Testing and Selection Sort

One of the most important skills an intermediate to advanced programmer can have is the ability to tell when your code is correct. In this chapter, we'll discuss how you can write tests to evaluate code correctness. Along the way, we'll also discuss an algorithm for sorting called Selection Sort.

A New Way

When you write a program, it may have errors. In a classroom setting, you gain confidence in your code's correctness through some combination of user interaction, code analysis, and autograder testing, with this last item being of the greatest importance in many cases, particularly as it is how you earn points.

Autograders, of course, are not magic. They are code that the instructors write that is fundamentally not all that different from the code that you are writing. In the real world, these tests are written by the programmers themselves, rather than some benevolent Josh-Hug-like third party.

In this chapter, we'll explore how we can write our own tests. Our goal will be to create a class called Sort that provides a method sort(String[] x) that destructively sorts the strings in the array x.

As a totally new way of thinking, we'll start by writing testSort() first, and only after we've finished the test, we'll move on to writing the actual sorting code.

Writing a test for Sort.sort is relatively straightforward, albeit tedious. We simply need to create an input, call sort, and check that the output of the method is correct. If the output is not correct, we print out the first mismatch and terminate the test. For example, we might create a test class as follows:

public class TestSort {
/** Tests the sort method of the Sort class. */
public static void testSort() {
String[] input = {"i", "have", "an", "egg"};
String[] expected = {"an", "egg", "have", "i"};
Sort.sort(input);
for (int i = 0; i < input.length; i += 1) {
if (!input[i].equals(expected[i])) {
System.out.println("Mismatch in position " + i + ", expected: " + expected + ", but got: " + input[i] + ".");
break;
}
}
}

public static void main(String[] args) {
testSort();
}
}

We can test out our test by creating a blank Sort.sort method as shown below:

public class Sort {
/** Sorts strings destructively. */
public static void sort(String[] x) {
}
}

If we run the testSort() method with this blank Sort.sort method, we'd get:

Mismatch in position 0, expected: an, but got: i.

The fact that we're getting an error message is a good thing! This means our test is working. What's very interesting about this is that we've now created a little game for ourselves to play, where the goal is to modify the code for Sort.sort so that this error message no longer occurs. It's a bit of a psychological trick, but many programmers find the creation of these little mini-puzzles for themselves to be almost addictive.

In fact, this is a lot like the situation where you have an autograder for a class, and you find yourself hooked on the idea of getting the autograder to give you its love and approval. You now have the ability to create a judge for your code, whose esteem you can only win by completing the code correctly.

Important note: You may be asking "Why are you looping through the entire array? Why don't you just check if the arrays are equal using ==? ". The reason is, when we test for equality of two objects, we cannot simply use the == operator. The == operator compares the literal bits in the memory boxes, e.g. input == expected would test whether or not the addresses of input and expected are the same, not whether the values in the arrays are the same. Instead, we used a loop in testSort, and print out the first mismatch. You could also use the built-in method java.util.Arrays.equals instead of a loop.

While the single test above wasn't a ton of work, writing a suite of such ad hoc tests would be very tedious, as it would entail writing a bunch of different loops and print statements. In the next section, we'll see how the org.junit library saves us a lot of work.

JUnit Testing

The org.junit library provides a number of helpful methods and useful capabilities for simplifying the writing of tests. For example, we can replace our simple ad hoc test from above with:

public static void testSort() {
String[] input = {"i", "have", "an", "egg"};
String[] expected = {"an", "egg", "have", "i"};
Sort.sort(input);
org.junit.Assert.assertArrayEquals(expected, input);
}

This code is much simpler, and does more or less the exact same thing, i.e. if the arrays are not equal, it will tell us the first mismatch. For example, if we run testSort() on a Sort.sort method that does nothing, we'd get:

Exception in thread "main" arrays first differed at element ; expected:<[an]> but was:<[i]>
at org.junit.internal.ComparisonCriteria.arrayEquals(ComparisonCriteria.java:55)
at org.junit.Assert.internalArrayEquals(Assert.java:532)
...

