Cambridge IGCSE IGCSE & A-Level Sheet preview

Algorithms and Programming

AP Computer Science Principles · Topic 3

Train
Handout Vocabulary

Code below uses the AP CSP pseudocode – the exam's language-neutral reference. Assignment is written a ← expression, and list indices start at 1.

3.1

Variables and Assignments
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-1
To find specific solutions to generalizable problems, programmers represent and organize data in multiple ways.

AAP-1.A
Represent a value with a variable. [Skill 3.A]

  • AAP-1.A.1 A variable is an abstraction inside a program that can hold a value. Each variable has associated data storage that represents one value at a time, but that value can be a list or other collection that in turn contains multiple values.
  • AAP-1.A.2 Using meaningful variable names helps with the readability of program code and understanding of what values are represented by the variables.
  • AAP-1.A.3 Some programming languages provide types to represent data, which are referenced using variables. These types include numbers, Booleans, lists, and strings.
  • AAP-1.A.4 Some values are better suited to representation using one type of datum rather than another.

AAP-1.B
Determine the value of a variable as a result of an assignment. [Skill 4.B]

  • AAP-1.B.1 The assignment operator allows a program to change the value represented by a variable.

  • AAP-1.B.2 The exam reference sheet provides the "$\leftarrow$" operator to use for assignment. For example,

    Text:

    a ← expression

    Block:

    a ← expression

    evaluates expression and then assigns a copy of the result to the variable a.

  • AAP-1.B.3 The value stored in a variable will be the most recent value assigned. For example:

    a ← 1 b ← a a ← 2 display(b)

    still displays 1.

Source: College Board AP Course and Exam Description

A variable 变量 is a named place that holds a value. The assignment 赋值 operator stores the value on the right into the variable on the left:

A variable is a named store whose value can change A variable is a named store whose value can change

a ← 5
b ← a + 3      // b is now 8

A variable holds one value at a time; assigning again replaces it. Variables let a program store input, remember results, and reuse them.

Explore

Watch a variable hold and change its value

A variable is a named box that stores one value at a time. An assignment copies a value into the box; assigning again overwrites whatever was there.

Vocabulary Train
English Chinese Pinyin
variable 变量 biàn liàng
assignment 赋值 fù zhí
Exercise sheet
3.2

Data Abstraction
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-1
To find specific solutions to generalizable problems, programmers represent and organize data in multiple ways.

AAP-1.C
Represent a list or string using a variable. [Skill 3.A]

  • AAP-1.C.1 A list is an ordered sequence of elements. For example,

    [value1, value2, value3, ...]

    describes a list where value1 is the first element, value2 is the second element, value3 is the third element, and so on.

  • AAP-1.C.2 An element is an individual value in a list that is assigned a unique index.

  • AAP-1.C.3 An index is a common method for referencing the elements in a list or string using natural numbers.

  • AAP-1.C.4 A string is an ordered sequence of characters.

AAP-1.D
For data abstraction:
a. Develop data abstraction using lists to store multiple elements. [Skill 3.B]
b. Explain how the use of data abstraction manages complexity in program code. [Skill 3.C]

  • AAP-1.D.1 Data abstraction provides a separation between the abstract properties of a data type and the concrete details of its representation.

  • AAP-1.D.2 Data abstractions manage complexity in programs by giving a collection of data a name without referencing the specific details of the representation.

  • AAP-1.D.3 Data abstractions can be created using lists.

  • AAP-1.D.4 Developing a data abstraction to implement in a program can result in a program that is easier to develop and maintain.

  • AAP-1.D.5 Data abstractions often contain different types of elements.

  • AAP-1.D.6 The use of lists allows multiple related items to be treated as a single value. Lists are referred to by different names, such as array, depending on the programming language.

    • Exclusion statement (EK AAP-1.D.6): The use of linked lists is outside the scope of this course and the AP Exam.

  • AAP-1.D.7 The exam reference sheet provides the notation

    [value1, value2, value3, ...]

    to create a list with those values as the first, second, third, and so on items. For example,

    • Text:

      aList ← [value1, value2, value3, ...]

      Block:

      aList ← value1, value2, value3

      creates a new list that contains the values value1, value2, value3, and ... at indices 1, 2, 3, and ... respectively and assigns it to aList.

    • Text:

      aList ← []

      Block:

      aList ← (empty)

      creates a new empty list and assigns it to aList.

    • Text:

      aList ← bList

      Block:

      aList ← bList

      assigns a copy of the list bList to the list aList. For example, if bList contains [20, 40, 60], then aList will also contain [20, 40, 60] after the assignment.

  • AAP-1.D.8 The exam reference sheet describes a list structure whose index values are 1 through the number of elements in the list, inclusive. For all list operations, if a list index is less than 1 or greater than the length of the list, an error message is produced and the program will terminate.

