Foundations

Variables

Naming Values

You're tracking your monthly budget. Instead of typing 2500.00 every time you calculate savings, rent, and groceries, you store it in a variable called income. Now when your income changes, you update one number and all calculations adjust.

Store and use a value

Give a value a name, then use that name in calculations.

x
Basic.java
Replay: real traced execution (multi-file project)
public class Basic {
    public static void main(String[] args) {
        int x = 10;
        int y = x + 5;
        int z = x * x;
    }
}

public class Basic {
    public static void main(String[] args) {
        int x = 5;
        int y = x + 5;
        int z = x * x;
    }
}

public class Basic {
    public static void main(String[] args) {
        int x = 20;
        int y = x + 5;
        int z = x * x;
    }
}

  1. x ← 10, y ← 15, z ← 100

    1public class Basic {2    public static void main(String[] args) {3        int x→ 10 = 10;  //@x=5, 204        int y→ 15 = x10 + 5;5        int z→ 100 = x10 * x;6    }

  1. x ← 5, y ← 10, z ← 25

    1public class Basic {2    public static void main(String[] args) {3        int x→ 5 = 5;4        int y→ 10 = x5 + 5;5        int z→ 25 = x5 * x;6    }

  1. x ← 20, y ← 25, z ← 400

    1public class Basic {2    public static void main(String[] args) {3        int x→ 20 = 20;4        int y→ 25 = x20 + 5;5        int z→ 400 = x20 * x;6    }

A variable holds a value. Use it anywhere you'd use the value itself.

variable A named container for a value. Declare with type, then assign: `int x = 5;`

Building expressions step by step

Break a complex calculation into named pieces. Each piece has meaning.

example
Steps.java
Replay: real traced execution (multi-file project)
public class Steps {
    public static void main(String[] args) {
        int width = 7;
        int height = 5;
        int area = width * height;
        int perimeter = 2 * (width + height);
    }
}

public class Steps {
    public static void main(String[] args) {
        int width = 3;
        int height = 5;
        int area = width * height;
        int perimeter = 2 * (width + height);
    }
}

public class Steps {
    public static void main(String[] args) {
        int width = 10;
        int height = 5;
        int area = width * height;
        int perimeter = 2 * (width + height);
    }
}

public class Steps {
    public static void main(String[] args) {
        int width = 7;
        int height = 4;
        int area = width * height;
        int perimeter = 2 * (width + height);
    }
}

public class Steps {
    public static void main(String[] args) {
        int width = 7;
        int height = 8;
        int area = width * height;
        int perimeter = 2 * (width + height);
    }
}

  1. width ← 7, height ← 5, area ← 35, perimeter ← 24

    1public class Steps {2    public static void main(String[] args) {3        int width→ 7 = 7;  //@width=3, 104        int height→ 5 = 5;  //@height=4, 85        int area→ 35 = width7 * height5;6        int perimeter→ 24 = 2 * (width7 + height5);7    }

  1. width ← 3, height ← 5, area ← 15, perimeter ← 16

    1public class Steps {2    public static void main(String[] args) {3        int width→ 3 = 3;4        int height→ 5 = 5;5        int area→ 15 = width3 * height5;6        int perimeter→ 16 = 2 * (width3 + height5);7    }

  1. width ← 10, height ← 5, area ← 50, perimeter ← 30

    1public class Steps {2    public static void main(String[] args) {3        int width→ 10 = 10;4        int height→ 5 = 5;5        int area→ 50 = width10 * height5;6        int perimeter→ 30 = 2 * (width10 + height5);7    }

  1. width ← 7, height ← 4, area ← 28, perimeter ← 22

    1public class Steps {2    public static void main(String[] args) {3        int width→ 7 = 7;4        int height→ 4 = 4;5        int area→ 28 = width7 * height4;6        int perimeter→ 22 = 2 * (width7 + height4);7    }

  1. width ← 7, height ← 8, area ← 56, perimeter ← 30

    1public class Steps {2    public static void main(String[] args) {3        int width→ 7 = 7;4        int height→ 8 = 8;5        int area→ 56 = width7 * height8;6        int perimeter→ 30 = 2 * (width7 + height8);7    }

Reading area tells you more than reading 7 * 5. Variables make code self-documenting.

int `int` holds whole numbers: -2, 0, 42, 1000. Range: about ±2 billion.

Temperature conversion (Fahrenheit to Celsius)

Convert 98.6°F (body temperature) to Celsius using the formula: C = (F - 32) × 5 / 9

fahrenheit
Temperature.java
Replay: real traced execution (multi-file project)
public class Temperature {
    public static void main(String[] args) {
        double fahrenheit = 98.6;
        double celsius = (fahrenheit - 32) * 5 / 9;
    }
}

public class Temperature {
    public static void main(String[] args) {
        double fahrenheit = 32;
        double celsius = (fahrenheit - 32) * 5 / 9;
    }
}

public class Temperature {
    public static void main(String[] args) {
        double fahrenheit = 212;
        double celsius = (fahrenheit - 32) * 5 / 9;
    }
}

public class Temperature {
    public static void main(String[] args) {
        double fahrenheit = 0;
        double celsius = (fahrenheit - 32) * 5 / 9;
    }
}

