**Drawing complex hierarchical information manually is both cumbersome and time consuming. This task should not be done manually, but with a suitable piece of software. TreeJuggler is such a tool. It can layout hierarchical information compactly and optimize the drawing to any aspect ratio you need. Here is how to use it…** Continue reading

# Problem Reduction – The Most Reliable Path is Just Another Shortest Path

**Applications like Google Maps or navigation systems calculate shortest paths or fastest paths all the time. There have been very efficient algorithms to solve this task since the 50s. The most reliable path can be found via the same methods – using a little trick.** Continue reading

# Solving Knifflidiffels – A Legespiel With Duplicate Cards

**I recently stumbled upon a type of game that is not uncommon here in Germany. It is called a “Legespiel”, which can be translated into English as “tile-based game”. One of the most popular ones is called Knifflidiffels by Diddl. Similar pictures have to be put together. The different versions involving the cute mouse are not only very suitable for beginners, but also introduce another interesting aspect: duplicate cards.** Continue reading

# Juggling with Trees – How to Layout Hierarchical Information Compactly

**Hierarchical information is everywhere: Family trees, organizational charts, taxonomies or product breakdown structures. A good graphical representation can convey a lot of information very quickly. However, creating such a drawing manually is cumbersome. This article will show how such a task can be performed automatically.** Continue reading

# Rounding Errors And Arbitrary Precision Arithmetic

**The computer computes. Plus, minus, times and sometimes even divide. The results are always correct. Really? Computers usually use floating point numbers, which are very flexible, but still can cause quite substantial rounding errors – at least when you are doing complex calculations with many steps. These small inaccuracies can accumulate and become a creeping poison. Arbitrary precision arithmetic offers a way out.** Continue reading

# Backtracking in The Nursery – How to Solve a “Legespiel”

**I recently stumbled upon a type of game that is not uncommon here in Germany. It is called a “Legespiel”, which can be translated into english as “tile-based game”. The very specific type of tile-based game, this post will be about, has quadratic cards with pictures on them. These pictures must be arranged to a square in such a way that the pictures on each card fit together with the pictures of the cards around it. I will show how complex this problem is and also present an algorithm to solve it.** Continue reading