Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Find the sum of all the even-valued terms in the sequence which do not exceed four million.

The Thinking

The problem is similar to Problem 1, but this time instead of a natural number sequence, we're to use a fibbonacci sequence, evens only, less than 4 million. Then, we'll need to sum them up; that we did in Problem 1 with Seq.sum. How can we generate the sequence? I'll be taking a simple two-step approach. First, figure out a function to generate a fibbonacci sequence (up through 4,000,000), then take all the evens. We can Seq.sum that resulting sequence to find our answer.

Generating a Fibonacci Sequence

Generating a fibbonacci sequence in F# is a textboook case, and so much so that it's actually an example snippet for the built-in F# function we're going to use to generate it: Seq.unfold. Seq.unfold is a  function that returns a sequence, based on a function we provide. It takes two parameters: a sequence element generator function, and the inital value to start with.

Seq.unfold generator state

The generator function must be defined with a single input parameter (the "state value"), and returning an "option tuple of the next element in the sequence and the next state value" (from documentation).

A fibbonacci algorithm requires two inputs (the previous two digits), but we can only pass one parameter. Luckily in F# we have Tuples. A tuple lets us package up several values into a single group, and is written with as a comma separated list inside parenthesis:

let sometuple = ("this", "is", "a", "single", "tuple")

The return value is also something new, using the built-in Option module. We'll be returning an Option, either Some or None. None is a signal to unfold that this is the end of sequence, and for all the rest of the return results, we need to return Some-thing (the next element of the sequence as well as the next state value in tuple form) as we learned above, from the documentation for unfold.

This might seem like a lot to process all at once, but it ends up looking pretty simple when it's all put together. The generator function for fibbonacci numbers less than 4m looks like this:

let fibgen (x,y) = //define a function 'fibgen' and pass in a single parameter, a tuple that represents the most recent two digits of the fibbonacci sequence so far
if(x < 4000000) then // define a cut-off threshold to keep the sequence from going on forever
Some(x+y, (y, x+y)) // return an Option tuple; the next elemnet of the sequence: x+y (the two most recent elements added together), and the next state value- a single tuple that will be used next time the funciton is run
else None // we're up to 4m, so tell unfold we're done with the sequence

And now, we can plug that into Seq.unfold:

let fibseq = Seq.unfold fibgen (1,1) // (1,1) is a single tuple parameter with the initial values for the fibgen function

If we run this in the Interactive F# window in Visual Studio, we can confirm this produces the full fibbonacci sequence:

val it : seq = seq [2; 3; 5; 8; ...]

Getting Just The Evens

If you recall our solution to Problem 1, it should be easy to figure out how to make a new sequence with only the even values by using seq, modulo, and yield that we've already learned.

let fibevens = seq{for i in fibseq do if i % 2 = 0 then yield i}

My Solution

Putting it all together, with Seq.sum to add up the sequence:

let fibgen (x,y) = if(x < 4000000) then Some(x+y, (y, x+y)) else None
let fibseq = Seq.unfold fibgen (1,1)
let fibevens = seq{for i in fibseq do if i % 2 = 0 then yield i}
let result = Seq.sum fibevens
printfn "%A" result

Project Euler Problem 2: Answered

Further Reading

• Chapter 8- Functions & Functional Concepts, The F# Survival Guide
• Mark Pearl's post on Seq.Unfold, using tuple parameters and pipelines
• Seq.unfold
• Options module
• Tuples

A Post Script

Each part of the above solution is named for clarity. We could easily compose these functions for a more compact solution:

printfn "%A" (Seq.sum(seq{for i in ((1,1) |> Seq.unfold(fun (x,y) -> if(x < 4000000) then Some(x+y, (y, x+y)) else None)) do if i % 2 = 0 then yield i}))

The only thing that gets weird in this compact version is the anonymous replacement for fibgen, which uses lambda syntax fun & ->, and the pipeline operator, |> to pass in the intial state. There are some goofy rules for when you can and cannot use piplineing; check out the Pipeline section of Chapter 8 of The F# Survival Guide for a good primer.