Source: College Board AP Course and Exam Description

Data abstraction 数据抽象 lets you manage complexity by giving a single name to a collection of data – for example, a list rather than dozens of separate variables. It hides detail: you use the named collection without worrying about how it is stored. Lists (below) are the course's main data abstraction.

Vocabulary Train
English Chinese Pinyin
Data abstraction 数据抽象 shù jù chōu xiàng
Exercise sheet
3.3

Mathematical Expressions
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.A
Express an algorithm that uses sequencing without using a programming language. [Skill 2.A]

  • AAP-2.A.1 An algorithm is a finite set of instructions that accomplish a specific task.
  • AAP-2.A.2 Beyond visual and textual programming languages, algorithms can be expressed in a variety of ways, such as natural language, diagrams, and pseudocode.
  • AAP-2.A.3 Algorithms executed by programs are implemented using programming languages.
  • AAP-2.A.4 Every algorithm can be constructed using combinations of sequencing, selection, and iteration.

AAP-2.B
Represent a step-by-step algorithmic process using sequential code statements. [Skill 2.B]

  • AAP-2.B.1 Sequencing is the application of each step of an algorithm in the order in which the code statements are given.
  • AAP-2.B.2 A code statement is a part of program code that expresses an action to be carried out.
  • AAP-2.B.3 An expression can consist of a value, a variable, an operator, or a procedure call that returns a value.
  • AAP-2.B.4 Expressions are evaluated to produce a single value.
  • AAP-2.B.5 The evaluation of expressions follows a set order of operations defined by the programming language.
  • AAP-2.B.6 Sequential statements execute in the order they appear in the code segment.
  • AAP-2.B.7 Clarity and readability are important considerations when expressing an algorithm in a programming language.

AAP-2.C
Evaluate expressions that use arithmetic operators. [Skill 4.B]

  • AAP-2.C.1 Arithmetic operators are part of most programming languages and include addition, subtraction, multiplication, division, and modulus operators.

  • AAP-2.C.2 The exam reference sheet provides a MOD b, which evaluates to the remainder when a is divided by b. Assume that a is an integer greater than or equal to 0 and b is an integer greater than 0. For example, 17 MOD 5 evaluates to 2.

  • AAP-2.C.3 The exam reference sheet provides the arithmetic operators +, -, *, /, and MOD.

    Text and Block:

    • a + b
    • a - b
    • a * b
    • a / b
    • a MOD b

    These are used to perform arithmetic on a and b. For example, 17 / 5 evaluates to 3.4.

  • AAP-2.C.4 The order of operations used in mathematics applies when evaluating expressions. The MOD operator has the same precedence as the * and / operators.

Source: College Board AP Course and Exam Description

Programs compute with the operators +, -, *, /, and MOD (the remainder 余数 of a division, e.g. 17 MOD 5 is 2). Expressions follow the usual order of operations. MOD is especially useful for testing divisibility (n MOD 2 = 0 means n is even) and for wrapping values around a range.

Explore

Evaluate an expression step by step

An expression is evaluated with order of operations: multiplication and division happen before addition and subtraction, left to right.

Vocabulary Train
English Chinese Pinyin
remainder 余数 yú shù
Exercise sheet
3.4

Strings
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.D
Evaluate expressions that manipulate strings. [Skill 4.B]

  • AAP-2.D.1 String concatenation joins together two or more strings end-to-end to make a new string.
  • AAP-2.D.2 A substring is part of an existing string.

Source: College Board AP Course and Exam Description

A string 字符串 is an ordered sequence of characters, like "hello". Programs join strings (concatenation 拼接) and find their length. Strings represent text – names, messages, sequences – and are a common program input and output.

Vocabulary Train
English Chinese Pinyin
string 字符串 zì fú chuàn
concatenation 拼接 pīn jiē
Exercise sheet
3.5

Boolean Expressions
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.E
For relationships between two variables, expressions, or values:
a. Write expressions using relational operators. [Skill 2.B]
b. Evaluate expressions that use relational operators. [Skill 4.B]

  • AAP-2.E.1 A Boolean value is either true or false.

  • AAP-2.E.2 The exam reference sheet provides the following relational operators: =, ≠, >, <, ≥, and ≤.

    Text and Block:

    • a = b
    • a ≠ b
    • a > b
    • a < b
    • a ≥ b
    • a ≤ b

    These are used to test the relationship between two variables, expressions, or values. A comparison using a relational operator evaluates to a Boolean value. For example, a = b evaluates to true if a and b are equal; otherwise, it evaluates to false.

