AP CSP Unit 3 Cheat Sheet: Algorithms & Programming

The basics

What it covers: Building programs from variables, expressions, conditionals, iteration, lists, and procedures, and reasoning about algorithms, searching, efficiency, and computability.

Exam weight: Big Idea 3 is about 30–35% of the AP CSP multiple-choice exam — the most of any big idea.

The big question: How do we design, express, and evaluate algorithms and programs that solve problems?

Computational thinking practices: Computational Solution Design, Algorithms & Program Development, Abstraction, Code Analysis, Computing Innovations, and Responsible Computing.

Key topics at a glance

Variables & Assignment

A variable stores a value; assignment (x ← value) updates it. Strings are character sequences that can be concatenated.

Expressions

Arithmetic (+, −, *, /, MOD = remainder). Boolean expressions use relational (=, ≠, <, >) and logical (AND, OR, NOT) operators.

Selection

Conditionals (if / if-else) choose which code runs. Nested conditionals test further conditions inside a branch.

Iteration

Loops repeat code — count-controlled (a set number of times) or condition-controlled (while/until a condition holds).

Algorithms

An algorithm is finite step-by-step instructions built from sequencing, selection, and iteration.

Lists

Lists hold ordered elements accessed by index. Operations: access, append, insert, remove, length. Traverse with a loop.

Searching

Linear search: check each element (any list). Binary search: halve a sorted list — much faster.

Procedures, Libraries & Limits

Procedures (with parameters/return) enable reuse & abstraction; libraries/APIs share them. Also: RANDOM, simulations, efficiency, and undecidable problems.

The key terms you must know

Variable / assignment — a named store of a value; x ← value updates it.
MOD — the remainder operator (17 MOD 5 = 2).
String / concatenation — a character sequence; joining strings end to end.
Boolean expression — evaluates to true or false.
Relational / logical operators — compare values (=, <, >) and combine Booleans (AND, OR, NOT).
Conditional (selection) — if / if-else chooses which code runs.
Nested conditional — a conditional inside another conditional.
Iteration (loop) — repeating code, count- or condition-controlled.
Algorithm — finite steps built from sequencing, selection, iteration.
List / index — an ordered collection accessed by position.
Linear search — check each element in order (any list).
Binary search — halve a sorted list; much faster.
Procedure / parameter — reusable named code; a parameter is its input variable.
Library / API — reusable procedures and how to use them.
Efficiency / undecidable — how run time grows; a problem no algorithm can always solve.

Key themes to remember

Every algorithm is sequencing, selection, and iteration. Master these three and their combinations.
Abstraction manages complexity. Lists group data; procedures and libraries group behavior for reuse.
Sorted data unlocks binary search. It is far faster than linear search, but only works when the list is sorted.
Efficiency matters as input grows. Compare how the number of steps scales, not just whether it works.
Not everything is solvable. Some problems are undecidable — no algorithm can always answer them correctly.

Common exam traps

MOD is the remainder, not division. 17 MOD 5 = 2, not 3.
Binary search needs a sorted list. On unsorted data it can give wrong results — use linear search instead.
Watch the loop bounds. Off-by-one errors (running one too many or too few times) are common — trace carefully.
AND vs. OR. AND needs both true; OR needs only one. Mixing them changes which branch runs.
Parameter vs. argument. The parameter is in the definition; the argument is the value passed when calling.
A random range is usually inclusive. RANDOM(1, 6) can return 1 or 6, not just values in between.
Efficiency is about growth, not one run. A slower-looking algorithm may scale better for large inputs.