How you can help

Download Default Programs Editor, and poke around. Mess with stuff. Make little tweaks to your system, then reverse them. What feels right? What gets annoying? What could be better? Let me know!

• Add a comment to this post
• Vote on open ideas at Default Programs Editor's official UserVoice Feedback forum
• Send me an email

SndVolPlus is a replacement sound volume control. Looks and acts like the default volume control, plus a few extra features.

Changes

• Position Mixer and Volume Control windows next to the taskbar tray area, fixing issue #4

Get it

Info/Download
Changeset

I've wanted to take a crack at Project Euler for some time now. If you're not familiar, it's basically a list of mathematical problems. From the site:

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

And they keep score! In addition, I've also been looking for an excuse to learn F#. In truth, I've wanted to get down and dirty with some functional language, to learn the principles and hopefully become a better programmer. I chose F# because it's part of Visual Studio (starting with 2010), and I'm already handy with .NET, so in theory that will lower the barrier to entry just a little bit. At the very least, it allows me to dodge the hassle of installing another interpreter or environment on my system.

Blogging It

As I continue though Project Euler, I'll be posting my solutions here on my site under http://factormystic.net/projects/code, and you can also check my progress by looking at my Project Euler profile and I look forward to your mocking laughter gentle guidance as I fumble around in F#.

On to Problem 1

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

Straightforward enough, and easy to form a mental model around the problem. But how to implement this in F#? For a quick language primer, I skimmed An Introduction to Functional Programming for .NET Developers and noticed a few things I might need:

• An add function
  let add x y = x + y
  
• Sequence syntax and list comprehension
  let numbers = {0..10}
  
• Modulo and ternary operators
  string result = x % 2 == 0 ? "yes" : "no";

The Thinking

The thinking is this: sequences could be used to build a list of integers 1 to 1000; I could use modulo to get multiples of 3 and 5 (think FizzBuzz), and somehow use that add function to get the sum. Reading the documentation for sequence expressions turned out to be quite rewarding (!), as you can embed a filter on a sequence when you declare it:

let multiples = seq { for i in 1 .. 1000 do if i % 3 = 0 || i % 5 = 0 then yield i }

Yield is already a familiar concept from C#, from using Enumerables. In fact, from the documentation:

Sequences are represented by the seq<'T> type, which is an alias for IEnumerable<T>. Therefore, any .NET Framework type that implements System.IEnumerable can be used as a sequence. The Seq module provides support for manipulations involving sequences.

Thus our F# is roughly analogous to something like

public static IEnumerable GiveMults()
{
foreach (int i in Enumerable.Range(1, 1000))
if (i % 3 == 0 || i % 5 == 0)
yield return i;
}

Now that we have our sequence of natural numbers, let's figure out how to sum them up. I have the add function I grabbed from the article, and while poking around with the Seq module, I noticed a reduce function, which can apply an accumulator. That would give us

let multiples = seq { for i in 1 .. 1000 do if i % 3 = 0 || i % 5 = 0 then yield i }
let add x y = x + y
let result= Seq.reduce add multiples
printfn "%A" result

(Side note: printfn is how we can write to stdout, much like Console.Writeline. The "%A" stuff works like string.Format parameters- %A indicates "Formats any value, printed with the default layout settings." In the case of a sequence, that means printing the first few values)

...and that code does indeed sum the multiples, as you would expect. But there is a better way. After all, we should expect something as simple as adding up a list to be built in already, and we do have our Seq module functions available.