While this output is a little uglier than our ad hoc test, we'll see at the very end of this chapter how to make it nicer.

Selection Sort

Before we can write a Sort.sort method, we need some algorithm for sorting. Perhaps the simplest sorting algorithm around is "selection sort." Selection sort consists of three steps:

• Find the smallest item.
• Move it to the front.
• Selection sort the remaining N-1 items (without touching the front item).

For example, suppose we have the array {6, 3, 7, 2, 8, 1}. The smallest item in this array is 1, so we'd move the 1 to the front. There are two natural ways to do this: One is to stick the 1 at the front and slide all the numbers over, i.e. {1, 6, 3, 7, 2, 8}. However, the much more efficient way is to simply swap the 1 with the old front (in this case 6), yielding {1, 3, 7, 2, 8, 6}.

We'd simply repeat the same process for the remaining digits, i.e. the smallest item in ... 3, 7, 2, 8, 6} is 2. Swapping to the front, we get {1, 2, 7, 3, 8, 6}. Repeating until we've got a sorted array, we'd get {1, 2, 3, 7, 8, 6}, then {1, 2, 3, 6, 8, 7}, then finally {1, 2, 3, 6, 7, 8}.

We could mathematically prove the correctness of this sorting algorithm on any arrays by using the concept of invariants that was originally introduced in chapter 2.4, though we will not do so in this textbook. Before proceeding, try writing out your own short array of numbers and perform selection sort on it, so that you can make sure you get the idea.

Now that we know how selection sort works, we can write in a few short comments in our blank Sort.sort method to guide our thinking:

public class Sort {
/** Sorts strings destructively. */
public static void sort(String[] x) {
// find the smallest item
// move it to the front
// selection sort the rest (using recursion?)
}
}

In the following sections, I will attempt to complete an implementation of selection sort. I'll do so in a way that resembles how a student might approach the problem, so I'll be making a few intentional errors along the way. These intentional errors are a good thing, as they'll help demonstrate the usefulness of testing. If you spot any of the errors while reading, don't worry, we'll eventually come around and correct them.

findSmallest

The most natural place to start is to write a method for finding the smallest item in a list. As with Sort.sort, we'll start by writing a test before we even complete the method. First, we'll create a dummy findSmallest method that simply returns some arbitrary value:

public class Sort {
/** Sorts strings destructively. */
public static void sort(String[] x) {
// find the smallest item
// move it to the front
// selection sort the rest (using recursion?)
}

/** Returns the smallest string in x. */
public static String findSmallest(String[] x) {
return x;
}
}

Obviously this is not a correct implementation, but we've chosen to defer actually thinking about how findSmallest works until after we've written a test. Using the org.junit library, adding such a test to our TestSort class is very easy, as shown below:

public class TestSort {
...
public static void testFindSmallest() {
String[] input = {"i", "have", "an", "egg"};
String expected = "an";

String actual = Sort.findSmallest(input);
org.junit.Assert.assertEquals(expected, actual);
}

public static void main(String[] args) {
testFindSmallest(); // note: we changed this from testSort!
}
}

As with TestSort.testsort, we then run our TestSort.testFindSmallest method to make sure that it fails. When we run this test, we'll see that it actually passes, i.e. no message appears. This is because we just happened to hard code the correct return value x. Let's modify our findSmallest method so that it returns something that is definitely incorrect:

/** Returns the smallest string in x. */
public static String findSmallest(String[] x) {
return x;
}

After making this change, when we run TestSort.testFindSmallest, we'll get an error, which is a good thing:

Exception in thread "main" java.lang.AssertionError: expected:<[an]> but was:<[null]>
at org.junit.Assert.failNotEquals(Assert.juava:834)
at TestSort.testFindSmallest(TestSort.java:9)
at TestSort.main(TestSort.java:24)

As before, we've set up for ourselves a little game to play, where our goal is now to modify the code for Sort.findSmallest so that this error no longer appears. This is a smaller goal than getting Sort.sort to work, which might be even more addictive.

