Algorithm Repository
This page provides a comprehensive collection of algorithm implementations for seventy-five of the most fundamental problems in combinatorial algorithms. The problem taxonomy, implementations, and supporting material are all drawn from my book The Algorithm Design Manual. Since the practical person is more often looking for a program than an algorithm, we provide pointers to solid implementations
The Mathematics of 2048: Counting States by Exhaustive Enumeration
Updates 2017-12-11 This post was discussed on Hacker News. This post is the third in a series. Next: Optimal Play with Markov Decision Processes. So far in this series on the mathematics of 2048, we’ve seen that it takes at least 938.8 moves on average to win, and we’ve obtained some rough estimates on the number of possible states using combinatorics. In this post, we will try to refine those est
Adventures in enumerating balanced brackets
Since I’ve been coaching my school’s ACM ICPC programming team, I’ve been spending a bit of time solving programming contest problems, partly to stay sharp and be able to coach them better, but also just for fun. I recently solved a problem (using Haskell) that ended up being tougher than I thought, but I learned a lot along the way. Rather than just presenting a solution, I’d like to take you thr
Crystal Ball Connection Patterns via Species and Generating Functions
A couple weeks ago, Denise posted Puzzle: Crystal Ball Connection Patterns on her blog, Let’s Play Math. I had fun playing with it and thought I would demonstrate how to apply some high-powered combinatorial techniques to it (probably not what Denise had in mind!). The setup is that there are (distinct) friends who can talk to each other on the phone. Only two people can talk at a time (no confere
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The Erdős-Rényi Random Graph
Math 3012: Applied Combinatorics