Indeed, there is a Seq.sum function that does exactly what we're seeking to do, sum a sequence. Rewritten, we have:

let result = seq { for i in 1 .. 1000 do if i % 3 = 0 || i % 5 = 0 then yield i }
let total = Seq.sum result
printfn "%A" total

And this prints an answer, but that answer is WRONG. See the bug? The original problem stated that we're to "sum of all the multiples of 3 or 5 below 1000", but the list comprehension syntax (1..1000) is inclusive. Thus, our answer includes 1000, which is evenly divisible by 5, and is summed into the final total. The fix is simple, just write 1..999:

My Solution

let multiples = seq { for i in 1 .. 999 do if i % 3 = 0 || i % 5 = 0 then yield i }
let result = Seq.sum multiples
printfn "%A" result

Bingo.
Project Euler Problem 1: Answered

Further Reading

• An Introduction to Functional Programming for .NET Developers
• Sequences
• Core.Printf Module

A Post Script

For the code golf crew:

printfn "%A" (Seq.sum (seq { for i in 1 .. 999 do if i % 3 = 0 || i % 5 = 0 then yield i }))

SndVolPlus Volume Control

It functions exactly the same as the original "SndVol.exe", with two huge extras:

• Middle clicking the volume icon toggles mute
• Double clicking it opens the Volume Mixer directly

Windows 7 Volume Mixer

I wrote it out of frustration when I couldn't easily mute Windows Media Center when watching live television. Now that I can, I've put it up so you can to! This, like most of my recent projects, is BSD licensed open source, with it's own repository on BitBucket (link).

Info Page + Download

Version 2.6.1837.1459 (February 14, 2010)

Bugs Fixed:

- Fixed a discrepancy between value data types when saving to a .reg file vs saving to the registry when changing a context menu item name.

- DDE Message was not deleted if the program was running with elevated privileges.

- File type icon would sometimes not be detected correctly when the icon source was the default program.

Crashes Fixed:

- Deleting a context menu item would sometimes result in a crash.

- Inputting invalid character for context menu item name sometimes caused a crash.

- In some cases, opening the autoplay handlers page for some media types caused a crash.

- Saving context menu changes after editing a command label (including implicit edits) caused a crash.

Download now

Version 2.5.1823.2023 (February 9, 2010)

New Features:

+ Added support for DropTarget objects as context menu commands.

+ Added support for DelegateExecute objects as context menu commands.

+ Added support for Dynamic Data Exchange messages invoked with context menu commands.

+ On the Icon page, the raw resource path is now viewable and can be manually changed. It is also now possible to specify a file's own image in one click.

+ When changing an extension's file type, a revamped file type selection process shows all file types, even unused ones.

+ Added a checkbox to select/deselect all extensions on the extension selection page for Default Programs associations.

+ Added file path display to the final success page when changes are saved to file.

Bugs Fixed:

- Fixed a bug where the exported command path wouldn't be a normal string like it should have been.

- Fixed a bug where the wrong context menu item would be detected as the default.

- Fixed blank autoplay handler showing on the media options list after cancelling the creation of a new handler.

- Fixed incorrect default context menu item detection in some cases.

- Fixed a bug where an exported context menu .reg file could have a malformed key path.

- Saving edited file type Descriptions and Icons to file now correctly saves only those changed properties.

- The .reg file comment for Description and Icon changes will now also correctly describe which property is edited.

- The main instruction text on the Delete Extension page now reads appropriately.

- The link button to set a context menu item as default now enables or disables uniformly with the other controls.

- Some resource strings were not resolved properly (such as certain file type descriptions).

- Missing publisher information added to Control Panel uninstall data.

- Burnable Blu-ray discs now show correctly in the Autoplay media list.

- Fixed wrong capitalization for Blu-ray disc entry in the Autoplay media list.

- The behavior of the Done button on the Success page was not uniform for all page paths when launched from the Control Panel.

- The page history is cleared on the Success page to prevent old pages appearing as current.

- Fixed some extensions not being correctly detected as being registered for a Default Program.

- Fixed some extensions with blank descriptions on the Default Programs registration page.

- Additional small internal improvements, optimizations, and interface adjustments.

Crashes Fixed:

- Fixed a crash when saving a new file type without an icon set.