Side note: It might have seem rather contrived that I just happened to return the right value x. However, when I was recording this lecture video, I actually did make this exact mistake without intending to do so!

Next we turn to actually writing findSmallest. This seems like it should be relatively straightforward. If you're a Java novice, you might end up writing code that looks something like this:

/**  Returns the smallest string in x. */
public static String findSmallest(String[] x) {
String smallest = x;
for (int i = 0; i < x.length; i += 1) {
if (x[i] < smallest) {
smallest = x[i];
}
}
return smallest;
}

However, this will yield the compilation error "< cannot be applied to 'java.lang.String'". The issue is that Java does not allow comparisons between Strings using the < operator.

When you're programming and get stuck on an issue like this that is easily describable, it's probably best to turn to a search engine. For example, we might search "less than strings Java" with Google. Such a search might yield a Stack Overflow post like this one.

One of the popular answers for this post explains that the str1.compareTo(str2) method will return a negative number if str1 < str2, 0 if they are equal, and a positive number if str1 > str2.

Incorporating this into our code, we might end up with:

/** Returns the smallest string in x.
* @source Got help with string compares from https://goo.gl/a7yBU5. */
public static String findSmallest(String[] x) {
String smallest = x;
for (int i = 0; i < x.length; i += 1) {
int cmp = x[i].compareTo(smallest);
if (cmp < 0) {
smallest = x[i];
}
}
return smallest;
}

Note that we've used a @source tag in order to cite our sources. I'm showing this by example for those of you who are taking 61B as a formal course. This is not a typical real world practice.

Since we are using syntax features that are totally new to us, we might lack confidence in the correctness of our findSmallest method. Luckily, we just wrote that test a little while ago. If we try running it, we'll see that nothing gets printed, which means our code is probably correct.

We can augment our test to increase our confidence by adding more test cases. For example, we might change testFindSmallest so that it reads as shown below:

public static void testFindSmallest() {
String[] input = {"i", "have", "an", "egg"};
String expected = "an";

String actual = Sort.findSmallest(input);
org.junit.Assert.assertEquals(expected, actual);

String[] input2 = {"there", "are", "many", "pigs"};
String expected2 = "are";

String actual2 = Sort.findSmallest(input2);
org.junit.Assert.assertEquals(expected2, actual2);
}

Rerunning the test, we see that it still passes. We are not absolutely certain that it works, but we are much more certain that we would have been without any tests.

Swap

Looking at our sort method below, the next helper method we need to write is something to move an item to the front, which we'll call swap.

/** Sorts strings destructively. */
public static void sort(String[] x) {
// find the smallest item
// move it to the front
// selection sort the rest (using recursion?)
}

Writing a swap method is very straightforward, and you've probably done so before. A correct implementation might look like:

public static void swap(String[] x, int a, int b) {
String temp = x[a];
x[a] = x[b];
x[b] = temp;
}

However, for the moment, let's introduce an intentional error so that we can demonstrate the utility of testing. A more naive programmer might have done something like:

public static void swap(String[] x, int a, int b) {
x[a] = x[b];
x[b] = x[a];
}

Writing a test for this method is quite easy with the help of JUnit. An example test is shown below. Note that we have also edited the main method so that it calls testSwap instead of testFindSmallest or testSort.

public class TestSort {
...

/** Test the Sort.swap method. */
public static void testSwap() {
String[] input = {"i", "have", "an", "egg"};
int a = 0;
int b = 2;
String[] expected = {"an", "have", "i", "egg"};

Sort.swap(input, a, b);
org.junit.Assert.assertArrayEquals(expected, input);
}

public static void main(String[] args) {
testSwap();
}
}

Running this test on our buggy swap yields an error, as we'd expect.

