## The 6×7×6 palette (Coding with fractions of bits, Part I)

August 6, 2019

Remember ye olde dayes when we had to be mindful of the so-called “web safe palette“? Once upon a time, screens could display 24-bits colors, but only 256 at a time in some “hi-res” modes. But that’s not what I’m going to tell you about: I’d rather tell you about the encoding of the palette, and about a somewhat better palette. And also about using fractions of bits for more efficient encodings.

## Serializing Trees

September 6, 2016

Quite a while ago I discussed using flat arrays and address calculations to store a tree in a simple array. The trick wasn’t new (I think it’s due to Williams, 1964 [1]), but is only really practical when we consider heaps, or otherwise very well balanced trees. If you have a misshapen tree, that trick doesn’t help you. It doesn’t help you either if you try to serialize a misshapen tree to disk.

But what if we do want to serialize arbitrarily-shaped trees to disk? Is it painful? Fortunately, no! Let’s see how.

## Of Drunkards

August 6, 2013

In a city with orthogonal streets and regular city block, a party-goer leaves a bar and walks back home. His home is North East from the bar, $N$ blocks up, and $E$ blocks east. At each intersection, he decide to go either north or east randomly—but whatever’s left of his sobriety keeps from backtracking: he always moves closer to home. How many ways can the drunkard get get back home?

## Huffman Codes

May 17, 2011

Some time ago, I presented a piece on compressing voxel worlds and I just realized that I discussed different types of variable length codes quite a few times, but that I never took the time to present you the basic method of Huffman coding!

The problem of finding an optimal variable length code is to find an uniquely decodable binary code (that is, a code using only 0 and 1 for which there exists only one way of decoding a message) that encodes each symbol in a number of bits that is proportional to its probability of occurrence. A first strategy was devised by Robert Fano, Huffman’s teacher at one point. The so-called Shannon-Fano code is a top-down approach to solving the problem but it was shown to be suboptimal. The code proposed by David Huffman solves the problem optimally by taking exactly the opposite approach, that is, building the code bottom-up.