Question

In this part of the Java tutorial, we will talk about expressions.

Expressions are constructed from operands and operators. The operators of an expression indicate which operations to apply to the operands. The order of evaluation of operators in an expression is determined by the precedence and associativity of the operators.

An operator is a special symbol which indicates a certain process is carried out. Operators in programming languages are taken from mathematics. Programmers work with data. The operators are used to process data. An operand is one of the inputs (arguments) of an operator.

An operator usually has one or two operands. Those operators that work with only one operand are called unary operators. Those who work with two operands are called binary operators. There is also one ternary operator ?: which works with three operands.

Certain operators may be used in different contexts. For example the + operator. It can be used in different cases. It adds numbers, concatenates strings or indicates the sign of a number. We say that the operator is overloaded.

Sign operators

There are two sign operators: + and - . They are used to indicate or change the sign of a value.

package com.zetcode;

public class SignOperators {

  public static void main(String[] args) {
    
    System.out.println(2);
    System.out.println(+2);
    System.out.println(-2);
  }
}

The + and - signs indicate the sign of a value. The plus sign can be used to signal that we have a positive number. It can be omitted and it is mostly done so.

package com.zetcode;

public class MinusSign {

  public static void main(String[] args) {
    
    int a = 1;
    
    System.out.println(-a);
    System.out.println(-(-a));  
  }
}

The minus sign changes the sign of a value.

The assignment operator

The assignment operator = assigns a value to a variable. A variable is a placeholder for a value. In mathematics, the = operator has a different meaning. In an equation, the = operator is an equality operator. The left side of the equation is equal to the right one.

int x = 1;

Here we assign a number to the x variable.

x = x + 1;

This expression does not make sense in mathematics. But it is legal in programming. The expression adds 1 to the x variable. The right side is equal to 2 and 2 is assigned to x.

3 = x;

This code line results in syntax error. We cannot assign a value to a literal.

Concatenating strings

In Java the + operator is also used to concatenate strings.

package com.zetcode;

public class ConcatenateStrings {

  public static void main(String[] args) {
  
    System.out.println("Return " + "of " + "the king.");
    System.out.println("Return".concat(" of").concat(" the king."));
  }
}

We join three strings together.

System.out.println("Return " + "of " + "the king.");

Strings are joined with the + operator.

System.out.println("Return".concat(" of").concat(" the king."));

An alternative method for concatenating strings is the concat method.

$ java com.zetcode.ConcatenateStrings 
Return of the king.
Return of the king.

This is the output of the com.zetcode.ConcatenateStrings program.

Increment, decrement operators

Incrementing or decrementing a value by one is a common task in programming. Java has two convenient operators for this: ++ and -- .

x++;
x = x + 1;
...
y--;
y = y - 1;

The above two pairs of expressions do the same.

package com.zetcode;

public class IncDec {

  public static void main(String[] args) {

    int x = 6;

    x++;
    x++;

    System.out.println(x);

    x--;
    System.out.println(x);
  }
}

In the above example, we demonstrate the usage of both operators.

int x = 6;
  
x++;
x++;

We initiate the x variable to 6. Then we increment the x two times. Now the variable equals to 8.

x--;

We use the decrement operator. Now the variable equals to 7.

$ java com.zetcode.IncDec 
8
7

And here is the output of the example.

Arithmetic operators

The following is a table of arithmetic operators in Java.

Symbol	Name
+	Addition
-	Subtraction
*	Multiplication
/	Division
%	Remainder

The following example shows arithmetic operations.

package com.zetcode;

public class Arithmetic {

  public static void main(String[] args) {
    
    int a = 10;
    int b = 11;
    int c = 12;

    int add = a + b + c;
    int sb = c - a;
    int mult = a * b;
    int div = c / 3;
    int rem = c % a;

    System.out.println(add);
    System.out.println(sb);
    System.out.println(mult);
    System.out.println(div);
    System.out.println(rem);
  }
}

In the preceding example, we use addition, subtraction, multiplication, division, and remainder operations. This is all familiar from the mathematics.

int rem = c % a;

The % operator is called the remainder or the modulo operator. It finds the remainder of division of one number by another. For example, 9 % 4 , 9 modulo 4 is 1, because 4 goes into 9 twice with a remainder of 1.