AAP-2.F
For relationships between Boolean values:
a. Write expressions using logical operators. [Skill 2.B]
b. Evaluate expressions that use logic operators. [Skill 4.B]

  • AAP-2.F.1 The exam reference sheet provides the logical operators NOT, AND, and OR, which evaluate to a Boolean value.

  • AAP-2.F.2 The exam reference sheet provides

    Text:

    NOT condition

    Block:

    NOT condition

    which evaluates to true if condition is false; otherwise it evaluates to false.

  • AAP-2.F.3 The exam reference sheet provides

    Text:

    condition1 AND condition2

    Block:

    condition1 AND condition2

    which evaluates to true if both condition1 and condition2 are true; otherwise it evaluates to false.

  • AAP-2.F.4 The exam reference sheet provides

    Text:

    condition1 OR condition2

    Block:

    condition1 OR condition2

    which evaluates to true if condition1 is true or if condition2 is true or if both condition1 and condition2 are true; otherwise it evaluates to false.

  • AAP-2.F.5 The operand for a logical operator is either a Boolean expression or a single Boolean value.

Source: College Board AP Course and Exam Description

A Boolean expression 布尔表达式 evaluates to true or false. It uses relational operators (=, ≠, <, >, ≤, ≥) and logical operators NOT, AND, OR:

The three families of operators: arithmetic, relational, and logical The three families of operators: arithmetic, relational, and logical

  • NOT reverses a value,
  • AND is true only when both sides are true,
  • OR is true when at least one side is true.

These conditions drive every decision and loop.

Explore

Try the OR truth table

A Boolean expression is either true (1) or false (0). OR is true when at least one input is true; flip the inputs to see every case.

Vocabulary Train
English Chinese Pinyin
Boolean expression 布尔表达式 bù ěr biǎo dá shì
Exercise sheet
3.6

Conditionals
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.G
Express an algorithm that uses selection without using a programming language. [Skill 2.A]

  • AAP-2.G.1 Selection determines which parts of an algorithm are executed based on a condition being true or false.

AAP-2.H
For selection:
a. Write conditional statements. [Skill 2.B]
b. Determine the result of conditional statements. [Skill 4.B]

  • AAP-2.H.1 Conditional statements, or "if-statements," affect the sequential flow of control by executing different statements based on the value of a Boolean expression.

  • AAP-2.H.2 The exam reference sheet provides

    Text:

    IF(condition) { <block of statements> }

    Block:

    IF condition block of statements

    in which the code in block of statements is executed if the Boolean expression condition evaluates to true; no action is taken if condition evaluates to false.

  • AAP-2.H.3 The exam reference sheet provides

    Text:

    IF(condition) { <first block of statements> } ELSE { <second block of statements> }

    Block:

    IF condition first block of statements ELSE second block of statements

    in which the code in first block of statements is executed if the Boolean expression condition evaluates to true; otherwise, the code in second block of statements is executed.

Source: College Board AP Course and Exam Description

A conditional (selection) 条件语句 chooses which code to run. IF runs a block only when its condition is true; ELSE gives an alternative:

Selection chooses between paths based on a condition Selection chooses between paths based on a condition

IF (score ≥ 60)
{
    DISPLAY("Pass")
}
ELSE
{
    DISPLAY("Fail")
}
Explore

Follow an if / else decision

A conditional runs one branch or another depending on whether its condition is true. Slide the value across the threshold and watch which branch is taken.

Vocabulary Train
English Chinese Pinyin
conditional (selection) 条件语句 tiáo jiàn yǔ jù
Exercise sheet
3.7

Nested Conditionals
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.I
For nested selection:
a. Write nested conditional statements. [Skill 2.B]
b. Determine the result of nested conditional statements. [Skill 4.B]

  • AAP-2.I.1 Nested conditional statements consist of conditional statements within conditional statements.

Source: College Board AP Course and Exam Description

A nested conditional 嵌套条件 places one IF inside another (or chains ELSE IF) to choose among more than two paths. Only the first matching branch runs:

IF (g ≥ 90)      { grade ← "A" }
ELSE IF (g ≥ 80) { grade ← "B" }
ELSE             { grade ← "C" }
Vocabulary Train
English Chinese Pinyin
nested conditional 嵌套条件 qiàn tào tiáo jiàn
Exercise sheet
3.8

Iteration
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.J
Express an algorithm that uses iteration without using a programming language. [Skill 2.A]

  • AAP-2.J.1 Iteration is a repeating portion of an algorithm. Iteration repeats a specified number of times or until a given condition is met.

AAP-2.K
For iteration:
a. Write iteration statements. [Skill 2.B]
b. Determine the result or side effect of iteration statements. [Skill 4.B]

  • AAP-2.K.1 Iteration statements change the sequential flow of control by repeating a set of statements zero or more times, until a stopping condition is met.

