Global Nerdy

After reading the previous article on FizzBuzz solutions, Reginald “raganwald” Braithwaite, whom I know from my days as part of the Toronto tech scene, tweeted this:

FWIW, I prefer the “grit” solutions. No modulo, no faking/implementing modulo.

Why?

Because the original child’s game isn’t about “if a number is divisible by X.” It’s about “every Xth number.”

And directly implementing “every Xth” is actually interesting.

— Reginald Braithwaite (@raganwald) June 17, 2020

JenniferPlusPlus agrees:

Yeah, I agree. In fact I like “every Nth” counting problem better than the factorization problem it’s usually treated as. So I was disappointed at all the solutions that didn’t just count, like so

Int n, x
Next(){
If (x == 0) x=n
Return –x
}

— Jenniferplusplus⚧🏳️‍🌈👩🏻‍💻 (@jennplusplus) June 17, 2020

They both make a good point. If you’re playing the FizzBuzz game as the original children’s game and not as an exercise to prove that you can actually write a program, you’d do it like this:

• Players sit in a circle, not unlike “the circle” in That ’70s Show.(Players don’t have to be high, unless it helps.)
• The player designated to go first says the number 1, and each player afterwards counts one number in turn. The next player in the circle says 2, and so on.
• However, for every third number, instead of calling out the number, the player whose turn it is should say “Fizz”.
• …and for every fifth number, instead of calling out the number, the player whose turn it is should say “Buzz”.
• The “Fizz” and “Buzz” rules, as the kids would say, stack. In other words, for every number that is both the third and fifth, the player needs to say “Fizz” followed by “Buzz”, or “FizzBuzz”.

So in the spirit of the original game, I’ve put together a FizzBuzz solution that uses “watchers” to keep track of  “every xth number”, with one watcher to keep track of when it’s time to say “Fizz”, and another for when it’s time to say “Buzz”. When it’s time to say “FizzBuzz”, they’ll work in tandem.

I created a class called WordWatcher, which can be summarized as shown below:

Here’s its code:

class WordWatcher:

  def __init__(self, interval, word):
    self.counter = 0
    self.time_for_word = False
    self.interval = interval
    self.word = word

  def observe_next_turn(self):
    self.counter += 1
    if self.counter == self.interval:
      self.counter = 0
      self.time_for_word = True
    else:
      self.time_for_word = False

  def speak(self):
    if self.time_for_word:
      return self.word
    else:
      return ""

Some notes about this code:

• • For those of you who aren’t familiar with Python’s approach to class methods, the first parameter for every method in a class is self. It’s the one parameter you don’t fill when calling a method, because Python calls it implicitly (seemingly in violation of Python’s general guideline that explicit is better than implicit). There’s a reason behind this, and it’s explained in this article: Understanding self in Python.
  • Also note that instance variables are declared and defined in the initializer method, __init__(), and any reference to them is always preceded by self.
  • The observe_next_turn() method is meant to be called as the fizzBuzz method proceeds to each new number. It updates the watcher’s internal counter and sets the time_for_word flag accordingly.
  • The speak() method outputs the watcher’s word if it’s time to say the word, or an empty string otherwise.

For FizzBuzz, we’ll need to create two watchers:

1. One to keep watch for every third turn, at which point it should say “Fizz”, and
2. one to keep watch for every third turn, at which point it should say “Buzz”.

With the WordWatcher class defined, we can create these two watchers like so:

fizz_watcher = WordWatcher(3, "Fizz")
buzz_watcher = WordWatcher(5, "Buzz")

It will become handy to have these two watchers in the same place. Since the “ha ha only serious” joke about Python is that everything is a list, let’s put them into a list:

word_watchers = [fizz_watcher, buzz_watcher]

Let’s define a fizzBuzz() function that makes use of this list of word watchers:

def fizzBuzz(word_watchers = [], first = 1, last = 100):
  final_result = ""

  for number in range(1, 101):
    current_result = ""

    if len(word_watchers) > 0:
      # This part might need some explaining
      _ = [word_watcher.observe_next_turn() for word_watcher in word_watchers]
      words = map(lambda word_watcher : word_watcher.speak(), word_watchers)
      current_result += functools.reduce(lambda total, next_element : total + next_element, list(words))
    
    if current_result == "":
      current_result = str(number)

    final_result += current_result

    if number < last:
      final_result += ", "
    else:
      final_result += "."

  return final_result

If you’ve been following the FizzBuzz series of articles, most of this code will be familiar. The part that might need explaining is the part with the comment “This part might need some explaining”.

Explaining the part that needs explaining

Let’s look at the first of the three lines of code in that part:

_ = [word_watcher.observe_next_turn() for word_watcher in word_watchers]

• The _ on the left side of the = sign is a throwaway variable. It says “I don’t care about what you do on the other side of the = sign; only that you do something on the other side of the = sign”.
• On the right side of the= sign is a list comprehension, which is Python’s “show, don’t tell” way of building lists. This list comprehension simply says “call the observe_next_turn() method of every object in the list”.

