TOPIC 3.1
Variables and Assignments
◊ AP CSP pseudocode — the arrow ← means "assign"
score ← 100 stores 100 in score
score ← score + 1 reads old value, adds 1
A variable names a value
A variable is a named location that
holds a value you can read and change.
Assignment evaluates the RIGHT side,
then stores it in the LEFT variable.
Input & output
n ← INPUT()
gets a value from the user
DISPLAY(n)
shows the value, followed by a space
a ← expression assigns the evaluated right side into the variable a.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.2
Data Abstraction
Manage complexity with abstraction
A variable is a simple abstraction — one
name that stands for a value.
A LIST bundles MANY values under one
name so you don't need dozens of
separate variables.
Why it helps
Abstraction lets you focus on WHAT data
represents, not how it's stored.
A clear name (like temperatures) makes
a program easier to read and change.
Lists let one algorithm work on any amount of data.
// one list holds all the scores instead of score1, score2, score3...
scores ← [88 , 92 , 75 , 100 ]
Data abstraction (variables & lists) hides detail and manages complexity.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.3
Mathematical Expressions
// arithmetic operators
+ - * /
a MOD b remainder of a ÷ b
17 / 5 → 3.417 MOD 5 → 2// order of operations applies
MOD is everywhere on the exam
n MOD 2 = 0 → n is EVEN.
n MOD 2 = 1 → n is ODD.
MOD wraps values around a range
(clock arithmetic, cycling colors).
MOD shares precedence with * and /.
Expressions produce a single value
An expression combines values, variables, and operators, and evaluates to ONE result you can store or display.
Know MOD (remainder) : n MOD 2 tests even/odd; 17 MOD 5 = 2.
The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.4
Strings
A string is ordered text
A sequence of characters, such as
a word or a sentence.
CONCATENATION joins strings together
end to end.
LENGTH gives the number of characters.
// building a greeting
name ← "Ada"
msg ← "Hi, " + name
DISPLAY(msg)
→ Hi, Ada
LEN("Ada") = 3
Substrings & procedures
Different languages use different string procedures (substring, position, length). On the exam, read the given procedure descriptions.
A string is ordered text; concatenation (+) joins strings together.
The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.5
Boolean Expressions
TRUTH TABLE
A B A AND B A OR B
T T T T
T F F T
F T F T
F F F F
AND · OR · NOT
A Boolean expression evaluates to true
or false.
AND: true only if BOTH are true.
OR: true if AT LEAST ONE is true.
NOT: flips true ↔ false.
Relational ops: = ≠ > < ≥ ≤
Boolean expressions use AND, OR, NOT and relational operators to give true/false.
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TOPIC 3.6
Conditionals
IF (age ≥ 18)
{
DISPLAY("Adult" )
}
ELSE
{ DISPLAY("Minor" ) }
Selection chooses a path
IF runs its block only when the
condition is true.
ELSE gives the alternative path when
the condition is false.
Exactly one of the two blocks runs.
Conditionals create branching
Different inputs lead the program down different paths — the basis of decision-making in every algorithm.
IF runs when true; ELSE runs when false — selection chooses a path.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.7
Nested Conditionals
IF (score ≥ 90)
{ grade ← "A" }
ELSE
{ IF (score ≥ 80)
{ grade ← "B" }
ELSE { grade ← "C" }
}
Conditionals inside conditionals
A conditional placed inside another
lets you choose among MANY options.
The inner IF is only reached when the
outer condition already decided a path.
Order the conditions carefully so the
right branch is chosen.
Nested conditionals select among many options — order the conditions with care.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.8
Iteration
// repeat a fixed number of times
REPEAT 5 TIMES
{ DISPLAY("Hi" ) }
// repeat until a condition holds
REPEAT UNTIL (x = 0) { ... }
Two kinds of loops
REPEAT n TIMES: runs exactly n times.
REPEAT UNTIL: runs until the condition
becomes true.
If the condition never becomes true → infinite loop.
Iteration avoids repeating yourself
A loop repeats a block of statements, so one short piece of code can process many items or run many times.
REPEAT UNTIL checks its condition before each pass — make sure the loop moves toward stopping.
REPEAT n TIMES counts; REPEAT UNTIL loops until a condition is true.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.9
Developing Algorithms
An algorithm is a clear recipe
A finite sequence of steps that solves
a problem or accomplishes a task.
Built from the three building blocks:
SEQUENCING, SELECTION, ITERATION.
Different algorithms can solve the same problem.
Comparing algorithms
Two algorithms are EQUIVALENT if they
always produce the same result.
Choose based on clarity, speed, and
how well they handle edge cases.
Plan with pseudocode or a flowchart first.
Combine the building blocks
Most algorithms mix sequencing, selection, and iteration — e.g. loop through a list and use an IF to act on each item.
Algorithms combine sequencing, selection, and iteration to solve a problem.
The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.10
Lists
nums ← [12, 5, 8, 20] AP CSP lists start at index 1
12 1
5 2
8 3
20 4
nums[1] → 12
LENGTH(nums) → 4
// list procedures
APPEND(nums, 7) add to end
INSERT(nums, 2, 9) at index 2
REMOVE(nums, 3) delete index 3
LENGTH(nums) size of list
Traverse with FOR EACH
FOR EACH n IN nums
{ sum ← sum + n }
Visits every element in order — great
for sum, count, min/max, and search.
