AP CSP Unit 3 Essentials: Key Terms & Core Concepts

Key Concept 1

Programs are built from sequencing, selection, and iteration

Every algorithm is assembled from three foundations: sequencing (running steps in order), selection (conditionals that choose which code runs based on Boolean expressions), and iteration (loops that repeat code). These operate on variables that store values updated by assignment, using arithmetic (including MOD), string, and logical operations. Combining these building blocks is how you develop a working algorithm.

Variables Selection Iteration

Key Concept 2

Lists and procedures manage complexity through abstraction

As programs grow, abstraction keeps them manageable. A list holds many values in one indexed collection that you can traverse and search — with linear search on any list, or the much faster binary search on sorted data. Procedures (with parameters and return values) name and reuse blocks of behavior, and libraries (accessed through an API) share procedures across programs. Abstraction lets you use these pieces without worrying about their internal detail.

Lists & Search Procedures Abstraction

Key Concept 3

Programs use randomness and simulation — and algorithms have limits

Programs can generate random values to add variability and build simulations that model real phenomena more cheaply and safely than real experiments (though only as well as their assumptions). Not all algorithms are equal: algorithmic efficiency describes how run time grows with input size — a key reason binary search beats linear search at scale. And some problems are undecidable: no algorithm can always produce a correct answer, showing that computing has fundamental limits.

Simulation Efficiency Undecidable Problems

Variable

A named location that stores a value which can change as the program runs.

Building Blocks

Assignment

Storing a value in a variable (for example, x ← 5).

Building Blocks

Data abstraction

Managing complexity by hiding detail, such as using a list instead of many variables.

Building Blocks

MOD operator

An operator that returns the remainder of a division (17 MOD 5 = 2).

Building Blocks

String

An ordered sequence of characters; strings can be concatenated (joined).

Building Blocks

Boolean value

A value that is either true or false.

Logic

Relational operator

An operator that compares two values and yields a Boolean (=, ≠, <, >, ≤, ≥).

Logic

Logical operator

AND, OR, or NOT, used to combine or reverse Boolean expressions.

Logic

Conditional (selection)

An if / if-else statement that chooses which code runs based on a condition.

Control

Nested conditional

A conditional placed inside another conditional.

Control

Iteration

Repeating a block of code using a count-controlled or condition-controlled loop.

Control

Algorithm

A finite sequence of step-by-step instructions built from sequencing, selection, and iteration.

Control

List

An ordered collection of elements accessed by index.

Lists

Index

The position of an element within a list.

Lists

Traversal

Visiting each element of a list in order, usually with a loop.

Lists

Linear search

Checking each element of a list in order until the target is found.

Binary search

Repeatedly halving a sorted list to find a target efficiently.

Procedure

A named, reusable group of statements that may take parameters and return a value.

Procedures

Parameter

A variable in a procedure's definition that receives an argument when called.

Procedures

Library / API

A collection of reusable procedures, and the description of how to use them.

Procedures

Random value

A value produced by a generator such as RANDOM(a, b), returning an integer from a to b inclusive.

Programs

Simulation

A program that models a real-world phenomenon.

Programs

Algorithmic efficiency

A measure of how an algorithm's run time grows as the input size grows.

Programs

Undecidable problem

A problem for which no algorithm can always give a correct yes-or-no answer.

Programs