Exception in thread "main" arrays first differed in element ; expected:<[i]> but was:<[an]>
at TestSort.testSwap(TestSort.java:36)

It's worth briefly noting that it is important that we call only testSwap and not testSort as well. For example, if our main method was as below, the entire main method will terminate execution as soon as testSort fails, and testSwap will never run:

public static void main(String[] args) {
testSort();
testFindSmallest();
testSwap();
}

We will learn a more elegant way to deal with multiple tests at the end of this chapter that will avoid the need to manually specify which tests to run.

Now that we have a failing test, we can use it to help us debug. One way to do this is to set a breakpoint inside the swap method and use the visual debugging feature in IntelliJ. If you would like more information about and practice on debugging, check out Lab2. Stepping through the code line-by-line makes it immediately clear what is wrong (see video or try it yourself), and we can fix it by updating our code to include a temporary variable as that the beginning of this section:

public static void swap(String[] x, int a, int b) {
String temp = x[a];
x[a] = x[b];
x[b] = temp;
}

Rerunning the test, we see that it now passes.

Revising findSmallest

Now that we have multiple pieces of our method done, we can start trying to connect them up together to create a Sort method.

/** Sorts strings destructively. */
public static void sort(String[] x) {
// find the smallest item
// move it to the front
// selection sort the rest (using recursion?)
}

It's clear how to use our findSmallest and swap methods, but when we do so, we immediately realize there is a bit of a mismatch: findSmallest returns a String, and swap expects two indices.

/** Sorts strings destructively. */
public static void sort(String[] x) {
// find the smallest item
String smallest = findSmallest(x);

// move it to the front
swap(x, 0, smallest);

// selection sort the rest (using recursion?)
}

In other words, what findSmallest should have been returning is the index of the smallest String, not the String itself. Making silly errors like this is normal and really easy to do, so don't sweat it if you find yourself doing something similar. Iterating on a design is part of the process of writing code.

Luckily, this new design can be easily changed. We simply need to adjust findSmallest to return an int, as shown below:

public static int findSmallest(String[] x) {
int smallestIndex = 0;
for (int i = 0; i < x.length; i += 1) {
int cmp = x[i].compareTo(x[smallestIndex]);
if (cmp < 0) {
smallestIndex = i;
}
}
return smallestIndex;
}

Since this is a non-trivial change, we should also update testFindSmallest and make sure that findSmallest still works.

public static void testFindSmallest() {
String[] input = {"i", "have", "an", "egg"};
int expected = 2;

int actual = Sort.findSmallest(input);
org.junit.Assert.assertEquals(expected, actual);

String[] input2 = {"there", "are", "many", "pigs"};
int expected2 = 1;

int actual2 = Sort.findSmallest(input);
org.junit.Assert.assertEquals(expected2, actual2);
}

After modifying TestSort so that this test is run, and running TestSort.main, we see that our code passes the tests. Now, revising sort, we can fill in the first two steps of our sorting algorithm.

/** Sorts strings destructively. */
public static void sort(String[] x) {
// find the smallest item
// move it to the front
// selection sort the rest (using recursion?)
int smallestIndex = findSmallest(x);
swap(x, 0, smallestIndex);
}

All that's left is to somehow selection sort the remaining items, perhaps using recursion. We'll tackle this in the next section. In the meantime, in the figure below, we have detailed the evolution of our design. It's worth noting how we created tests first, and used these to build confidence that the actual methods work before we ever tried to use them for anything. This is an incredibly important idea, and one that will serve you well if you decide to adopt it.

FIGURECOMINGSOON

Recursive Helper Methods

To begin this section, consider how you might make the recursive call needed to complete sort:

/** Sorts strings destructively. */
public static void sort(String[] x) {
int smallestIndex = findSmallest(x);
swap(x, 0, smallestIndex);
// recursive call??
}

For those of you who are used to a language like Python, it might be tempting to try and use something like slice notation, e.g.