AP CSP lists are 1-indexed ; traverse with FOR EACH, size with LENGTH.
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TOPIC 3.11
Binary Search
Halve the search each step
Check the MIDDLE element. If it's the
target, done. If the target is smaller,
search the LEFT half; if larger, the RIGHT.
REQUIRES the list to be SORTED first.
Much faster than linear
Each step throws away HALF the remaining
items.
1,000 items → about 10 checks;
1,000,000 → about 20 checks.
Search space halves each step:
16
8
4
2
1
16 → 8 → 4 → 2 → 1: found in ~4 steps instead of up to 16.
Binary search halves a SORTED list each step — far faster than checking one by one.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.12
Calling Procedures
result ← max (8 , 3 ) // call max with arguments 8 and 3 return value
procedure name
arguments
A procedure = a named block
Also called a method or function.
CALLING it runs its code.
ARGUMENTS are the values you pass in;
they fill the procedure's PARAMETERS.
Return values
A procedure may RETURN a value that you
store or use in an expression.
You can call a procedure without knowing
how it works inside — that's abstraction.
Calling a procedure runs its code with the arguments you pass in.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.13
Developing Procedures
PROCEDURE area (w, h)
{
a ← w * h
RETURN (a)
}
DISPLAY(area(4, 5)) → 20
Procedural abstraction
Writing a procedure lets you name a task
and reuse it — no copy-pasting code.
Benefits: less repetition, easier to read,
test, and fix in ONE place.
PARAMETERS generalize it to work on
many inputs.
Writing procedures with parameters reduces repetition and manages complexity.
The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.14
Libraries
Reuse code others wrote
A LIBRARY is a collection of procedures
you can use in your own program.
An API describes each procedure's
behavior, inputs, and outputs.
Why use libraries?
• Save time — don't reinvent the wheel.
• Use tested, reliable code.
• Focus on YOUR program's unique logic.
You call library procedures without seeing inside.
Abstraction at a larger scale
Libraries are procedural abstraction taken further: a whole toolbox of ready-made procedures behind simple names.
Reading the documentation tells you how to call each one — what to pass and what you get back.
A library is reusable procedures; its API documents how to call them.
The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.15
Random Values
RANDOM (1 , 6 ) // returns 1, 2, 3, 4, 5, or 6 — each equally likely // RANDOM(a, b) includes BOTH endpoints a and b
Generating randomness
RANDOM(a, b) returns a random integer
from a to b, inclusive.
Used for games, shuffling, sampling,
and simulations.
Every value in the range is equally likely.
Different runs, different output
A program using RANDOM can produce a
DIFFERENT result each time it runs.
This adds unpredictability and variety —
but makes testing harder to reproduce.
Great for games; central to simulations (3.16).
RANDOM(a, b) returns an equally-likely integer from a to b, inclusive.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.16
Simulations
A model of the real world
A simulation is a program that models a
real phenomenon to study it.
It SIMPLIFIES reality — it can't include
every detail, so it makes assumptions.
Random values give realistic variation.
Why simulate?
Simulations are useful when the real
thing is too costly, slow, dangerous,
or impossible to test directly.
Examples: weather, crash tests, disease
spread, rolling dice thousands of times.
Results guide decisions — but a model is not reality
A simulation's accuracy depends on its assumptions. Better models give better predictions, but always simplify.
A simulation models reality with simplifying assumptions — safer and cheaper than the real thing.
The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.17
Algorithmic Efficiency
Efficiency = work vs. input size
Efficiency estimates how the number of
steps grows as the input grows.
REASONABLE time: steps grow like a
polynomial (n, n², n³ …).
UNREASONABLE: grows exponentially (2ⁿ).
Faster approaches
Binary search (halving) beats linear
search (one by one).
A HEURISTIC gives a good-enough answer
quickly when the exact one is too slow.
Fewer nested loops usually means faster.
Reasonable vs. unreasonable time
Some problems can be solved in reasonable time; others (exponential) become impractical as input grows large.
Reasonable time grows polynomially ; exponential growth becomes impractical — heuristics help.The Review Hub · AP Computer Science Principles · Big Idea 3
TOPIC 3.18
Undecidable Problems
Some problems cannot be solved by ANY algorithm
An UNDECIDABLE problem is one for which no algorithm can give a correct yes/no answer for EVERY possible
input. This is a fundamental LIMIT of computation — not just a matter of needing a faster computer.
Decidable vs. undecidable
DECIDABLE: an algorithm always gives the
correct answer (e.g. "is n even?").
UNDECIDABLE: no algorithm can work for
all inputs.
Not the same as "hard"
Undecidable ≠ slow or difficult.
A slow problem still HAS a solution;
an undecidable one provably does not.
There is no general "will this program halt?" test.
An undecidable problem has no algorithm that solves it correctly for every input.
The Review Hub · AP Computer Science Principles · Big Idea 3
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