  • AAP-2.K.2 The exam reference sheet provides

    Text:

    REPEAT n TIMES { <block of statements> }

    Block:

    REPEAT n TIMES block of statements

    in which the block of statements is executed n times.

  • AAP-2.K.3 The exam reference sheet provides

    Text:

    REPEAT UNTIL(condition) { <block of statements> }

    Block:

    REPEAT UNTIL condition block of statements

    in which the code in block of statements is repeated until the Boolean expression condition evaluates to true.

  • AAP-2.K.4 In REPEAT UNTIL(condition) iteration, an infinite loop occurs when the ending condition will never evaluate to true.

  • AAP-2.K.5 In REPEAT UNTIL(condition) iteration, if the conditional evaluates to true initially, the loop body is not executed at all, due to the condition being checked before the loop.

Source: College Board AP Course and Exam Description

Iteration (a loop) 迭代 repeats instructions. AP pseudocode has two forms:

A pre-condition (WHILE) loop tests before the body, so it may run zero times A pre-condition (WHILE) loop tests before the body, so it may run zero times

REPEAT 5 TIMES        // a fixed count
{
    DISPLAY("hi")
}

REPEAT UNTIL (found)  // until a condition becomes true
{
    ...
}

A loop that never meets its stopping condition is an infinite loop 无限循环.

Explore

Trace a loop one pass at a time

A loop repeats a block while its counter runs through a range. Step through to watch the counter and the running total update each pass.

Vocabulary Train
English Chinese Pinyin
Iteration (a loop) 迭代 dié dài
infinite loop 无限循环 wú xiàn xún huán
Exercise sheet
3.9

Developing Algorithms
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.L
Compare multiple algorithms to determine if they yield the same side effect or result. [Skill 1.D]

  • AAP-2.L.1 Algorithms can be written in different ways and still accomplish the same tasks.
  • AAP-2.L.2 Algorithms that appear similar can yield different side effects or results.
  • AAP-2.L.3 Some conditional statements can be written as equivalent Boolean expressions.
  • AAP-2.L.4 Some Boolean expressions can be written as equivalent conditional statements.
  • AAP-2.L.5 Different algorithms can be developed or used to solve the same problem.

AAP-2.M
For algorithms:
a. Create algorithms. [Skill 2.A]
b. Combine and modify existing algorithms. [Skill 2.B]

  • AAP-2.M.1 Algorithms can be created from an idea, by combining existing algorithms, or by modifying existing algorithms.
  • AAP-2.M.2 Knowledge of existing algorithms can help in constructing new ones. Some existing algorithms include:
    • determining the maximum or minimum value of two or more numbers
    • computing the sum or average of two or more numbers
    • identifying if an integer is or is not evenly divisible by another integer
    • determining a robot's path through a maze
  • AAP-2.M.3 Using existing correct algorithms as building blocks for constructing another algorithm has benefits such as reducing development time, reducing testing, and simplifying the identification of errors.

Source: College Board AP Course and Exam Description

An algorithm 算法 is a finite sequence of steps that solves a problem, built from sequencing, selection, and iteration. Different algorithms can solve the same problem, and you should be able to combine and modify existing algorithms (for example, count the values in a list that meet a condition, or find the largest). Trace an algorithm by hand to check it is correct.

A flowchart lays out an algorithm using the standard symbols A flowchart lays out an algorithm using the standard symbols

Vocabulary Train
English Chinese Pinyin
algorithm 算法 suàn fǎ
Exercise sheet
3.10

Lists
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.N
For list operations:
a. Write expressions that use list indexing and list procedures. [Skill 2.B]
b. Evaluate expressions that use list indexing and list procedures. [Skill 4.B]

  • AAP-2.N.1 The exam reference sheet provides basic operations on lists, including:

    • accessing an element by index

      Text:

      aList[i]

      Block:

      aList i

      accesses the element of aList at index i. The first element of aList is at index 1 and is accessed using the notation aList[1].

    • assigning a value of an element of a list to a variable

      Text:

      x ← aList[i]

      Block:

      x ← aList i

      assigns the value of aList[i] to the variable x.

    • assigning a value to an element of a list

      Text:

      aList[i] ← x

      Block:

      aList i ← x

      assigns the value of x to aList[i].

      Text:

      aList[i] ← aList[j]

      Block:

      aList i ← aList j

      assigns the value of aList[j] to aList[i].

    • inserting elements at a given index

      Text:

      INSERT(aList, i, value)

      Block:

      INSERT aList, i, value

      shifts to the right any values in aList at indices greater than or equal to i. The length of the list is increased by 1, and value is placed at index i in aList.

    • adding elements to the end of the list

      Text:

      APPEND(aList, value)

      Block:

      APPEND aList, value

      increases the length of aList by 1, and value is placed at the end of aList.