$ java com.zetcode.Arithmetic 
33
2
110
4
2

This is the output of the example.

Next we will show the distinction between integer and floating point division.

package com.zetcode;

public class Division {

  public static void main(String[] args) {
    
    int c = 5 / 2;
    System.out.println(c);

    double d = 5 / 2.0;
    System.out.println(d);  
  }
}

In the preceding example, we divide two numbers.

int c = 5 / 2;

In this code, we have done integer division. The returned value of the division operation is an integer. When we divide two integers the result is an integer.

double d = 5 / 2.0;

If one of the values is a double or a float, we perform a floating point division. In our case, the second operand is a double so the result is a double.

$ java com.zetcode.Division
2
2.5

We see the result of the com.zetcode.Division program.

Boolean operators

In Java we have three logical operators. The boolean keyword is used to declare a Boolean value.

Symbol	Name
&&	logical and
||	logical or
!	negation

Boolean operators are also called logical.

package com.zetcode;

public class BooleanOperators {

  public static void main(String[] args) {

    int x = 3;
    int y = 8;

    System.out.println(x == y);
    System.out.println(y > x);

    if (y > x) {
      
      System.out.println("y is greater than x");
    }
  }
}

Many expressions result in a boolean value. Boolean values are used in conditional statements.

System.out.println(x == y);
System.out.println(y > x);

Relational operators always result in a boolean value. These two lines print false and true.

if (y > x) {
  
  System.out.println("y is greater than x");
}

The body of the if statement is executed only if the condition inside the parentheses is met. The y > x returns true, so the message "y is greater than x" is printed to the terminal.

The true and false keywords represent boolean literals in Java.

package com.zetcode;

public class AndOperator {

  public static void main(String[] args) {

    boolean a = true && true;
    boolean b = true && false;
    boolean c = false && true;
    boolean d = false && false;

    System.out.println(a);
    System.out.println(b);
    System.out.println(c);
    System.out.println(d);
  }
}

The code example shows the logical and operator. It evaluates to true only if both operands are true.

$ java com.zetcode.AndOperator 
true
false
false
false

Only one expression results in true.

The logical or || operator evaluates to true if either of the operands is true.

package com.zetcode;

public class OrOperator {

  public static void main(String[] args) {
    
    boolean a = true || true;
    boolean b = true || false;
    boolean c = false || true;
    boolean d = false || false;

    System.out.println(a);
    System.out.println(b);
    System.out.println(c);
    System.out.println(d);  
  }
}

If one of the sides of the operator is true, the outcome of the operation is true.

$ java com.zetcode.OrOperator 
true
true
true
false

Three of four expressions result in true.

The negation operator ! makes true false and false true.

package com.zetcode;

public class Negation {

  public static void main(String[] args) {
    
    System.out.println(! true);
    System.out.println(! false);
    System.out.println(! (4 < 3));  
  }
}

The example shows the negation operator in action.

$ java com.zetcode.Negation 
false
true
true

This is the output of the com.zetcode.Negation program.

The || , and && operators are short circuit evaluated. Short circuit evaluation means that the second argument is only evaluated if the first argument does not suffice to determine the value of the expression: when the first argument of the logical and evaluates to false, the overall value must be false; and when the first argument of logical or evaluates to true, the overall value must be true. Short circuit evaluation is used mainly to improve performance.