- Saving Autoplay settings after cancelling the creation of a new handler would cause a crash.

- Clicking the Help button would sometimes result in a crash on some systems.

- Attempting to install while another instance of the program was running caused a crash.

- Selecting a new default verb sometimes caused a crash when saving changes to file.

- Viewing certain file type descriptions sometimes caused a crash on the Extension Selection page.

- In certain cases, the program crashed when attempting to add or edit a context menu item where the destination registry key didn't yet exist.

- Adding a new file type but not entering optional details caused a crash when saving changes to file.

- Fixed a crash after clicking the Next button on the Default Programs selection page.

Holy cow! With the addition of DelegateExecute, DropTarget, and DDE support, Default Programs Editor is now the most powerful and easy to use file association utility on the planet.

Download now at http://defaultprogramseditor.com
Have an idea or feature request? Put it on the feedback forum: http://defaultprogramseditor.uservoice.com

What are Aero.Wizard and Aero.Controls?

Aero.Wizard is an WinForms implementation of an Aero Wizard Dialog. Aero.Controls is a package of a half dozen WinForms controls, intended for use with an Aero Wizard Dialog. These are some of the components I wrote for the creation of Default Programs Editor 2.0 with the revised user interface, and I'm now freely releasing them to the public.

Aero.Wizard:

Aero.Wizard Info Screenshot

Aero.Wizard Features:

• History/Navigation handled automatically
• Page contents are children of separate container controls, which can be created in design time like a regular Windows form
• Glass title area degrades gracefully when running a theme without glass, or on XP
• Blank Wizard Page template included
• Use with Aero.Controls pack to make Windows UX Guidelines compatible user interfaces

Aero.Controls:

Aero.Controls Info Screenshot

Aero.Controls Includes:

• Main Instructions Label
• Command Link button
• Instant Search Box
• UAC Shield Button
• Split Button
• Listview with Mixed State checkbox
• Aero Link Label

Both of these projects strive to adhere to the Windows User Experience Guidelines, freely available documentation from Microsoft which provided the basis for the DPE 2.0 restructuring.

Licensing

I debated for some time on this issue, trying to figure out a permissive license where I could retain some amount of ownership without being overbearing. I settled on BSD, which in my opinion is very permissive and seems to be low-friction for other developers to use this code in their projects.

Downloading

Both projects are hosted on Bitbucket (Mercurial) and you can either clone the repositories, or download the latest revision as a zip file. I encourage anyone to contribute bug fixes or report issues on each project's public issue ticketing system.

Aero.Wizard on Bitbucket

Aero.Controls on Bitbucket

What's next?

With the release of this code pack, my plan for fully releasing Default Programs Editor is underway. It is now possible to fully replicate the UI with this release. The next step is for me to continue refining and documenting the base file association library the project is built on, then release that as well as the UI logic for the program itself. Be looking for that in the next few months.

Version 2.4.1299.1247 (October 6, 2009)
Bugs Fixed:
- On the Delete Extension page, pressing the enter key on the selected item or in the search box, or double clicking the item now performs the primary action as it does on other similar pages.

Crashes Fixed:
- Fixed a crash resulting from not properly detecting the selection when trying to delete an extension.

Download
Leave some feedback on UserVoice

Also, Default Programs Editor was recently featured on both MakeUseOf and The How To Geek. Spread the word!

Version 2.3.1269.2247 (September 15, 2009)
New Features:
+ Option added to view (only) context menu shell extensions, restoring similar functionality that was present in 1.3.

Bugs Fixed:
- Fixed not being able to add autoplay options to media in some situations.
- It was not possible to click "Next" on the Extension Selection page when multiple extensions were selected using the shift key.
- With multiple extensions selected, the context menu page would not show all common verbs.

Crashes Fixed:
- Selecting multiple extensions caused a crash in some cases.

Download now from the main site
Leave feedback and vote on issues at the UserVoice page