Algorithms and Programming

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.

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.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.

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.

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.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.

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.

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.

• 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

• 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.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.

• 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-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.

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.

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.

• 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.

• Exclusion statement (AAP-4.A.9): Specific heuristic solutions are outside the scope of this course and the AP Exam.

• 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.