    • removing elements

      Text:

      REMOVE(aList, i)

      Block:

      REMOVE aList, i

      removes the item at index i in aList and shifts to the left any values at indices greater than i. The length of aList is decreased by 1.

    • determining the length of a list

      Text:

      LENGTH(aList)

      Block:

      LENGTH aList

      evaluates to the number of elements currently in aList.

  • AAP-2.N.2 List procedures are implemented in accordance with the syntax rules of the programming language.

AAP-2.O
For algorithms involving elements of a list:
a. Write iteration statements to traverse a list. [Skill 2.B]
b. Determine the result of an algorithm that includes list traversals. [Skill 4.B]

  • AAP-2.O.1 Traversing a list can be a complete traversal, where all elements in the list are accessed, or a partial traversal, where only a portion of elements are accessed.

    • Exclusion statement (EK AAP-2.O.1): Traversing multiple lists at the same time using the same index for both (parallel traversals) is outside the scope of this course and the AP Exam.

  • AAP-2.O.2 Iteration statements can be used to traverse a list.

  • AAP-2.O.3 The exam reference sheet provides

    Text:

    FOR EACH item IN aList { <block of statements> }

    Block:

    FOR EACH item IN aList block of statements

    The variable item is assigned the value of each element of aList sequentially, in order, from the first element to the last element. The code in block of statements is executed once for each assignment of item.

  • AAP-2.O.4 Knowledge of existing algorithms that use iteration can help in constructing new algorithms. Some examples of existing algorithms that are often used with lists include:

    • determining a minimum or maximum value in a list
    • computing a sum or average of a list of numbers

  • AAP-2.O.5 Linear search or sequential search algorithms check each element of a list, in order, until the desired value is found or all elements in the list have been checked.

Source: College Board AP Course and Exam Description

A list 列表 is an ordered collection of values under one name, the course's key data abstraction. AP pseudocode indexes from 1:

A list holds many values in one variable, each found by its index A list holds many values in one variable, each found by its index

scores ← [88, 74, 95]
DISPLAY(scores[1])          // 88
scores[2] ← 80              // replace the 2nd value
APPEND(scores, 60)          // add to the end
INSERT(scores, 1, 100)      // insert at index 1
REMOVE(scores, 3)           // delete the 3rd element
LENGTH(scores)              // how many elements

Traverse a list with a loop to sum, count, search, or find a maximum:

FOR EACH x IN scores
{
    total ← total + x
}
Vocabulary Train
English Chinese Pinyin
list 列表 liè biǎo
Exercise sheet
3.11

Binary Search
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-2
The way statements are sequenced and combined in a program determines the computed result. Programs incorporate iteration and selection constructs to represent repetition and make decisions to handle varied input values.

AAP-2.P
For binary search algorithms:
a. Determine the number of iterations required to find a value in a data set. [Skill 1.D]
b. Explain the requirements necessary to complete a binary search. [Skill 1.A]

  • AAP-2.P.1 The binary search algorithm starts at the middle of a sorted data set of numbers and eliminates half of the data; this process repeats until the desired value is found or all elements have been eliminated.
    • Exclusion statement (EK AAP-2.P.1): Specific implementations of the binary search are outside the scope of the course and the AP Exam.
  • AAP-2.P.2 Data must be in sorted order to use the binary search algorithm.
  • AAP-2.P.3 Binary search is often more efficient than sequential/linear search when applied to sorted data.

Source: College Board AP Course and Exam Description

Binary search 二分搜索 finds a value in a sorted list far faster than checking each element. It looks at the middle element, then discards the half that cannot contain the target, repeating until found. Each step halves the search space, so a list of $n$ items takes about $\log_2 n$ steps. It requires the data to be sorted first.

Binary search halves the range at each step (the list must be sorted) Binary search halves the range at each step (the list must be sorted)

Worked example. Searching a sorted list of $8$ items, binary search halves the range each step: $8\rightarrow4\rightarrow2\rightarrow1$, at most $3$ comparisons ($\log_2 8=3$), whereas a linear search could take up to $8$. The advantage grows explosively: about $1{,}000$ items need only $\approx10$ binary-search steps (but up to $1{,}000$ linear ones), and $1{,}000{,}000$ items need just $\approx20$. Halving is what makes it a reasonable-time algorithm.

Vocabulary Train
English Chinese Pinyin
Binary search 二分搜索 èr fēn sōu suǒ
Exercise sheet
3.12

Calling Procedures
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-3
Programmers break down problems into smaller and more manageable pieces. By creating procedures and leveraging parameters, programmers generalize processes that can be reused. Procedures allow programmers to draw upon existing code that has already been tested, allowing them to write programs more quickly and with more confidence.

