Exercise: Sequence In Range

Inside the directory you created for this course on JavaScript, create a new folder called Exercise-11-Sequence-In-Range and put the .html solution files for this exercise within it.

Let's start by enumerating the four cases in which there is no sequence to consider and when we must print the message 'Nothing to print'.

Here are these four cases:

• When d is 0, the sequence isn't progressing; thus, we have our first case.
• When a is equal to b, there is nothing to consider in the sequence. Thus, we have our second case.
• When a is less than b, the sequence should be increasing; thus d must be positive. If this is not the case (that is, if d is not positive), we have our third case.
• When a is greater than b, the sequence should be decreasing; thus d must be negative. If this is not the case (that is, if d is not negative), we have our fourth case.

First, let's implement these four cases using an if conditional and a couple of basic logical operators:

function printSequence(a, b, d) {
   if (d === 0 || a === b || (b < a && d > 0) || (a < b && d < 0)) {
      document.write('Nothing to print');
      return;
   }
}

So far, so good.

Beyond the if conditional, we know that the given parameters a, b and d are fine, and that we must proceed with printing the underlying sequence.

Doing so is very straightforward: just use a for loop, beginning at a, ending at b (exclusive), and incrementing by d (when d is negative, an increment would automatically become a decrement).

This is accomplished below:

function printSequence(a, b, d) {
   if (d === 0 || a === b || (b < a && d > 0) || (a < b && d < 0)) {
      document.write('Nothing to print');
      return;
   }
   for (var x = a; Math.sign(d) * (x - b) < 0; x += d) {
      var sep = ', ';
      if (x === a) {
         sep = '';
      }
      document.write(sep + x);
   }
}

A crucial point worth noting here is the condition of the loop: Math.sign(d) * (x - b) < 0. What is this and why do we use it instead of something like a < b?

Well, sometimes, depending on the values of a, b, and d, the given sequence would be increasing or decreasing. In the case of increasing, we need to use the condition x < b. However, in the latter case, i.e. when the sequence is decreasing, we need to use the condition x > b.

This difference in the operators used in each case means that we can't use either of these expressions, x < b or x > b, without some condition to determine which specific expression to use.

To solve this problem, we can take a number of different approaches. But perhaps the simplest would be to use the sign of d and a slight rearrangement of the inequalities shown above to cater to both the given cases.

• When d is positive, we need to use x < b which can be rearranged as x - b < 0.
• When d is negative, we need to use x > b which can be rearranged as -1 * (x - b) < 0.

This means that we can simply multiply the sign of d with (x - b) in order to get the correct expression to compare with < 0. And that's exactly what we do above, employing the Math.sign() method.

Another important thing to note in the code above is how we implement the ', ' separator between individual elements. On all but the first iteration, the separator sep is prepended to x.

This completes the function.

Let's now write the main program, asking the user to input the three parameters and then printing the sequence that corresponds to them.

Fortunately, it's very simple:

function printSequence(a, b, d) { /* ... */ }

var a = Number(prompt('a:'));
var b = Number(prompt('b:'));
var d = Number(prompt('d:'));
printSequence(a, b, d);

Here's how the program works:

Live Example

Perfect! Just as we wanted.

And this completes this exercise.