Mathematical Expression and Strings

Algorithms

An algorithm: a set of instructions that can accomplish a specific task

An Algorithm has three

  1. Sequencing: Algorithms do taks in the order of specification
  2. Selection: Helps choose two different outcomes based off a decision
  3. Iteration: If a conditions is true, then the code can repeat

Algorithms can be Represented in Two Ways

1.Flowcharts: Use shapes and arrows to represent the steps of an algorithm

Aflowcharts use shapes and arrows to represent the steps of an algorithm

  • different shapes represent different functions
  • For example, the circle represents the start and end whereas an arrow represents a relationship between relative shapes. There is also a rectangle, parallelogram, and diamond which have their specific functions.
  • Pseudocode: A blend of human language and coding format

Arithmetic Operations

Arithmetic operations exist in most programming languages

Basic Operations

Subtraction:

  • represented by “-“ Ex: num1 = 2 - 1

Addition:

  • represented by “+” Ex: num1 = 2 +1

Multiplication

  • represented by “*” Ex: num1 = 2 * 1

Division

  • represented by “/” num1 = 2/1

Getting the Remainder represented by “MOD” (% in python) num1 = 5 % 2

Different Uses

Items can be numbers or variables Example: num1 = 10 num2 = num1 -25 num3 = 100 * num1 num4 = num1 / num2 num5 = 9 % num4

Order of Operations

Arithmetic operations in programming are performed in the same order as operations in mathematics:

  • operations in parentheses should be done first
  • division and multiplication should be done before addition and subtraction
  • modulus works similar to multiplication and division Example: Evaluate num1 num1 = 9 % 2 * (8 - 2) + 8 / (6 - 4) num1 = 10.0

Variables

Different Ways Values are Stored in Variables

  1. Numerical value stored in a variable
  2. Value of another variable stored in a variable
  3. result of an operation stored in a variable
  4. Result of a procedure call stored in a variable

score = 0 score = newScore score = newScore + 2 avgScore = allscores(20, 60, 80)

Sequencing is Important!

Changing the order of the steps changes the overall outcome, since every time the value assigned to a variable is changed, it overrides the last value which was assigned to the same variable. That is why it is important to track the value of variables, especially in code where the value is constantly changing.

num1 = 2 num2 = 4 num3 = 6 num1 = num2 + num3 num2 = num1 + num3 Vs. num1 = 2 num2 = 4 num3 = 6 num2 = num1 + num3 num1 = num2 + num3

Tracking Variables

Tracking variables is a common question found on AP exams and is an important thing to keep in mind when writing any code. If the value of your variables changes a lot, not accounting for these changes can result in an unwanted outcome.

var1 = 9 var2 = 7 var3 = 2 print(var1) print(var2) print(var3)