  1. fahrenheit ← 98.6, celsius ← 37.0

    1public class Temperature {2    public static void main(String[] args) {3        double fahrenheit→ 98.6 = 98.6;  //@fahrenheit=32, 212, 04        double celsius→ 37.0 = (fahrenheit98.6 - 32) * 5 / 9;5    }

  1. fahrenheit ← 32.0, celsius ← 0.0

    1public class Temperature {2    public static void main(String[] args) {3        double fahrenheit→ 32.0 = 32;4        double celsius→ 0.0 = (fahrenheit32.0 - 32) * 5 / 9;5    }

  1. fahrenheit ← 212.0, celsius ← 100.0

    1public class Temperature {2    public static void main(String[] args) {3        double fahrenheit→ 212.0 = 212;4        double celsius→ 100.0 = (fahrenheit212.0 - 32) * 5 / 9;5    }

  1. fahrenheit ← 0.0, celsius ← -17.77777777777778

    1public class Temperature {2    public static void main(String[] args) {3        double fahrenheit→ 0.0 = 0;4        double celsius→ -17.77777777777778 = (fahrenheit0.0 - 32) * 5 / 9;5    }

Variables make the formula readable: fahrenheit, celsius - you know what they mean.

double `double` holds decimal numbers: 3.14, -0.5, 98.6. Use for measurements.

Fibonacci sequence (without loops)

Each Fibonacci number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8...

Fibonacci.java
Replay: real traced execution (multi-file project)
public class Fibonacci {
    public static void main(String[] args) {
        int c0 = 0;
        int c1 = 1;
        int c2 = c0 + c1;
        int c3 = c1 + c2;
        int c4 = c2 + c3;
        int c5 = c3 + c4;
        int c6 = c4 + c5;
        int c7 = c5 + c6;
    }
}

  1. c0 ← 0, c1 ← 1, c2 ← 1, c3 ← 2, c4 ← 3, c5 ← 5, c6 ← 8, c7 ← 13

    1public class Fibonacci {2    public static void main(String[] args) {3        int c0→ 0 = 0;4        int c1→ 1 = 1;5        int c2→ 1 = c00 + c11;6        int c3→ 2 = c11 + c21;7        int c4→ 3 = c21 + c32;8        int c5→ 5 = c32 + c43;9        int c6→ 8 = c43 + c55;10        int c7→ 13 = c55 + c68;11    }

Watch how each variable depends on the previous ones. This pattern is called building up from base cases.

Circle calculations

Given a radius, calculate circumference and area.

radius
Circle.java
Replay: real traced execution (multi-file project)
public class Circle {
    public static void main(String[] args) {
        double pi = 3.14159;
        double radius = 5;

        double circumference = 2 * pi * radius;
        double area = pi * radius * radius;
    }
}

public class Circle {
    public static void main(String[] args) {
        double pi = 3.14159;
        double radius = 1;

        double circumference = 2 * pi * radius;
        double area = pi * radius * radius;
    }
}

public class Circle {
    public static void main(String[] args) {
        double pi = 3.14159;
        double radius = 10;

        double circumference = 2 * pi * radius;
        double area = pi * radius * radius;
    }
}

public class Circle {
    public static void main(String[] args) {
        double pi = 3.14159;
        double radius = 2.5;

        double circumference = 2 * pi * radius;
        double area = pi * radius * radius;
    }
}

  1. pi ← 3.14159, radius ← 5.0, circumference ← 31.4159, area ← 78.53975

    1public class Circle {2    public static void main(String[] args) {3        double pi→ 3.14159 = 3.14159;4        double radius→ 5.0 = 5;  //@radius=1, 10, 2.55        6        double circumference→ 31.4159 = 2 * pi3.14159 * radius5.0;7        double area→ 78.53975 = pi3.14159 * radius5.0 * radius;8    }

  1. pi ← 3.14159, radius ← 1.0, circumference ← 6.28318, area ← 3.14159

    1public class Circle {2    public static void main(String[] args) {3        double pi→ 3.14159 = 3.14159;4        double radius→ 1.0 = 1;5        6        double circumference→ 6.28318 = 2 * pi3.14159 * radius1.0;7        double area→ 3.14159 = pi3.14159 * radius1.0 * radius;8    }

  1. pi ← 3.14159, radius ← 10.0, circumference ← 62.8318, area ← 314.159

    1public class Circle {2    public static void main(String[] args) {3        double pi→ 3.14159 = 3.14159;4        double radius→ 10.0 = 10;5        6        double circumference→ 62.8318 = 2 * pi3.14159 * radius10.0;7        double area→ 314.159 = pi3.14159 * radius10.0 * radius;8    }

  1. pi ← 3.14159, radius ← 2.5, circumference ← 15.70795, area ← 19.6349375

    1public class Circle {2    public static void main(String[] args) {3        double pi→ 3.14159 = 3.14159;4        double radius→ 2.5 = 2.5;5        6        double circumference→ 15.70795 = 2 * pi3.14159 * radius2.5;7        double area→ 19.6349375 = pi3.14159 * radius2.5 * radius;8    }

pi and radius as named values make the formulas clear.