examples.circuits

Class Triangle

java.lang.Object

examples.circuits.Triangle

public class Triangle
extends java.lang.Object

Given a list of elements, determines if they represent the lengths of the sides of a valid triangle. This is a rephrasing of the "self-assessment exercise" that opens Glenford Myers' book:

• G. J. Myers. (1979). The Art of Software Testing, Wiley, ISBN 0471043281.

Given a vector, the program verifies the following conditions, in this order:

1. The vector must contain exactly three elements
2. The three elements must be numbers
3. The three numbers must be positive
4. Each pair of positive numbers must verify the triangle inequality with respect to the third

These conditions are evaluated in a fail-fast manner: the first that fails stops the operation. Indeed, if the vector does not contain three elements, attempting to evaluate the second condition on it would throw an exception —and so on.

The circuit itself is described in Triangle.IsValidTriangle.

Explanation

It is interesting to examine the lineage graphs one can obtain, depending on the input vector. This is done in the program by changing the contents of variable vector that is given to the function.

Incorrect number of elements

The first graph corresponds to the execution of the program on the vector [1, 2] (click on the graph to see it full size):

The function that is mentioned in the graph is GetSize; the other parts of the circuit are not present. Therefore, the graph correctly "explains" that the issue with the input vector is related to its size.

Incorrect element type

The second graph corresponds to the execution of the program on the vector [1, 2, "foo"]:

This time, the function that appears in the lineage graph is InstanceOf. Moreover, one can observe that the only part of the input vector that is mentioned is its third element ([2]). This correctly reveals that this element, and only this one, is of an invalid type.

Negative values

The third graph corresponds to the execution of the program on the vector [1, 2, -1]:

The function that appears in the explanation is ">0"; again this time, the only part of the input involved in the explanation is the third element of the vector ([2]). Therefore, this graph contains all the pieces to explain that the element is not positive.

Violation of the triangle inequality

The fourth graph corresponds to the execution of the program on the vector [1, 2, 1]:

Triangle.TriangleInequality is the function that appears in the graph. Since the inequality involves all three elements of the vector, it is normal to see all three as leaves of the graph. However, the graph also reveals that, among the three possible ways of grouping sides to form the inequality, only one of them is invalid. The leaves corresponding to the first and third element ([0] and [2]) are grouped under the addition, while the second [1] is compared to them. Indeed, we see that 1+1 is not greater than 2. The other two inequalities are satisfied, and therefore are not present in the graph.

Valid triangle

The last graph corresponds to the execution of the program on the vector [2, 3, 4], which corresponds to a valid triangle:

This time, one can see that all parts of the circuit are present. Indeed, all conditions must be true for the circuit to produce the value true.

This small example shows that a lineage graph can not only identify the parts of the inputs that explain a result, but also the parts of the circuit that are relevant for this result.

Author:

Sylvain Hallé

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected static class	Triangle.AllNumbers Determines if all three elements of of vector are positive numbers.
protected static class	Triangle.AllPositive Determines if the first three elements of a vector are positive.
protected static class	Triangle.IsPositive Function that determines if a number is positive.
static class	Triangle.IsValidTriangle Determines if a vector contains the lengths of sides of a valid triangle.
protected static class	Triangle.TriangleInequality Verifies the triangle inequality on a vector of three numbers.

Constructor Summary

Constructors

Constructor and Description
Triangle()

Method Summary

Modifier and Type	Method and Description
static void	main(java.lang.String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Triangle

public Triangle()

Method Detail

main

public static void main(java.lang.String[] args)