Comparables and Comparators

In this lesson, we’re going to learn about the Comparable and Comparator interfaces in Java. These interfaces help us to, well, compare pairs of objects to determine and order between them.

The sorting problem

Consider the problem of sorting a list of objects, any objects. You’ve probably studied a number of sorting algorithms like insertion sort, merge sort, quick sort, etc. They all work slightly differently, but ultimately the outcome is the same: applying a sort function to a collection of data should give you back that same collection, with the items arranged in order.

The “in order” in the sentence above is actually doing a lot of work.

Every sort function needs to, at some point, do a pairwise comparisons of objects in the collection that’s being sorted. All other parts of the sort function could stay the same, but we need some way to define how that pairwise comparison is carried out.

When we think about sorting a list of numbers, its meaning is often clear: we often mean to order the numbers in ascending order, i.e., smallest-to-largest. That is, for any pair of numbers, we know the smaller one should come before the larger one. Suppose, instead, you have a list of strings. Slightly more complicated, sure. But again, the meaning is often clear: we mean to sort the list in alphabetical order.

Now consider more complex objects, say, an Album object that contains a number of fields (or instance variables):

• String title
• String artist
• int year
• double price

How should a list of Albums be sorted? By title, artist, year? Some combination of fields?

Consider the following sort function that implements insertion sort.¹ How we perform that pairwise comparison is going to depend on what is being sorted. That is, we don’t want to have to re-write this function for different types of data.

The blank in the if statement is where the comparison should take place. That is, we need to check if arr[j] is “less than” arr[j - 1], whatever that means for the particular data being sorted. How should that comparison take place?

public static void sort(Album[] arr) {
  for (int i = 1; i < arr.length; i++) {
    for (int j = i; j > 0; j--) {
      if (______________________) { // Compare arr[j] and arr[j - 1]
        // Swap arr[j] and arr[j-1]
        Album temp = arr[j];
        arr[j] = arr[j - 1];
        arr[j - 1] = temp;
      } else {
        break;
      }
    }
  }
}

How should we compare Albums? We can write custom code to compare any two Albums using whatever criterion we think is a good “natural ordering” for Albums.

Observe that, no matter what type of data we’re sorting, the rest of that sort function will stay the same. The only part of the function that needs to change is the comparison in the if statement.

Can we abstract out that comparison so that the sort doesn’t need to know how it’s being done?

Comparable

That’s where the Comparable interface comes in. It is used when we create a class and we want to define a “natural” ordering between any pair of objects created from that class. The Comparable interface contains a single abstract method that must be implemented by implementing subclasses:

public int compareTo(T o)

Two things are worth discussing about the method signature above.

1. The parameter T o: The T here is a placeholder type. The Comparable interface doesn’t know what type of data is going to be compared, and doesn’t care.
2. The int return type.

The compareTo function’s job is to compare this object (the calling object) with the parameter object (o), to decide their ordering relative to each other. This is not a binary decision: there are three possible outcomes. So we cannot use a boolean as the return type.

The “contract” for the compareTo function is:

• If this is “less than” o, i.e., it should come before o, return a negative number.
• If this is “greater than” o, i.e., should come after o, return a positive number.
• If this and o are equal, return 0. In general, it’s recommended that if this.equals(o) is true, then this.compareTo(o) should return 0.

Consider the code below. We have an Album class that is declared to be Comparable. We are saying Album objects are comparable to other Album objects. This means the Album must define a compareTo method.

In the example below, we are saying that, by default, Albums are compared using their titles. Notice that we are not ourselves writing a lexicographic comparison of this.title and o.title: title is a String, which itself implements the Comparable interface. We can use that.

public class Album implements Comparable<Album> {
  private final String title;
  private final String artist;
  private final int year;
  private double price;

  // ... Assume we have written a constructor, getters, setters etc.

  @Override
  public int compareTo(Album o) {
    return this.title.compareTo(o.title);
  }
}

What does this get us?

Consider our sort function example from above. If, instead of using Album[] as our parameter type, we used a Comparable[] as our parameter type, we can now use the same sort function for any data type, as long as that data type implements the Comparable interface.

See the if statement in the updated sort function below.

public static void sort(Comparable[] arr) {
  for (int i = 1; i < arr.length; i++) {
    for (int j = i; j > 0; j--) {
      if (arr[j].compareTo(arr[j - 1]) < 0) { // If arr[j] is "less than" arr[j - 1]
        // Swap arr[j] and arr[j-1]
        Album temp = arr[j];
        arr[j] = arr[j - 1];
        arr[j - 1] = temp;
      } else {
        break;
      }
    }
  }
}

This is an example of using abstraction — we are ignoring or abstracting away the details of the specific object being sorted, and only focusing on the salient detail, i.e., the fact that it can be compared to other objects of its own type. Because we can use compareTo, we don’t need to know or care what specific type of object is stored in arr.