Let’s look at the next line:

words = map(lambda word_watcher : word_watcher.speak(), word_watchers)

• This line creates a map that converts the watchers in the list into the words they should say for this turn. If the current turn means that it’s time for any one of them to speak, the watcher will be mapped to the word it’s supposed to say. Otherwise, it will be mapped to an empty string.

And now, the final line:

current_result += functools.reduce(lambda total, next_element : total + next_element, list(words))

• For some reason, map() comes built into Python, but you have to import the functools library in order to use map()’s partner in crime, reduce(). Remember reduce() is a functional programming thingy that takes a collection of items, performs some kind of calculation on that collection, and returns a single value (which you might call a reduction of the collection).
• The first argument that I’ve provided to reduce() is a lambda — a small function that isn’t given a name — that simply takes the current item in the list and adds it to the previous collected items. Applied over the entire list, it builds a “total”, which in this case is all the words output by the watchers’ speak() methods concatenated together.
• The second argument is the words map converted into a list. This is the list that the reduce() method will operate on.

At the end of those three lines, current_result will contain one of the following:

• The empty string
• Fizz
• Buzz
• FizzBuzz

If current_result is still empty at this point, it means that it’s not time for any of the watchers’ words. If this is the case, the string version of the current number is concatenated to current_result:

if current_result == "":
      current_result += str(number)

Here’s the code in its entirety:

import functools

class WordWatcher:

  def __init__(self, interval, word):
    self.counter = 0
    self.time_for_word = False
    self.interval = interval
    self.word = word

  def observe_next_turn(self):
    self.counter += 1
    if self.counter == self.interval:
      self.counter = 0
      self.time_for_word = True
    else:
      self.time_for_word = False

  def speak(self):
    if self.time_for_word:
      return self.word
    else:
      return ""


def fizzBuzz(word_watchers = [], first = 1, last = 100):
  final_result = ""

  for number in range(1, 101):
    current_result = ""

    if len(word_watchers) > 0:
      _ = [word_watcher.observe_next_turn() for word_watcher in word_watchers]
      words = map(lambda word_watcher : word_watcher.speak(), word_watchers)
      current_result += functools.reduce(lambda total, next_element : total + next_element, list(words))
    
    if current_result == "":
      current_result += str(number)

    final_result += current_result

    if number < last:
      final_result += ", "
    else:
      final_result += "."

  return final_result

fizz_watcher = WordWatcher(3, "Fizz")
buzz_watcher = WordWatcher(5, "Buzz")
word_watchers = [fizz_watcher, buzz_watcher]
print(fizzBuzz(word_watchers))

And for completeness’ sake, here’s the test file:

import pytest
from fizzbuzz_with_watchers import fizzBuzz, WordWatcher

plain_1_to_100_result = "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100."
fizzBuzz_1_to_100_result = "1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz, 16, 17, Fizz, 19, Buzz, Fizz, 22, 23, Fizz, Buzz, 26, Fizz, 28, 29, FizzBuzz, 31, 32, Fizz, 34, Buzz, Fizz, 37, 38, Fizz, Buzz, 41, Fizz, 43, 44, FizzBuzz, 46, 47, Fizz, 49, Buzz, Fizz, 52, 53, Fizz, Buzz, 56, Fizz, 58, 59, FizzBuzz, 61, 62, Fizz, 64, Buzz, Fizz, 67, 68, Fizz, Buzz, 71, Fizz, 73, 74, FizzBuzz, 76, 77, Fizz, 79, Buzz, Fizz, 82, 83, Fizz, Buzz, 86, Fizz, 88, 89, FizzBuzz, 91, 92, Fizz, 94, Buzz, Fizz, 97, 98, Fizz, Buzz."

def test_fizzBuzz_null():
  result = fizzBuzz()
  assert result == plain_1_to_100_result, f"The watcher solution returned the wrong result:\nExpected: {plain_1_to_100_result}\nActual: {result}."

def test_fizzBuzz_fizz_and_buzz():
  fizz_watcher = WordWatcher(3, "Fizz")
  buzz_watcher = WordWatcher(5, "Buzz")
  word_watchers = [fizz_watcher, buzz_watcher]
  result = fizzBuzz([fizz_watcher, buzz_watcher])
  assert result == fizzBuzz_1_to_100_result, f"The watcher solution returned the wrong result:\nExpected: {fizzBuzz1To100Result}\nActual: {result}."

You can download fizzbuzz_with_watchers.py and test_fizzbuzz_with_watchers.py here (2KB, zipped folder with 2 Python files).

That’s a lot of fuss for Fizzbuzz. Why did you do all that?

1. Reginald asked me to, and I’ve known and respected him for ages, and JenniferPlusPlus seconded the request.
2. Wait until you see what customers ask you to do.

Did any of this stuff fly over your head?

1. Don’t feel bad. I had the same trouble when I first learned functional programming, and that was back in 1991, when the computers that ran functional language interpreters were in labs. I spent a lot of time in Queen’s University’s DEClab, which was full of machines that were cutting edge at the time made by a vendor that no longer exists. Computer time, as well as info on any kind of programming, never mind functional programming, was a lot harder to come by. (In case you were wondering, the language we learned was Miranda.)
2. If you’ve never worked in Python, some of it can be quite weird. It does eventually make sense.
3. Let me know, either via email or in the comments, if there’s anything you’d like me to cover in greater detail.