AAP-3.A
For procedure calls:
a. Write statements to call procedures. [Skill 3.B]
b. Determine the result or effect of a procedure call. [Skill 4.B]

  • AAP-3.A.1 A procedure is a named group of programming instructions that may have parameters and return values.

  • AAP-3.A.2 Procedures are referred to by different names, such as method or function, depending on the programming language.

  • AAP-3.A.3 Parameters are input variables of a procedure. Arguments specify the values of the parameters when a procedure is called.

  • AAP-3.A.4 A procedure call interrupts the sequential execution of statements, causing the program to execute the statements within the procedure before continuing. Once the last statement in the procedure (or a return statement) has executed, flow of control is returned to the point immediately following where the procedure was called.

  • AAP-3.A.5 The exam reference sheet provides

    procName(arg1, arg2, ...)

    as a way to call

    Text:

    PROCEDURE procName(parameter1, parameter2, ...) { <block of statements> }

    Block:

    PROCEDURE procName parameter1, parameter2,... block of statements

    which takes zero or more arguments; arg1 is assigned to parameter1, arg2 is assigned to parameter2, and so on.

  • AAP-3.A.6 The exam reference sheet provides the procedure

    Text:

    DISPLAY(expression)

    Block:

    DISPLAY expression

    to display the value of expression, followed by a space.

  • AAP-3.A.7 The exam reference sheet provides the

    Text:

    RETURN(expression)

    Block:

    RETURN expression

    statement, which is used to return the flow of control to the point where the procedure was called and to return the value of expression.

  • AAP-3.A.8 The exam reference sheet provides

    result ← procName(arg1, arg2, ...)

    to assign to result the "value of the procedure" being returned by calling

    Text:

    PROCEDURE procName(parameter1, parameter2, ...) { <block of statements> RETURN(expression) }

    Block:

    PROCEDURE procName parameter1, parameter2,... block of statements RETURN expression

  • AAP-3.A.9 The exam reference sheet provides procedure

    Text:

    INPUT()

    Block:

    INPUT

    which accepts a value from the user and returns the input value.

Source: College Board AP Course and Exam Description

A procedure (function) 过程 is a named, reusable block of code. Calling it runs its code with the arguments you supply, and it may return a value:

sum ← Add(3, 4)      // call, passing 3 and 4

Procedures let you use code without knowing its inner workings – procedural abstraction 过程抽象.

Vocabulary Train
English Chinese Pinyin
procedure (function) 过程 guò chéng
procedural abstraction 过程抽象 guò chéng chōu xiàng
Exercise sheet
3.13

Developing Procedures
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-3
Programmers break down problems into smaller and more manageable pieces. By creating procedures and leveraging parameters, programmers generalize processes that can be reused. Procedures allow programmers to draw upon existing code that has already been tested, allowing them to write programs more quickly and with more confidence.

AAP-3.B
Explain how the use of procedural abstraction manages complexity in a program. [Skill 3.C]

  • AAP-3.B.1 One common type of abstraction is procedural abstraction, which provides a name for a process and allows a procedure to be used only knowing what it does, not how it does it.
  • AAP-3.B.2 Procedural abstraction allows a solution to a large problem to be based on the solutions of smaller subproblems. This is accomplished by creating procedures to solve each of the subproblems.
  • AAP-3.B.3 The subdivision of a computer program into separate subprograms is called modularity.
  • AAP-3.B.4 A procedural abstraction may extract shared features to generalize functionality instead of duplicating code. This allows for program code reuse, which helps manage complexity.
  • AAP-3.B.5 Using parameters allows procedures to be generalized, enabling the procedures to be reused with a range of input values or arguments.
  • AAP-3.B.6 Using procedural abstraction helps improve code readability.
  • AAP-3.B.7 Using procedural abstraction in a program allows programmers to change the internals of the procedure (to make it faster, more efficient, use less storage, etc.) without needing to notify users of the change as long as what the procedure does is preserved.

AAP-3.C
Develop procedural abstractions to manage complexity in a program by writing procedures. [Skill 3.B]

  • AAP-3.C.1 The exam reference sheet provides

    Text:

    PROCEDURE procName(parameter1, parameter2, ...) { <block of statements> }

    Block:

    PROCEDURE procName parameter1, parameter2,... block of statements

    which is used to define a procedure that takes zero or more arguments. The procedure contains block of statements.

  • AAP-3.C.2 The exam reference sheet provides

    Text:

    PROCEDURE procName(parameter1, parameter2, ...) { <block of statements> RETURN(expression) }

    Block:

    PROCEDURE procName parameter1, parameter2,... block of statements RETURN expression

    which is used to define a procedure that takes zero or more arguments. The procedure contains block of statements and returns the value of expression. The RETURN statement may appear at any point inside the procedure and causes an immediate return from the procedure back to the calling statement.

