## A random Golden Ratio Appears!

November 12, 2013

Well, we all make errors once in a while, but sometimes they’re more interesting than others. So I inadvertently forgot a square in a calculation and the series suddenly started converging, to the most beautiful of convergences of all: $\phi$.

So, let’s see how I got the golden ratio to emerge from a broken algorithm.

## Hash Table and Magic (Relatively Primes) Numbers

September 17, 2013

Today, let’s talk about hash tables. Or, more precisely, one type of secondary probing technique, one that uses some number theory—but not quadratic residues, just relatively prime numbers.

I don’t know if you’re like me, but it often bugs me when I read something in a textbook that seems to make sense, but is claimed without proof nor demonstration (oh, I think I said that before). That seems to happen particularly often when I read stuff about data structures, and this time I decided to explore one of those claims.

## Cats, Pharaohs, and the Golden Ratio

December 8, 2009

Certain numbers keep showing up in nature. The Golden Ratio,

$\phi \approx \displaystyle\frac{1+\sqrt{5}}{2}$

is one of them. It shows up in cats, sunflowers, and Egyptian pyramids.

## Generating Random Sequences (part I)

September 29, 2009

Every once in a while, we need a random sequence. Whether to test a data structure’s performance or to run probabilistic unit tests, the provided rand primitive from your favorite programming language has several limitations. First, it’s been known for a while that if most implementations of the C standard library rand() function are not very random, despite being “good enough” in great many cases. Second, and more importantly, it does not allow you to easily control the period nor to generate a permutation on $0\ldots n-1$, for example.

There are many methods of generating pseudo-random number sequences. Not all exhibit the same properties and, accordingly, a method may be more useful in one case and perfectly useless in another. High quality pseudo-random number generation is a notoriously hard endeavor, but there is a number of very simple algorithms that will get you out of trouble for certain specific tasks. Let us consider, for example, the example where the pseudo-random generator must generate the numbers in $0\ldots{}n-1$ exactly once, in a random order, of course, in exactly $n$ draws.