An example may clarify this a bit more.

package com.zetcode;

public class ShortCircuit {

  public static boolean One() {
    
    System.out.println("Inside one");
    return false;
  }

  public static boolean Two() {
    
    System.out.println("Inside two");
    return true;
  }

  public static void main(String[] args) {

    System.out.println("Short circuit");
    
    if (One() && Two()) {
      
      System.out.println("Pass");
    }

    System.out.println("#############");
    
    if (Two() || One()) {
      
      System.out.println("Pass");
    }
  }
}

We have two methods in the example. They are used as operands in boolean expressions. We will see if they are called or not.

if (One() && Two()) {
  
  System.out.println("Pass");
}

The One() method returns false. The short circuit && does not evaluate the second method. It is not necessary. Once an operand is false, the result of the logical conclusion is always false. Only "Inside one" is only printed to the console.

if (Two() || One()) {
  
  System.out.println("Pass");
}

In the second case, we use the || operator and use the Two() method as the first operand. In this case, "Inside two" and "Pass" strings are printed to the terminal. It is again not necessary to evaluate the second operand, since once the first operand evaluates to true, the logical or is always true.

$ java com.zetcode.ShortCircuit 
Short circuit
Inside one
#############
Inside two
Pass

We see the result of the com.zetcode.ShortCircuit program.

Relational Operators

Relational operators are used to compare values. These operators always result in a boolean value.

Symbol	Meaning
<	less than
<=	less than or equal to
>	greater than
>=	greater than or equal to
==	equal to
!=	not equal to

Relational operators are also called comparison operators.

package com.zetcode;

public class Relational {

  public static void main(String[] args) {
    
    System.out.println(3 < 4);
    System.out.println(3 == 4);
    System.out.println(4 >= 3);
    System.out.println(4 != 3);
  }
}

In the code example, we have four expressions. These expressions compare integer values. The result of each of the expressions is either true or false. In Java we use the == to compare numbers. Some languages like Ada, Visual Basic, or Pascal use = for comparing numbers.

Bitwise operators

Decimal numbers are natural to humans. Binary numbers are native to computers. Binary, octal, decimal, or hexadecimal symbols are only notations of a same number. Bitwise operators work with bits of a binary number. Bitwise operators are seldom used in higher level languages like Java.

Symbol	Meaning
~	bitwise negation
^	bitwise exclusive or
&	bitwise and
|	bitwise or

The bitwise negation operator changes each 1 to 0 and 0 to 1.

System.out.println(~7); // prints -8
System.out.println(~ -8); // prints 7

The operator reverts all bits of a number 7. One of the bits also determines, whether the number is negative or not. If we negate all the bits one more time, we get number 7 again.

The bitwise and operator performs bit-by-bit comparison between two numbers. The result for a bit position is 1 only if both corresponding bits in the operands are 1.

    00110
   &  00011
   =  00010

The first number is a binary notation of 6, the second is 3 and the result is 2.

System.out.println(6 & 3); // prints 2
System.out.println(3 & 6); // prints 2

The bitwise or operator performs bit-by-bit comparison between two numbers. The result for a bit position is 1 if either of the corresponding bits in the operands is 1.

   00110
   | 00011
   = 00111

The result is 00110 or decimal 7.

System.out.println(6 | 3); // prints 7
System.out.println(3 | 6); // prints 7

The bitwise exclusive or operator performs bit-by-bit comparison between two numbers. The result for a bit position is 1 if one or the other (but not both) of the corresponding bits in the operands is 1.

    00110
   ^  00011
   =  00101

The result is 00101 or decimal 5.

System.out.println(6 ^ 3); // prints 5
System.out.println(3 ^ 6); // prints 5

Compound assignment operators

The compound assignment operators consist of two operators. They are shorthand operators.

a = a + 3;
a += 3;

The += compound operator is one of these shorthand operators. The above two expressions are equal. Value 3 is added to the a variable.

Other compound operators are:

-=   *=   /=   %=   &=   |=   <<=   >>= 

package com.zetcode;

public class CompoundOperators {

  public static void main(String[] args) {
    
    int a = 1;
    a = a + 1;
 
    System.out.println(a); 
    
    a += 5;
    System.out.println(a);  
    
    a *= 3;
    System.out.println(a);  
  }
}

In the example, we use two compound operators.

int a = 1;
a = a + 1;

The a variable is initiated to one. 1 is added to the variable using the non-shorthand notation.

a += 5;

Using a += compound operator, we add 5 to the a variable. The statement is equal to a = a + 5; .

a *= 3;

Using the *= operator, the a is multiplied by 3. The statement is equal to a = a * 3; .

