Euler problem 19

I started writing this blog entry a year ago. It's about an Euler problem I solved in F#. The code makes more sense to me now than it did a year ago and I haven't touched F# since then. I guess I'm just way smarter now.

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Solving Euler problem no. 19 is the solution I'm most proud of. It's the first problem that I solved in F# with no assistance by the 'net.

The problem:

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?

It isn't an overly complex problem but there a couple of tricky aspects. The approach that I used was to start on the first Sunday of 1901 (6th Jan) and add seven days over and over (i.e., only counting Sundays) until the end of 2000. I could have used the .NET DateTime type to solve this problem very easily, but I decided to see if I could solve the problem using my own date type.

I solved the problem by using a few F# features, namely:

• pattern matching
• tuple
• record
• list

The first problem was February. February is a prickly month. Pattern matching will solve it! The febDays function accepts a year as a parameter and returns the number of days that February has.

    let febDays y = match y with
                            | y when y % 400 = 0 -> 29
                            | y when y % 100 = 0 -> 28
                            | y when y % 4 = 0 -> 29
                            | _ -> 28

After February was ready, I needed to know the number of days in any month, given the month (as a number) and the year. I used pattern matching again. Therefore,

    let daysInMonth (m, y) =
            match m with
            | 2 -> febDays y
            | 4 | 6 | 9 | 11 -> 30
            | _ -> 31

The other interesting function was to be able to add a day to a date. I did:

    let addDay date =
        match date.day with
        | d when d < 1 || d > daysInMonth(date.month, date.year) -> failwith "Not a valid day of the month."
        | d when d = daysInMonth(date.month, date.year) -> match date.month with
                                      | m when m < 1 || m > 12 -> failwith "Not a valid month."
                                      | m when m = 12 -> { day = 1; month = 1; year = date.year + 1}
                                      | _ -> { day = 1; month = date.month + 1; year = date.year}
        | _ -> { day = date.day + 1; month = date.month; year = date.year}

The code above isn't the whole solution, but it's the interesting parts. As you can see, I pretty much pattern matched the whole solution. It's a shame that C# doesn't have pattern matching because it's a really powerful language concept.

Tools for learning F#

Every few months I try to learn me some more F#. It isn’t easy.

I stumbled across a nice learning tool by Chris Marinos. It works on the premise that you learn by making the unit tests pass (initially, they all fail). It's a nice idea. The only issue is that the testing framework it uses was written in NUnit. I don't use NUnit anymore. With a couple of little changes I switched it to Microsoft's unit testing framework. You can get my version here.

There is also http://www.tryfsharp.org/. It gives a good intro to F# that you can do online (don't need Visual Studio or nothink).

I tried to do some interoperability between C# and F#. When testing an F# console app in a C# test project, my functions didn't return results. I changed my F# console app to a F# library and it worked correctly. (Don't know why C# can't use an F# console app.)

Learning a new (programming) language

I'm attempting to learn a new programming language. The main issue here is that F# isn't just a new language, it's a new type of language. There are three main (i.e. popular) paradigms of programming languages: imperative (the one you learn at school), object-orientated (the one most programmers use), and functional (the one I'm trying to learn). Object-orientated is really just an extension of imperative programming, so for me, learning F# is about learning how to re-think how to do things.

I thought I'd try to do the Euler problems like Andrew is doing at a misdirected effort.

My solution for problem 1 in F#:

let multiple x = if x % 3 = 0 || x % 5 = 0 then x else 0

let sequenceOfNumbers n = [1 .. n]

let euler1 numbers =
numbers
|> Seq.map multiple
|> Seq.sum

printf "Result = %i" (euler1 (sequenceOfNumbers 999))

The way I'd do it in C#, however, is:

static int Euler1(int maxValue)
{
 var sum = 0;
 for (var i = 1; i <= maxValue; i++
  if (i % 3 == 0 || i % 5 == 0)
   sum += i;

 return sum;
}

Is there really all that much difference? Could I have expressed it in F# in a more functional way? I don't know. Hopefully I can change the way I think about functional programming as I move through the problems.