/** Sorts strings destructively. */
public static void sort(String[] x) {
int smallestIndex = findSmallest(x);
swap(x, 0, smallestIndex);
sort(x[1:])
}

However, there is no such thing in Java as a reference to a sub-array, i.e. we can't just pass the address of the next item in the array.

This problem of needing to consider only a subset of a larger array is very common. A typical solution is to create a private helper method that has an additional parameter (or parameters) that delineate which part of the array to consider. For example, we might write a private helper method also called sort that consider only the items starting with item start.

/** Sorts strings destructively starting from item start. */
private static void sort(String[] x, int start) {
// TODO
}

Unlike our public sort method, it's relatively straightforward to use recursion now that we have the additional parameter start, as shown below. We'll test this method in the next section.

/** Sorts strings destructively starting from item start. */
private static void sort(String[] x, int start) {
int smallestIndex = findSmallest(x);
swap(x, start, smallestIndex);
sort(x, start + 1);
}

Now that we have a helper method, we need to set up the correct original call. If we set the start to 0, we effectively sort the entire array.

/** Sorts strings destructively. */
public static void sort(String[] x) {
sort(x, 0);
}

This approach is quite common when trying to use recursion on a data structure that is not inherently recursive, e.g. arrays.

Debugging and Completing Sort

Running our testSort method, we immediately run into a problem:

Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 4
at Sort.swap(Sort.java:16)

Using the Java debugger, we see that the problem is that somehow start is reaching the value 4. Stepping through the code carefully (see video above), we find that the issue is that we forgot to include a base case in our recursive sort method. Fixing this is straightforward:

/** Sorts strings destructively starting from item start. */
private static void sort(String[] x, int start) {
if (start == x.length) {
return;
}
int smallestIndex = findSmallest(x);
swap(x, start, smallestIndex);
sort(x, start + 1);
}

Rerunning this test again, we get another error:

Exception in thread "main" arrays first differed at element ;
expected<[an]> bit was:<[have]>

Again, with judicious use of the IntelliJ debugger (see video), we can identify a line of code whose result does not match our expectations. Of note is the fact that I debugged the code at a higher level of abstraction than you might have otherwise, which I achieve by using Step Over more than Step Into. As discussed in lab 3, debugging at a higher level of abstraction saves you a lot of time and energy, by allowing you to compare the results of entire function calls with your expectation.

Specifically, we find that when sorting the last 3 (out of 4) items, the findSmallest method is giving as the 0th item ("an") rather than the 3rd item ("egg") when called on the input {"an", "have", "i", "egg"}. Looking carefully at the definition of findSmallest, this behavior is not a surprise, since findSmallest looks at the entire array, not just the items starting from position start. This sort of design flaw is very common, and writing tests and using the debugger is a great way to go about fixing them.

To fix our code, we revise findSmallest so that it takes a second parameter start, i.e. findSmallest(String[] x, int start). In this way, we ensure that we're finding the smallest item only out of the last however many are still unsorted. The revision is as shown below:

public static int findSmallest(String[] x, int start) {
int smallestIndex = start;
for (int i = start; i < x.length; i += 1) {
int cmp = x[i].compareTo(x[smallestIndex]);
if (cmp < 0) {
smallestIndex = i;
}
}
return smallestIndex;
}

Given that we've made a significant change to one of our building blocks, i.e. findSmallest, we should ensure that our changes are correct.

We first modify testFindSmallest so that it uses our new parameter, as shown below:

public static void testFindSmallest() {
String[] input = {"i", "have", "an", "egg"};
int expected = 2;

int actual = Sort.findSmallest(input, 0);
org.junit.Assert.assertEquals(expected, actual);

String[] input2 = {"there", "are", "many", "pigs"};
int expected2 = 2;

int actual2 = Sort.findSmallest(input2, 2);
org.junit.Assert.assertEquals(expected2, actual2);
}

We then modify TestSort.main so that it runs testFindSmallest. This test passes, strongly suggesting that our revisions to findSmallest were correct.