$ java com.zetcode.CompoundOperators 
2
7
21

This is the example output.

The instanceof operator

The instanceof operator compares an object to a specified type.

package com.zetcode;

class Base {}
class Derived extends Base {}

public class InstanceofOperator {

  public static void main(String[] args) {
    
    Base b = new Base();
    Derived d = new Derived();
    
    System.out.println(d instanceof Base);
    System.out.println(b instanceof Derived);
    System.out.println(d instanceof Object);  
  }
}

In the example, we have two classes: one base and one derived from the base.

System.out.println(d instanceof Base);

This line checks if the variable d points to the class that is an instance of the Base class. Since the Derived class inherits from the Base class, it is also an instance of the Base class too. The line prints true.

System.out.println(b instanceof Derived);

The b object is not an instance of the Derived class. This line prints false.

System.out.println(d instanceof Object);  

Every class has Object as a superclass. Therefore, the d object is also an instance of the Object class.

$ java com.zetcode.InstanceofOperator 
true
false
true

This is the output of the com.zetcode.InstanceofOperator program.

Operator precedence

The operator precedence tells us which operators are evaluated first. The precedence level is necessary to avoid ambiguity in expressions.

What is the outcome of the following expression, 28 or 40?

3 + 5 * 5

Like in mathematics, the multiplication operator has a higher precedence than addition operator. So the outcome is 28.

(3 + 5) * 5

To change the order of evaluation, we can use parentheses. Expressions inside parentheses are always evaluated first. The result of the above expression is 40.

The following table shows common Java operators ordered by precedence (highest precedence first):

Operator	Meaning	Associativity
[] () .	array access, method invoke, object member access	Left-to-right
++ -- + -	increment, decrement, unary plus and minus	Right-to-left
! ~ (type) new	negation, bitwise NOT, type cast, object creation	Right-to-left
* / %	multiplication, division, modulo	Left-to-right
+ -	addition, subtraction	Left-to-right
+	string concatenation	Left-to-right
<< >> >>>	shift	Left-to-right
< <= > >=	relational	Left-to-right
instanceof	type comparison	Left-to-right
== !=	equality	Left-to-right
&	bitwise AND	Left-to-right
^	bitwise XOR	Left-to-right
|	bitwise OR	Left-to-right
&&	logical AND	Left-to-right
||	logical OR	Left-to-right
? :	ternary	Right-to-left
=	simple assignment	Right-to-left
+= -= *= /= %= &=	compound assignment	Right-to-left
^= |= <<= >>= >>>=	compound assignment	Right-to-left

Table: Operator precedence and associativity

Operators on the same row of the table have the same precedence. If we use operators with the same precedence, then the associativity rule is applied.

package com.zetcode;

public class Precedence {

  public static void main(String[] args) {
    
    System.out.println(3 + 5 * 5);
    System.out.println((3 + 5) * 5);

    System.out.println(! true | true);
    System.out.println(! (true | true));  
  }
}

In this code example, we show a few expressions. The outcome of each expression is dependent on the precedence level.

System.out.println(3 + 5 * 5);

This line prints 28. The multiplication operator has a higher precedence than addition. First, the product of 5*5 is calculated, then 3 is added.

System.out.println(! true | true);

In this case, the negation operator has a higher precedence than the bitwise OR. First, the initial true value is negated to false, then the | operator combines false and true, which gives true in the end.

$ java com.zetcode.Precedence 
28
40
true
false

This is the example output.

Associativity

Sometimes the precedence is not satisfactory to determine the outcome of an expression. There is another rule called associativity. The associativity of operators determines the order of evaluation of operators with the same precedence level.

9 / 3 * 3

What is the outcome of this expression, 9 or 1? The multiplication, deletion and the modulo operator are left to right associated. So the expression is evaluated this way: (9 / 3) * 3 and the result is 9.

