Skyline puzzle

One of my colleagues brought the following puzzle to work:

Skyline puzzle

The puzzle is called Skyline and it’s a packing puzzle. The objective is to place the metal rod in one of the holes in the base and place the nine wooden pieces around it. It was designed by Jean Claude Constantin. When solved, the puzzle looks something like this:

Skyline solution

Sometimes with these kinds of puzzles it’s quicker to write a program that finds a solution than trying to solve it by hand. Check out this github repository for a Prolog program that finds solutions for a given rod location.

To use this program open the file skyline.pl in your favorite Prolog interpreter (e.g. SWI-Prolog) and execute the following:

You can press ; to find alternative solutions. The pos(X,Y) part refers to the location of the metal rod.

MLP in C++11

In this post I present my Christmas gift to the world: A multilayer perceptron written in C++11.

I mainly wrote this to get some practice with some of the new C++11 features such as variadic templates and lambda functions. It uses template metaprogramming to construct (but not train) the neural network at compile time. You can download the code from its github repository. It’s lacking proper documentation, but I’ve included two examples that should get you started: the xor problem and Fisher’s Iris data set.

Happy Holidays.

Statisticians are evil

I’ve made it my life’s goal to replace all statisticians with cute little robot bunnies. Watch the following video for a demo of my first prototype.

I developed a server in Prolog for the Nabaztag:tag bunny and hooked it up with a dialogue system I created during my masters. It uses an unofficial Google API for speech recognition and generation. It’s quite slow sometimes because of the poor Wi-Fi connection, the inefficient polling of the Nabaztag and the speech recognition. I have some ideas though for improving its speed. Read on for a transcript of the dialogue with comments.

Continue reading

Win32 PPlot

A while ago I was looking for a simple lightweight c++ library that could produce some basic charts. I quickly found the PPlot library which is designed to easily integrate with different GUI toolkits and also comes with bindings for ruby and python. To make the library usable within different GUI frameworks the drawing part has been abstracted to a Painter class. For each GUI framework a different Painter class must be implemented. The library comes with ready made implementations for GUI toolkits like wxWidgets and QT. However, I wanted to use the PPlot library in a pure win32 application and had to implement my own Painter class. If you’re in a similar situation check out my source for an example.

 

Chip-8 emulator

I’ve always been interested in emulators and just finished my Chip-8/SCHIP emulator. Chip-8 is an interpreted programming language that was first used on some early homecomputers and later on the HP48 calculator. The emulator allows you to play some retro games like pong and invaders.

The emulator is written in C++ and is available for download here. Besides the program and source code I’ve also included some games that seem to work ok. The original machines that ran a chip-8 interpreter had a 16 key hex-keypad that looked like this:

1 2 3 C
4 5 6 D
7 8 9 E
A 0 B F

This keypad is emulated on the PC keyboard like this:

1 2 3 4
Q W E R
A S D F
Z X C V

Happy gaming!

Bridge and torch puzzle

Four people need to cross a bridge at night which only supports two people at the same time. Person A needs 1 minute to cross the bridge, B needs 2 minutes, C needs 5 minutes and D needs 10 minutes. When two people cross the bridge they move at the slowest person’s pace.  They have a torch which has battery left for only 17 minutes. They can’t cross the bridge without light. How can they manage to cross the bridge?

One might guess that an obvious solution would be to let the fastest person (A) shuttle each other person over the bridge and return alone with the torch. This would give the following schedule:

A, B -> 2
A <- 1
A,C -> 5
A <- 1
A,D -> 10

The total duration of this schedule would be 19 minutes, so the torch would run out of battery while person A and D are still on the bridge.

The optimal solution consists of letting the two slowest people (C and D) cross the bridge together, giving the following schedule:

A, B -> 2
B <- 2
C,D -> 10
A <- 1
A,B -> 2

Which gives a total crossing time of exactly 17 minutes.

Writing a prolog program to solve this kind of river crossing problems is a walk in the park. Check it out if you want to know an alternative solution.

Checkers game

Long, long time ago, when I was still a full time student, I once became first in a checkers cup with a program I wrote. Alas, those days of glory are over. Looking back, the program was pretty simple. Choosing an efficient board representation made generating the moves a piece of cake and my program didn’t make use of any opening libraries or endgame strategies. It just implemented minimax search with alpha-beta pruning. Although it wasn’t really sophisticated, I still think the program was pretty sweet and I felt disappointed when I realized I had lost the source code. That’s why I decided to implement this game again only this time in Java (the original was written in C++). I fired up NetBeans and this is the result.

Happy birthday to Benoît Mandelbrot

Today the father of fractal geometry turns 83. Benoît Mandelbrot is known for the Mandelbrot set, a set of points in the complex plane that forms a fractal. To see if a point c belongs to the Mandelbrot set start with z0 = 0 and generate the sequence z1, z2, z3,.. by iterating the function zn+1 = zn2 + c. If the value z remains close to the origin, the value c belongs to the Mandelbrot set. If it runs away to infinity, it doesn’t. Plotting the set of points in the complex plane gives you this picture.

mandelbrot.jpg

The picture is the result of running a small program I wrote on the TI-83+ calculator. You can download it from here. The program runs for several hours. The zip-file also includes two of my other TI-Basic fractal programs. A Julia fractal and the Sierpinski triangle.

Prolog solution to Einstein’s riddle

The following puzzle is said to be invented by Einstein. Supposedly, he also claimed that only 2% of the world’s population would be smart enough to solve it.

There are 5 houses in 5 different colors in a row. In each house lives a person with a different nationality. These 5 owners drink a certain drink, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar or drink the same drink.

The question is: WHO OWNS THE FISH?

HINTS:

  • the Brit lives in the red house
  • the Swede keeps dogs as pets
  • the Dane drinks tea
  • the green house is on the immediate left of the white house
  • the green house owner drinks coffee
  • the person who smokes Pall Mall rears birds
  • the owner of the yellow house smokes Dunhill
  • the man living in the house right in the center drinks milk
  • the Norwegian lives in the first house
  • the man who smokes blends lives next to the one who keeps cats
  • the man who keeps horses lives next to the one who smokes Dunhill
  • the owner who smokes Bluemaster drinks beer
  • the German smokes prince
  • the Norwegian lives next to the blue house
  • the man who smokes blends has a neighbor who drinks water

Working out the solution with nothing more that a pen and some paper is certainly doable by, I suspect hope, a larger percentage of people than the 2 % mentioned above. But as an example of how to solve these kinds of logic puzzles using Prolog, I wrote this code.

Sudoku solver

It’s pretty straightforward to make a Sudoku solver in Prolog especially when applying CLP (Constraint Logic Programming).

Here is how to use my program:

Then you can enter the known numbers one by one.

When complete, the program determines and prints the solution.

Typing

Gives

By pressing ; over and over again, you could enumerate all 6,670,903,752,021,072,936,960 possible Sudoku solution grids, but this might take a while..

It shouldn’t be too hard to extend this program to actually create new puzzles. If anyone does, let me know.

The prolog environment I used here is SWI-Prolog.