We next modify Sort.sort so that it uses the new start parameter in findSmallest:

/** Sorts strings destructively starting from item start. */
private static void sort(String[] x, int start) {
if (start == x.length) {
return;
}
int smallestIndex = findSmallest(x, start);
swap(x, start, smallestIndex);
sort(x, start + 1);
}

We then modify TestSort so that it runs TestSort.sort and voila, the method works. We are done! You have now seen the "new way" from the beginning of this lecture, which we'll reflect on for the remainder of this chapter.

Reflections on the Development Process

When you're writing and debugging a program, you'll often find yourself switching between different contexts. Trying to hold too much in your brain at once is a recipe for disaster at worst, and slow progress at best.

Having a set of automated tests helps reduce this cognitive load. For example, we were in the middle of writing sort when we realized there was a bug in findSmallest. We were able to switch contexts to consider findSmallest and establish that it was correct using our testFindSmallest method, and then switch back to sort. This is in sharp contrast to a more naive approach where you would simply be calling sort over and over and trying to figure out if the behavior of the overall algorithm suggests that the findSmallest method is correct.

As an analogy, you could test that a parachute's ripcord works by getting in an airplane, taking off, jumping out, and pulling the ripcord and seeing if the parachute comes out. However, you could also just pull it on the ground and see what happens. So, too, is it unnecessary to use sort to try out findSmallest.

As mentioned earlier in this chapter, tests also allow you to gain confidence in the basic pieces of your program, so that if something goes wrong, you have a better idea of where to start looking.

Lastly, tests make it easier to refactor your code. Suppose you decide to rewrite findSmallest so that it is faster or more readable. We can safely do so by making our desired changes and seeing if the tests still work.

Better JUnit

First, let's reflect on the new syntax we've seen today, namely org.junit.Assert.assertEquals(expected, actual). This method (with a very long name) tests that expected and actual are equal, and if they are not, terminates the program with a verbose error message.

JUnit has many more such methods other than assertEquals, such as assertFalse, assertNotNull, fail, and so forth, and they can be found in the official JUnit documentation. JUnit also has many other complex features we will not describe or teach in 61B, though you're free to use them.

While JUnit certainly improved things, our test code from before was a bit clumsy in several ways. In the remainder of this section, we'll talk about two major enhancements you can make so that your code is cleaner and easier to use. These enhancements will seem very mysterious from a syntax point of view, so just copy what we're doing for now, and we'll explain some (but not all) of it in a later chapter.

The first enhancement is to use what is known as a "test annotation". To do this, we:

• Precede each method with @org.junit.Test (no semi-colon).
• Change each test method to be non-static.
• Remove our main method from the TestSort class.

Once we've done these three things, if we re-run our code in JUnit using the Run->Run command, all of the tests execute without having to be manually invoked. This annotation based approach has several advantages:

• No need to manually invoke tests.
• All tests are run, not just the ones we specify.
• If one test fails, the others still run.
• A count of how many tests were run and how many passed is provided.
• The error messages on a test failure are much nicer looking.
• If all tests pass, we get a nice message and a green bar appears, rather than simply getting no output.

The second enhancement will let us use shorter names for some of the very lengthy method names, as well as the annotation name. Specifically, we'll use what is known as an "import statement".

We first add the import statement import org.junit.Test; to the top of our file. After doing this, we can replace all instances of @org.junit.Test with simply @Test.

We then add our second import statement import static org.junit.Assert.*. After doing this, anywhere we can omit anywhere we had org.junit.Assert.. For example, we can replace org.junit.Assert.assertEquals(expected2, actual2); with simply assertEquals(expected2, actual2);

We will explain exactly why import statements are in a later lecture. For now, just use and enjoy.

Testing Philosophy

No text provided. Video only.