Do you have an alternate solution?

I’ve love to hear about it and present it here! Again, let me know via email or in the comments.

What’s next

An elegant JavaScript implementation.

Previously, in the “Programmer interview challenge” series

• Programmer interview challenge 1: Anagram
• Programmer interview challenge 1, revisited: Revising “Anagram” in Python and implementing it in JavaScript
• Programmer interview challenge 1, revisited again: “Anagram” in Swift, the easy and hardcore way
• Programmer interview challenge 1, revisited once more: “Anagram” in Ruby and C#
• Programmer interview challenge 2: The dreaded FizzBuzz, in Python
• Programmer interview challenge 2, part 2: Functional FizzBuzz
• Programmer interview challenge 2, part 3: FizzBuzz, minus the modulo operator, plus grit

The modulo operator

The standard FizzBuzz solution relies on the modulo operator, which it uses to determine if a number is a multiple of 3 or 5.

If you have a math, computer science, or engineering background, the odds are good that you encountered the modulo operator in your studies, as your courses tended to take a mathematical approach to  programming. (Remember relational calculus from your intro to databases course?)

If you came into programming from some other field and really got into it because you have a knack for problem-solving, you might not be aware of modulo math. That doesn’t mean that you can’t come up with a FizzBuzz solution.

FizzBuzz minus the modulo operator

When you present the FizzBuzz challenge to a large enough group of programmers — typically a dozen or more — there will be a very determined person who will insist that you provide them with no hints whatsoever. It happens.

When that happens, there’s invariably someone who’s either never heard of the modulo operator (%, which returns the remainder of a division operation) or has forgotten it exists. I’ve also seen a competition comprising quick programming challenges where contestants were told to implement FizzBuzz, but without using modulo.

The more mathematically-inclined will use a method like this:

def multiple_of_n(factor, number):
  return math.floor(number / factor) == number / factor

multiple_of_n() determines if a number n is a multiple of a factor f if the result of n / f is the same as n / f with the fractional part removed.

Occasionally, you’ll run into programmers who are unaware that there are functions to remove the fractional part of a number, either through rounding or truncation. Some of them make up for their lack of math background with a combination of creativity and grit.

I’ve seen one solution that looked something like this:

def multiple_of_5(number):
  number_as_string = str(number)
  last_digit = number_as_string[-1]
  return last_digit in ['0', '5']

This function turns the given number into a string, isolates the rightmost character of that string, and then returns True if that character is “0” or “5”, which is true for the string form of numbers that are multiples of 5.

My reaction:

That was nothing compared to one method I saw that someone cobbled together to determine if a number was a multiple of 3. They remembered the old grade-school rule that if you add the digits of a number and the total is a multiple of 3, then the number is a multiple of 3.

Based on that, they wrote something like this:

def multiple_of_3(number):
  number_as_string = str(number)
  total_of_digits = 0
  for digit in number_as_string:
    total_of_digits += int(digit)
  return total_of_digits in [3, 6, 9, 12, 15, 18]

Again, this function starts by converting the given number into a string. It then iterates through that string character by character, turning each character into a number and adding it to a running total. It then checks to see if that total is in a list of multiples of 3.

Since the standard FizzBuzz challenge is supposed to be performed on the numbers 1 through 100, the largest multiple of 3 will be 99, and the sum of its digits will be 18. Hence the list of multiples of 3 starts with 3 and ending with 18.

My reaction:

But hey, it works!

FizzBuzz plus grit

I’ve seen a handful of people with bachelors’ and even masters’ degrees in computer science face the FizzBuzz test and completely fail to produce working code. I’ve been more impressed by the self-taught coders who, in spite of not knowing about the modulo operator, charge head-first into the problem and solve it. These non-modulo solutions might cause a mathematician to react like this…

…but I think that they’re a sign of grit, which is an important quality for a programmer. These people took what they knew, applied a little creativity, and solved a problem that they shouldn’t have been able to solve. They remind me of a line from aviation pioneer Igor Sikorsky:

According to the laws of aerodynamics, the bumblebee can’t fly, but the bumblebee doesn’t know the laws of aerodynamics, so it goes ahead and flies.

Sooner or later, if you’re working on applications that actually matter, you’re going to run into seemingly insurmountable problems. There will always be the fear that something is just too hard to do. Impostor syndrome may rear its ugly head. Developing grit — and yes, it can be developed — is important, and it’s a quality I look for when forming a team.

What’s next

Using “watchers” to play FizzBuzz “properly”. 

Previously, in the “Programmer interview challenge” series

• Programmer interview challenge 1: Anagram
• Programmer interview challenge 1, revisited: Revising “Anagram” in Python and implementing it in JavaScript
• Programmer interview challenge 1, revisited again: “Anagram” in Swift, the easy and hardcore way
• Programmer interview challenge 1, revisited once more: “Anagram” in Ruby and C#
• Programmer interview challenge 2: The dreaded FizzBuzz, in Python
• Programmer interview challenge 2, part 2: Functional FizzBuzz