Interactive Algorithms Textbook in Java: Arithmetic

1. Arithmetic Operators

Math operators

Addition "+", Subtraction "-", Multiplication "*" and Division "/" may already be familiar to you. Like in math, multiplication and division are performed before addition and subtraction. In addition, you can use parenthesis to force order.

Integers truncate during division, just like when you cast from double to int. Thus, 5/2 is 2, not 2.5 nor 3.

public class MyProgram {
    public static void main(String[] args) {
        int x = 5;
        System.out.println(x/2);   //prints 2
        System.out.println(x/2.0); //prints 2.5, Java autocasts
        System.out.println(x+4/2); //prints 5+2 or 7
        System.out.println(x+2*5); //prints 10
         
        double y = 5.0;
        System.out.println(y/2);   //prints 2.5
        System.out.println(y-2);   //prints 3.0
        System.out.println(x*y+x/(y-4)); //prints 25.0+5.0 or 30.0
    }
}

The modulo operator

The % operator is pronounced "modulo" or "mod", and it performs remainder. For example, 10 % 3 is 1, because 10 divided by 3 has a remainder of 1. 13 % 7 is 6. Modulo has the same operator precedence as multiplication and division.

Modulo also works on decimal numbers, and it is a great way to check if two numbers are divisible. If a % b equals zero, then a is divisible by b.

2. More Assignment Operators

= Returns a value

Take a look at the following example:

public class MyProgram {
    public static void main(String[] args) {
        int x = 1;
        int y = 2;
         
        int z = (y = x); //performs (y=x) first, then (z=1)
        System.out.println(x); //Prints 1
        System.out.println(y); //Also prints 1
        System.out.println(z); //Also prints 1
    }
}

With int z = (y = x);, the (y=x) is executed first, storing 1 into y. However, (y=x) also evaluates to the expression 1 of type int. Thus, the rest of the statement becomes int z = 1;

Incrementing

We often want to add a variable by a value, and store the new value into the variable. For example, if we want to increase x by 1, we would perform x = x + 1. Like any assignment, the right side is evaluated first, and it is then stored into the left side.

public class MyProgram {
    public static void main(String[] args) {
        int x = 1;
        int y = 2;
         
        int z = (y = x); //performs (y=x) first, then (z=1)
         
        x = x + 2; //Now x is 1+2, or 3
        y = y * 5; //Now y is 1*5, or 5
        z = z - 3; //Now z is 1-3, or -2
        System.out.println(x); 
        System.out.println(y); 
        System.out.println(z); 
        y = y / 2; //Now y is 5/2 or 2
        x = x % 2; //Now x is 3%2 or 1
        System.out.println(x); 
        System.out.println(y); 
    }
}

+=, -=, *=, /=, and %=

The +=, -=, *=, /=, and %= operators are sometimes called convenience operators, because they only exist to make your life easier. x += 42 is the same as x = x + 42. y *= 5 is the same as y = y * 5:

public class MyProgram {
    public static void main(String[] args) {
        int x = 1;
        int y = 2;
         
        int z = (y = x);
         
        x = x + 2; 
        y *= 5; //Now y is 1*5, or 5
        z -= 3; //Now z is 1-3, or -2
        System.out.println(x); 
        System.out.println(y); 
        System.out.println(z); 
        y /= 2; //Now y is 5/2 or 2
        x %= 2; //Now x is 3%2 or 1
        System.out.println(x); 
        System.out.println(y); 
    }
}

Prefix Increment and Decrement

In many programs, you want to increase a value by just 1. Since this is so common, the ++ and -- operators was created to make +=1 and -=1 easier to type:

public class MyProgram {
    public static void main(String[] args) {
        int x = 41;
        System.out.println(x);    //41
        ++x;
        System.out.println(x);    //42
        System.out.println(x+=1); //43 
        System.out.println(++x);  //44
         
        --x;
        System.out.println(x);    //43
        System.out.println(--x);  //42
    }
}

Postfix Increment and Decrement

You can also type x++ instead of ++x. These two expressions both add one to x, but they are different when used in a expression such as y = (++x) vs y = (x++).

Advanced programmers should recognize that postfix returns the value *before* increment. For example int x=1,y=x++; has y equal to 1 and x equal to 2. In contrast, int x=1,y=++x; has both variables equal to 2. If this confuses you, avoid using increment and decrement operators as part of an expression.