Arithmetic, boolean, relational, and bitwise operators are all left to right associated. The assignment operators, ternary operator, increment, decrement, unary plus and minus, negation, bitwise NOT, type cast, object creation operators are right associated.

package com.zetcode;

public class Associativity {

  public static void main(String[] args) {

    int a, b, c, d;
    a = b = c = d = 0;

    String str = String.format("%d %d %d %d", a, b, c, d);
    System.out.println(str);

    int j = 0;
    j *= 3 + 1;
    System.out.println(j);
  }
}

In the example, we have two cases where the associativity rule determines the expression.

int a, b, c, d;
a = b = c = d = 0;

The assignment operator is right to left associated. If the associativity was left to right, the previous expression would not be possible.

int j = 0;
j *= 3 + 1;

The compound assignment operators are right to left associated. We might expect the result to be 1. But the actual result is 0. Because of the associativity. The expression on the right is evaluated first and than the compound assignment operator is applied.

$ java com.zetcode.Associativity 
0 0 0 0
0

Output of the com.zetcode.Associativity program.

The ternary operator

The ternary operator ?: is a conditional operator. It is a convenient operator for cases where we want to pick up one of two values, depending on the conditional expression.

cond-exp ? exp1 : exp2

If cond-exp is true, exp1 is evaluated and the result is returned. If the cond-exp is false, exp2 is evaluated and its result is returned.

package com.zetcode;

public class TernaryOperator {

  public static void main(String[] args) {
    
    int age = 31;

    boolean adult = age >= 18 ? true : false;

    System.out.println(String.format("Adult: %s", adult));  
  }
}

In most countries the adulthood is based on your age. You are adult if you are older than a certain age. This is a situation for a ternary operator.

bool adult = age >= 18 ? true : false;

First the expression on the right side of the assignment operator is evaluated. The first phase of the ternary operator is the condition expression evaluation. So if the age is greater or equal to 18, the value following the ? character is returned. If not, the value following the : character is returned. The returned value is then assigned to the adult variable.

$ java com.zetcode.TernaryOperator 
Adult: true

A 31 years old person is adult.

Calculating prime numbers

In the following example, we are going to calculate prime numbers.

package com.zetcode;

public class PrimeNumbers {

  public static void main(String[] args) {

    int[] nums = {1, 2, 3, 4, 5, 6, 7, 8,
      9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
      19, 20, 21, 22, 23, 24};

    System.out.print("Prime numbers: ");

    for (int num : nums) {
      
      if (num == 1 || num == 2 || num == 3) {
        
        System.out.print(num + " ");
        continue;
      }

      int i = (int) Math.sqrt(num);

      boolean isPrime = true;

      while (i > 1) {
        
        if (num % i == 0) {
          
          isPrime = false;
        }
        
        i--;
      }

      if (isPrime) {
        
        System.out.print(num + " ");
      }
    }

    System.out.print('\n');
  }
}

In the above example, we deal with several operators. A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. We pick up a number and divide it by numbers, from 1 up to the picked up number. Actually, we do not have to try all smaller numbers; we can divide by numbers up to the square root of the chosen number. The formula will work. We use the remainder division operator.

int[] nums = {1, 2, 3, 4, 5, 6, 7, 8,
  9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
  19, 20, 21, 22, 23, 24};

We will calculate primes from these numbers.

if (num == 1 || num == 2 || num == 3) {
  
  System.out.print(num + " ");
  continue;
}

We skip the calculations for the 1, 2, and 3 numbers. They are primes. Note the usage of the equality and conditional or operators. The == has a higher precedence than the || operator. So we do not need to use parentheses.

int i = (int) Math.sqrt(num);

We are OK if we only try numbers smaller than the square root of a number in question.

while (i > 1) { 
  ...
  i--;
}

This is a while loop. The i is the calculated square root of the number. We use the decrement operator to decrease the i by one each loop cycle. When the i is smaller than 1, we terminate the loop. For example, we have number 9. The square root of 9 is 3. We will divide the 9 number by 3 and 2. This is sufficient for our calculation.

if (num % i == 0) {
  
  isPrime = false;
}

If the remainder division operator returns 0 for any of the i values, then the number in question is not a prime.

In this part of the Java tutorial, we covered Java expressions.