The Month Lengths Problem

The first time I've heard of this problem, I was 14.

At school, during the math class, we started to learn the basics of programming using a language called L2P (no, you won't find it on Wikipedia and, no, it's not worth learning it).

Anyway, this is, more or less, the problem the teacher gave us to solve:

Write a function that returns the number of days of a month in a given year.

Plain Solutions

Any solution must start with the management of February.

    if (month == 2) {
        if (!(year % 100) && (year % 400))
                days = 28;
        else if (!(year % 4))
                days = 29;
                days = 28;

Once we have done with the most troublesome month, one solution can involve an array of twelve integers filled at design time with the right numbers. This is probably the way that I'd solve it today but I don't think the teacher would have liked it.

Another good solution is to check first the months with 30 days since they are only four: April, June, September and November.

if ((month == 4) || (month == 6) || (month == 9) || (month == 11))  
        days = 30;
        days = 31;

Obviously the above solution can be rewritten, in a more readable way, with a switch statement. I'll leave it to you as homework ;-)

Well, you can say that the above code is the solution to the problem. And, when I was 14, I was convinced too. But the teacher was not satisfied. She had another solution.

C'mon, Show Me How Smart You Are

The management of February was the same, but for other months the code was a little tricky.

if (((month < 8) && !(month % 2)) || ((month > 8) && (month % 2)))  
        days = 30;
        days = 31;

Have you understood the logic behind this? Basically, the months with 30 days are:

  • the even ones between March and July and
  • the odd ones after August.You can tell this if you think deeply about the numbers (like a math teacher is supposed to do). But is this a good solution? No, it isn't. And probably it's the worst.

Keep It Simple, Schoolteacher

It has at least two weaknesses: performances* and **readability. Speaking about the execution speed, two comparisons and two modules are definitely slower than four comparisons.

But the biggest issue is the second: you don't have to show me that you are a good programmer. If you write code that is not easily understandable, you will never be a good member for a development team where everyone should be able to modify each others code.

So, dear teacher, you have been rejected in Computer Science.

A Final Confession

OK, I confess. I've been a little too trenchant. The teacher's solution is not so bad. It has a big quality: the spur to think different, to explore different solutions. Because only comparing different things you can choose the best one.

Image taken from Wikimedia Commons (public domain).

Luca Sommacal

Luca Sommacal

Italian developer (mainly in C for embedded platforms), Linux learner, addicted to rock music, history, science and few other things. Follow me on Twitter

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