Category Archives: Computer Science

An experimental estimation of the entropy of English, in 50 lines of Python code

“Th_ onl_ wa_ to ge_ ri_ of a tempta____ is to yie__ to it. Resi__ it, an_ you_ soul gro__ sic_ wi__ longi__ fo_ th_ thin__ it ha_ forbi____ to itse__.”

(Osc__ Wil__, The Picture __ ______ ____)

entrop_Thanks to the verbosity of the English language, proficient English speakers generally find it relatively easy to decipher the above passage despite the numerous omissions.

How does one quantify this redundancy? This article introduces the notions of Shannon entropy and information rate, and experimentally estimates the information rate of written English by training a Markov model on a large corpus of English texts. This model is finally used to generate gibberish that presents all the statistical properties of written English. Best of all, the entire source code fits in 50 lines of elegant Python code.

Continue reading

Linear time probabilistic pattern matching and the Rabin-Karp algorithm

Output of a multi-patterns string searching algorithmMost linear-time string searching algorithms are tricky to implement, and require heavy preprocessing of the pattern before running the search. This article presents the Rabin-Karp algorithm, a simple probabilistic string searching algorithm based on hashing and polynomial equality testing, along with a Python implementation. A streaming variant of the algorithm and a generalization to searching for multiple patterns in one pass over the input are also described, and performance aspects are discussed.

The algorithm is probabilistic in that it doesn’t always return correct results; more precisely, it returns all valid matches and (with reasonably small probability) a few incorrect matches (algorithms such as this one that tend to be over-optimistic in reporting their results are usually said to be true-biased).

Continue reading

Six months of Windows Phone Development — Tips, tricks, and performance considerations

A stroke order diagram for the character 羲 TL;DR: I’ve taken plenty of notes while developing my YiXue Chinese dictionary for Windows Phone. Topics covered in this article include performance tips, best practices, and plenty of code snippets for Windows Phone.


This article presents notes and remarks that I gathered while working on a Chinese Dictionary App for Windows Phone, YiXue Chinese Dictionary: mistakes I made, fun tips I wrote down, and so on.
I initially didn’t really intend to create a full blog post out of these notes, but their increasing number, and my app recently placing second in Microsoft France’s App Awards contest, gave me enough motivation to share them with the community. Along with various tips and tricks and answers to often-asked (but seldom answered) questions, I will discuss a number of performance improvements that specifically apply to Windows Phone apps.

Continue reading

Modeling and measuring string comparison performance in C, C++, C# and Python.

O(1) Comparing strings is often — erroneously — said to be a costly process. In this article I derive the theoretical asymptotic cost of comparing random strings of arbitrary length, and measure it in C, C++, C# and Python.

Continue reading

Generating uniformly random data from skewed input: biased coins, loaded dice, skew correction, and the Von Neumann extractor

A spinning coin, about to fall on tailsIn a famous article published 1951, John Von Neumann presented a way of skew-correcting a stream of random digits so as to ensure that 0s and 1s appeared with equal probability. This article introduces a simple and mentally workable generalization of his technique to random dice, so a loaded die can be used to uniformly draw numbers from the set \(\{1, 2, 3, 4, 5, 6\}\), with reasonable success.

Continue reading

How random is pseudo-random? Testing pseudo-random number generators and measuring randomness

After introducing true and pseudo-random number generators, and presenting the methods used to measure randomness, this article details a number of common statistical tests used to evaluate the quality of random number generators.

Continue reading

Unscrambling shuffled text

A story which surfaced a few years ago, and met quite some success in the press and on the internet, pretended Cambridge University had been conducing research on some of the most amazing faculties of the human brain. According to a supposed study, the order in which letters were laid out when writing a word mattered very little, provided the first and last letter be kept in place : this conclusion was supported by a short excerpt of shuffled text, which anyone could easily decipher. As a short example, consider the following sentence:

Narlmloy, radneig tihs shdulon’t be too hrad.

As many commentators pointed out at the time, the trick works well because the words used are relatively short; the following passage should be much harder to understand:

The eofrft rureieqd to sfssllcceuuy dhiepecr sbecmrald pgsaases daiaarclltmy ianserecs as wdors get lehegtinr.

This article presents an efficient algorithm to unshuffle scrambled text.

Continue reading