topic.