Source: College Board AP Course and Exam Description

You define a procedure with a name, parameters (inputs), and a body, and optionally RETURN a result:

Decomposing a program into procedures and sub-procedures Decomposing a program into procedures and sub-procedures

PROCEDURE Add(a, b)
{
    RETURN(a + b)
}

Writing your own procedures reduces repetition, breaks a big problem into named pieces, and makes programs readable and easier to test – the essence of abstraction 抽象.

Vocabulary Train
English Chinese Pinyin
abstraction 抽象 chōu xiàng
Exercise sheet
3.14

Libraries
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-3
Programmers break down problems into smaller and more manageable pieces. By creating procedures and leveraging parameters, programmers generalize processes that can be reused. Procedures allow programmers to draw upon existing code that has already been tested, allowing them to write programs more quickly and with more confidence.

AAP-3.D
Select appropriate libraries or existing code segments to use in creating new programs. [Skill 2.B]

  • AAP-3.D.1 A software library contains procedures that may be used in creating new programs.
  • AAP-3.D.2 Existing code segments can come from internal or external sources, such as libraries or previously written code.
  • AAP-3.D.3 The use of libraries simplifies the task of creating complex programs.
  • AAP-3.D.4 Application program interfaces (APIs) are specifications for how the procedures in a library behave and can be used.
  • AAP-3.D.5 Documentation for an API/library is necessary in understanding the behaviors provided by the API/library and how to use them.

Source: College Board AP Course and Exam Description

A library 库 is a collection of ready-made procedures that others can reuse. An API (Application Program Interface) 应用程序接口 documents what each procedure does, its parameters, and its result – so you can use it without seeing its code. Libraries save time and let you build on existing, tested work.

Vocabulary Train
English Chinese Pinyin
library 库 kù
Interface 应用程序接口 yìng yòng chéng xù jiē kǒu
Exercise sheet
3.15

Random Values
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-3
Programmers break down problems into smaller and more manageable pieces. By creating procedures and leveraging parameters, programmers generalize processes that can be reused. Procedures allow programmers to draw upon existing code that has already been tested, allowing them to write programs more quickly and with more confidence.

AAP-3.E
For generating random values:
a. Write expressions to generate possible values. [Skill 2.B]
b. Evaluate expressions to determine the possible results. [Skill 4.B]

  • AAP-3.E.1 The exam reference sheet provides

    Text:

    RANDOM(a, b)

    Block:

    RANDOM a, b

    which generates and returns a random integer from a to b, inclusive. Each result is equally likely to occur. For example, RANDOM(1, 3) could return 1, 2, or 3.

  • AAP-3.E.2 Using random number generation in a program means each execution may produce a different result.

Source: College Board AP Course and Exam Description

RANDOM(a, b) returns a random integer from a to b (inclusive), letting a program produce unpredictable results – for games, sampling, or simulations. Each call may give a different value, so a program using randomness behaves differently each run.

Exercise sheet
3.16

Simulations
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-3
Programmers break down problems into smaller and more manageable pieces. By creating procedures and leveraging parameters, programmers generalize processes that can be reused. Procedures allow programmers to draw upon existing code that has already been tested, allowing them to write programs more quickly and with more confidence.

AAP-3.F
For simulations:
a. Explain how computers can be used to represent real-world phenomena or outcomes. [Skill 1.A]
b. Compare simulations with real-world contexts. [Skill 1.D]

  • AAP-3.F.1 Simulations are abstractions of more complex objects or phenomena for a specific purpose.
  • AAP-3.F.2 A simulation is a representation that uses varying sets of values to reflect the changing state of a phenomenon.
  • AAP-3.F.3 Simulations often mimic real-world events with the purpose of drawing inferences, allowing investigation of a phenomenon without the constraints of the real world.
  • AAP-3.F.4 The process of developing an abstract simulation involves removing specific details or simplifying functionality.
  • AAP-3.F.5 Simulations can contain bias derived from the choices of real-world elements that were included or excluded.
  • AAP-3.F.6 Simulations are most useful when real-world events are impractical for experiments (e.g., too big, too small, too fast, too slow, too expensive, or too dangerous).
  • AAP-3.F.7 Simulations facilitate the formulation and refinement of hypotheses related to the objects or phenomena under consideration.
  • AAP-3.F.8 Random number generators can be used to simulate the variability that exists in the real world.

Source: College Board AP Course and Exam Description

A simulation 模拟 is a program that models a real-world process to study it safely and cheaply. Simulations simplify reality (they leave out detail) and often use randomness to imitate chance events. They let you test scenarios that would be too costly, slow, or dangerous in real life – but their results are only as good as their assumptions.

