# Articles

## Iterative Tree Traversal

By memorizing a simple implementation of iterative tree traversal we simplify a large number of programming interview questions.

## How to Recover a Bitcoin Passphrase

How I recovered a Bitcoin passphrase by performing a Breadth-First search on typos of increasing Damerau-Levenshtein distances from an initial guess.

## Succinct de Bruijn Graphs

This post will give a brief explanation of a Succinct implementation for storing de Bruijn graphs [http://en.wikipedia.org/wiki/De_Bruijn_graph], which is recent (and continuing) work I have been doing with Sadakane. Using our new structure, we have squeezed a graph for a human genome (which

## Failing at Google Interviews

I’ve participated in about four sets of Google interviews (of about 3 interviews each) for various positions. I’m still not a Googler though, which I guess indicates that I’m not the best person to give this advice. However, I think it’s about time I put in

## FM-Indexes and Backwards Search

Last time (way back in June! I have got to start blogging consistently again) I discussed a gorgeous data structure called the Wavelet Tree [https://alexbowe.com/wavelet-trees/]. When a Wavelet Tree is stored using RRR sequences, it can answer rank and select operations in $\mathcal{O}(\log{A})$ time,

## Wavelet Trees: an Introduction

Today I will talk about an elegant way of answering rank queries on sequences over larger alphabets – a structure called the Wavelet Tree. In my last post [https://alexbowe.com/yarrr-me-hearties] I introduced a data structure called RRR, which is used to quickly answer rank queries on binary sequences, and

## RRR: A Succinct Rank/Select Index for Bit Vectors

This blog post will give an overview of a static bitsequence data structure known as RRR, which answers arbitrary length rank queries in $\mathcal{O}(1)$ time, and provides implicit compression. As my blog is informal, I give an introduction to this structure from a birds eye view. If you

## Generating Binary Permutations in Popcount Order

I’ve been keeping an eye on the search terms that land people at my site, and although I get the occasional “alex bowe: fact or fiction” and “alex bowe bad ass phd student” queries (the frequency strangely increased when I mentioned this on Twitter [http://www.twitter.com/alexbowe]

## Some Lazy Fun with Streams

Update:fellow algorithms researcherFrancisco Claude [http://fclaude.recoded.cl] just posteda great article about using lazy evaluation to solve Tic Tac Toe games in Common Lisp [http://fclaude.recoded.cl/archives/177]. Niki [http://niki.code-karma.com](my brother) also wrote a post using generators with asynchronous prefetching to hide