And this is exactly what is done in sort functions already available in the Java standard library. The Collections class provides a number of helpful static functions; among them is Collections.sort.

If you have a list of objects, and those objects are Comparable, you can call Collections.sort on that list to sort it according to the object’s “natural ordering”, i.e., according to its compareTo method.

Note that Collections.sort sorts the list in place, meaning it mutates the underlying list, instead of returning a new sorted list.

List<Album> albums = Arrays.asList(
  new Album("Rubber Soul", "The Beatles", 1965, 18.99),
  new Album("1989 (Taylor's Version)", "Taylor Swift", 2023, 18.99),
  new Album("1989", "Taylor Swift", 2014, 18.99),
  new Album("Leaving Eden", "The Carolina Chocolate Drops", 2012, 18.99)
);

// If Album does not implement Comparable, this line won't compile.
Collections.sort(albums);

for (Album current : albums) {
  System.out.println(current);
}

The code above would print:

1989
1989 (Taylor's Version)
Leaving Eden
Rubber Soul

Suppose you were asked to handle tie-breakers. E.g., for albums with the same title, break ties by artist name. How would you handle this in the compareTo function?

Can you change Album’s compareTo to induce a reversed ordering, i.e., in descending order?

Comparator

The ComparABLE interface is used to define a “natural ordering” for an object. What exactly does that mean?

You should use Comparable when there is an argument to made that there is an obvious way to compare two objects of a given type. For example, the String class in Java implements the Comparable interface. It defines what many would naturally expect when they compare two String objects, say, for the purpose of sorting. It compares Strings using their lexicographic ordering, i.e., their alphabetic order.

However, sometimes you need to order a collection of objects using something other than its natural order. Or you need to order a collection of objects that cannot be reasonably considered to have a “natural” ordering for all circumstances. These are cases in which you need to define, on an as-needed basis, a custom comparison between two objects.

That’s where the ComparATOR interface comes in. These two interfaces are annoyingly similarly named, I know.

Comparing albums by their price

So, for example, suppose we need to compare albums by their price, and not by their “natural” ordering based on title.

The Comparator interface defines one abstract method that must be implemented by subclasses:

public int compare(T o1, T o2)

This is very similar to the compareTo method for the Comparable. The only difference is now we take two parameters instead of one, because both items to be compared are being passed to the method. That is, the “calling object” is not the one being compared, so this is not really relevant here.

To compare Albums by price, we would create a new class that implements the Comparator interface, and implement the required compare function in that class.

public class AlbumPriceComparator implements Comparator<Album> {
  public int compare(Album o1, Album o2) {
    if (o1.getPrice() > o2.getPrice()) {
      return 1; // Can return any positive integer
    } else if (o1.getPrice() < o2.getPrice()) {
      return -1; // Can return any negative integer
    } else {
      return 0;
    }
  }
}

This comparator object can then be used to impose “custom” orderings on Albums.

How does this help us? The Collections.sort function has an overloaded version that takes two parameters:

• A collection of objects
• A comparator to use for pairwise comparisons

If you use this version of the Collections.sort function, you don’t need the objects being sorted to be ComparABLE. This is because the second parameter, the ComparATOR, knows how to compare those objects.

List<Album> albums = ...; // Same list as before
Comparator<Album> priceComp = new AlbumPriceComparator();

// Sort the albums in ascending order of price 
// Doesn't matter here whether or not Album implements Comparable
Collections.sort(albums, priceComp);

In the next lesson…

We can also dynamically create Comparators on an as-needed basis. Comparators are useful when you don’t know upfront how a collection of objects is going to be compared or sorted.

Continuing with the Album example, consider your music library in whatever application you use to manage and listen to your music. Chances are you’ve seen a “table view” that lists all the songs in your library, and you can click on the columns in that table to change how the songs are sorted. E.g., if you click on “Title” the songs will be sorted by title. If you click on “Artist” the order will change. If you click again, it’ll reverse it.

These are dynamic changes in the current sort order, i.e., they are happening while the program (the application, Spotify or whatever) is running. Can we programmatically spin up new Comparators to support these changes in desired sort orders?

Doesn’t this seem like a lot of work to just write one compare function? All we really care about is that compare function, but because we need to “pass” the compare function to the sort function, we went through the rigmarole of wrapping it in a class and creating an object.

In the next lesson, we’ll learn about using lambdas in Java to concisely create new Comparators. Lambdas allow us to treat functions as values that can be stored and passed around, e.g., as parameters to other functions. We’ll use that as a springboard to learn about lambdas and functional programming more generally.