Vocabulary Train
English Chinese Pinyin
simulation 模拟 mó nǐ
Exercise sheet
3.17

Algorithmic Efficiency
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-4
There exist problems that computers cannot solve, and even when a computer can solve a problem, it may not be able to do so in a reasonable amount of time.

AAP-4.A
For determining the efficiency of an algorithm:
a. Explain the difference between algorithms that run in reasonable time and those that do not. [Skill 1.D]
b. Identify situations where a heuristic solution may be more appropriate. [Skill 1.D]

  • AAP-4.A.1 A problem is a general description of a task that can (or cannot) be solved algorithmically. An instance of a problem also includes specific input. For example, sorting is a problem; sorting the list (2,3,1,7) is an instance of the problem.
  • AAP-4.A.2 A decision problem is a problem with a yes/no answer (e.g., is there a path from A to B?). An optimization problem is a problem with the goal of finding the "best" solution among many (e.g., what is the shortest path from A to B?).
  • AAP-4.A.3 Efficiency is an estimation of the amount of computational resources used by an algorithm. Efficiency is typically expressed as a function of the size of the input.
    • Exclusion statement (EK AAP-4.A.3): Formal analysis of algorithms (Big-O) and formal reasoning using mathematical formulas are outside the scope of this course and the AP Exam.
  • AAP-4.A.4 An algorithm's efficiency is determined through formal or mathematical reasoning.
  • AAP-4.A.5 An algorithm's efficiency can be informally measured by determining the number of times a statement or group of statements executes.
  • AAP-4.A.6 Different correct algorithms for the same problem can have different efficiencies.
  • AAP-4.A.7 Algorithms with a polynomial efficiency or slower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time. Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.
  • AAP-4.A.8 Some problems cannot be solved in a reasonable amount of time because there is no efficient algorithm for solving them. In these cases, approximate solutions are sought.
  • AAP-4.A.9 A heuristic is an approach to a problem that produces a solution that is not guaranteed to be optimal but may be used when techniques that are guaranteed to always find an optimal solution are impractical.
    • Exclusion statement (AAP-4.A.9): Specific heuristic solutions are outside the scope of this course and the AP Exam.

Source: College Board AP Course and Exam Description

Efficiency 效率 is how much time (or memory) an algorithm needs as its input grows. A reasonable-time algorithm's work grows like a polynomial of the input size (e.g. linear or quadratic); an unreasonable-time algorithm grows far faster (e.g. doubling with each added item), becoming impractical for large inputs. A faster algorithm can make a previously impossible problem solvable. Sometimes an exact answer takes too long, so a heuristic 启发式 – an approach that finds a good-enough answer quickly – is used instead.

How the running time of an algorithm grows with the input size n How the running time of an algorithm grows with the input size n

Vocabulary Train
English Chinese Pinyin
Efficiency 效率 xiào lǜ
heuristic 启发式 qǐ fā shì
Exercise sheet
3.18

Undecidable Problems
Syllabus
Enduring UnderstandingLearning ObjectiveEssential Knowledge

AAP-4
There exist problems that computers cannot solve, and even when a computer can solve a problem, it may not be able to do so in a reasonable amount of time.

AAP-4.B
Explain the existence of undecidable problems in computer science. [Skill 1.A]

  • AAP-4.B.1 A decidable problem is a decision problem for which an algorithm can be written to produce a correct output for all inputs (e.g., "Is the number even?").
  • AAP-4.B.2 An undecidable problem is one for which no algorithm can be constructed that is always capable of providing a correct yes-or-no answer.
    • Exclusion statement (EK AAP-4.B.2): Determining whether a given problem is undecidable is outside the scope of this course and the AP Exam.
  • AAP-4.B.3 An undecidable problem may have some instances that have an algorithmic solution, but there is no algorithmic solution that could solve all instances of the problem.

Source: College Board AP Course and Exam Description

Some problems are undecidable 不可判定: no algorithm can solve every case of them with a correct yes/no answer. This is a fundamental limit of computing – not a matter of needing a faster computer, but a proof that no such algorithm can exist.

Exam skill: be able to determine a code segment's result by tracing it, compare two algorithms' efficiency (reasonable vs unreasonable time), and recognize procedural and data abstraction in a program.

Vocabulary Train
English Chinese Pinyin
undecidable 不可判定 bù kě pàn dìng
Exercise sheet
3.18

Exam tips
  • Know a variable is a named store for a value and trace how assignment updates it step by step.
  • Read the AP pseudocode carefully — a <- expression assigns, and lists are 1-indexed on the exam reference sheet.
  • Distinguish a variable from a list (a collection accessed by index) and use list operations correctly.
  • Evaluate expressions with the right precedence and boolean logic (AND, OR, NOT).
  • Pick clear, meaningful variable names — the written tasks reward readable code.

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