After writing an application, a programmer typically tests it thoroughly. Creating an exhaustive set of tests often is quite difficult, and it is always possible that a particular case remains untested. One technique that can help you test your programs thoroughly is to use invariants. An invariant is an assertion (see Section 13.13) that is true before and after the a portion of your code executes. Invariants are mathematical in nature and their concepts are more applicable to the theoretical side of computer science.
The most common type of invariant is a loop invariant. A loop invariant is an assertion that remains true
A properly written loop invariant, can help you code a loop correctly. There are four steps to developing a loop from a loop invariant.
As an example, we will examine method linearSearch from class LinearArray in Fig. 16.2. The invariant for the linear search algorithm is:
for all k such that 0 <= k and k < index
data[ k ] != searchKey
For example, suppose index equals 3. If we pick any non-negative number less than 3 such as 1 for the value of k, the element in data at location k in the array does not equal the searchKey. This invariant basically states that the portion of the array, called a subarray, from the start of the array up to but not including the element at index does not contain the searchKey. A subarray can have no elements, or it can encompass the entire array.
According to Step 1, we must first initialize control variable index. From the invariant, we see that if we set index to 0, then the subarray contains zero elements. Therefore, the invariant is true because a subarray with no elements cannot contain a value that matches the searchKey.
The second step is to determine the condition that causes the loop to terminate. The loop should end after searching the entire arraywhen index equals the length of the array. In this case, no element of array data matches the searchKey. Once the index reaches the end of the array, the invariant remains trueno elements in the subarray (which in this case is the entire array) equal the searchKey.
For the loop to proceed to the next element, we increment control variable index. The last step is to ensure the invariant remains true after each iteration. The if statement (lines 2627 of Fig. 16.2) determines whether data[ index ] equals the searchKey. If so, the method finishes and returns index. Because index is the first occurrence of searchKey in data, the invariant is still truethe subarray up to index does not contain the searchKey.
Introduction to Computers, the Internet and the World Wide Web
Introduction to Java Applications
Introduction to Classes and Objects
Control Statements: Part I
Control Statements: Part 2
Methods: A Deeper Look
Classes and Objects: A Deeper Look
Object-Oriented Programming: Inheritance
Object-Oriented Programming: Polymorphism
GUI Components: Part 1
Graphics and Java 2D™
Files and Streams
Searching and Sorting
Introduction to Java Applets
Multimedia: Applets and Applications
GUI Components: Part 2
Accessing Databases with JDBC
JavaServer Pages (JSP)
Strings, Characters and Regular Expressions
Appendix A. Operator Precedence Chart
Appendix B. ASCII Character Set
Appendix C. Keywords and Reserved Words
Appendix D. Primitive Types
Appendix E. (On CD) Number Systems
Appendix F. (On CD) Unicode®
Appendix G. Using the Java API Documentation
Appendix H. (On CD) Creating Documentation with javadoc
Appendix I. (On CD) Bit Manipulation
Appendix J. (On CD) ATM Case Study Code
Appendix K. (On CD) Labeled break and continue Statements
Appendix L. (On CD) UML 2: Additional Diagram Types
Appendix M. (On CD) Design Patterns
Appendix N. Using the Debugger
Inside Back Cover