Operator Precedence Intro to Programming 1. Elements of Programming 1.1 Your First Program 1.2 Built-in Types of Data 1.3 Conditionals and Loops 1.4 Arrays 1.5 Input and Output 1.6 Case Study: PageRank 2. Functions 2.1 Static Methods 2.2 Libraries and Clients 2.3 Recursion 2.4 Case Study: Percolation 3. OOP 3.1 Using Data Types 3.2 Creating Data Types 3.3 Designing Data Types 3.4 Case Study: N-Body 4. Data Structures 4.1 Performance 4.2 Sorting and Searching 4.3 Stacks and Queues 4.4 Symbol Tables 4.5 Case Study: Small World Computer Science 5. Theory of Computing 5.1 Formal Languages 5.2 Turing Machines 5.3 Universality 5.4 Computability 5.5 Intractability 9.9 Cryptography 6. A Computing Machine 6.1 Representing Info 6.2 TOY Machine 6.3 TOY Programming 6.4 TOY Virtual Machine 7. Building a Computer 7.1 Boolean Logic 7.2 Basic Circuit Model 7.3 Combinational Circuits 7.4 Sequential Circuits 7.5 Digital Devices Beyond 8. Systems 8.1 Library Programming 8.2 Compilers 8.3 Operating Systems 8.4 Networking 8.5 Applications Systems 9. Scientific Computation 9.1 Floating Point 9.2 Symbolic Methods 9.3 Numerical Integration 9.4 Differential Equations 9.5 Linear Algebra 9.6 Optimization 9.7 Data Analysis 9.8 Simulation Related Booksites Web Resources FAQ Data Code Errata Lectures Appendices A. Operator Precedence B. Writing Clear Code C. Glossary D. TOY Cheatsheet E. Matlab Online Course Java Cheatsheet Programming Assignments Appendix A: Operator Precedence in Java Java has well-defined rules for specifying the order in which the operators in an expression are evaluated when the expression has several operators. For example, multiplication and division have a higher precedence than addition and subtraction. Precedence rules can be overridden by explicit parentheses. Precedence order. When two operators share an operand the operator with the higher precedence goes first. For example, 1 + 2 * 3 is treated as 1 + (2 * 3), whereas 1 * 2 + 3 is treated as (1 * 2) + 3 since multiplication has a higher precedence than addition. Associativity. When an expression has two operators with the same precedence, the expression is evaluated according to its associativity. For example x = y = z = 17 is treated as x = (y = (z = 17)), leaving all three variables with the value 17, since the = operator has right-to-left associativity (and an assignment statement evaluates to the value on the right hand side). On the other hand, 72 / 2 / 3 is treated as (72 / 2) / 3 since the / operator has left-to-right associativity. Some operators are not associative: for example, the expressions (x <= y <= z) and x++-- are invalid. Precedence and associativity of Java operators. The table below shows all Java operators from highest to lowest precedence, along with their associativity. Most programmers do not memorize them all, and even those that do still use parentheses for clarity. Level Operator Description Associativity 16 [] . () access array element access object member parentheses left to right 15 ++ -- unary post-increment unary post-decrement not associative 14 ++ -- + - ! ~ unary pre-increment unary pre-decrement unary plus unary minus unary logical NOT unary bitwise NOT right to left 13 () new cast object creation right to left 12 * / % multiplicative left to right 11 + - + additive string concatenation left to right 10 << >> >>> shift left to right 9 < <= > >= instanceof relational not associative 8 == != equality left to right 7 & bitwise AND left to right 6 ^ bitwise XOR left to right 5 | bitwise OR left to right 4 && logical AND left to right 3 || logical OR left to right 2 ?: ternary right to left 1 = += -= *= /= %= &= ^= |= <<= >>= >>>= assignment right to left There is no explicit operator precedence table in the Java Language Specification. Different tables on the web and in textbooks disagree in some minor ways. Order of evaluation of subexpressions. Associativity and precedence determine in which order Java applies operators to subexpressions but they do not determine in which order the subexpressions are evaluated. In Java, subexpressions are evaluated from left to right (when there is a choice). So, for example in the expression A() + B() * C(D(), E()), the subexpressions are evaluated in the order A(), B(), D(), E(), and C(). Although, C() appears to the left of both D() and E(), we need the results of both D() and E() to evaluate C(). It is considered poor style to write code that relies upon this behavior (and different programming languages may use different rules). Short circuiting. When using the conditional and and or operators (&& and ||), Java does not evaluate the second operand unless it is necessary to resolve the result. This allows statements like if (s != null && s.length() < 10) to work reliably. Programmers rarely use the non short-circuiting versions (& and |) with boolean expressions. Precedence order gone awry. Sometimes the precedence order defined in a language do not conform with mathematical norms. For example, in Microsoft Excel, -a^b is interpreted as (-a)^b instead of -(a^b). So -1^2 is equal to 1 instead of -1, which is the values most mathematicians would expect. Microsoft acknowledges this quirk as a “design choice.” One wonders whether the programmer was relying on the C precedence order in which unary operators have higher precedence than binary operators. This rule agrees with mathematical conventions for all C operators, but fails with the addition of the exponentiation operator. Once the order was established in Microsoft Excel 2.0, it could not easily be changed without breaking backward compatibility. Exercises. What is the result of the following code fragment?
int x = 5;
int y = 10;
int z = ++x * y--;
What is the result of the following code fragment? Explain.
System.out.println("1 + 2 = " + 1 + 2);
System.out.println("1 + 2 = " + (1 + 2));
Answer: 1 + 2 = 12 and 1 + 2 = 3, respectively. If either (or both) of the operands of the + operator is a string, the other is automatically cast to a string. String concatenation and addition have the same precedence. Since they are left-associative, the operators are evaluated left-to-right. The parentheses in the second statement ensures that the second + operator performs addition instead of string concatenation. Add parentheses to the following expression to make the order of evaluation more clear.
year % 4 == 0 && year % 100 != 0 || year % 400 == 0
Answer: LeapYear.java shows a variety of equivalent expressions, including the following reasonable alternative.
((year % 4 == 0) && (year % 100 != 0)) || (year % 400 == 0)
What does the following code fragment print?
System.out.println(1 + 2 + "abc");
System.out.println("abc" + 1 + 2);
Answer: 3abc and abc12, respectively. The + operator is left associative, whether it is string concatenation or addition. Last modified on July 27, 2017. Copyright © 2000–2019 Robert Sedgewick and Kevin Wayne. All rights reserved.
