Rantings from a guy with way too much free time

Recursion Revisited

2017-11-28 3 minute read python programming recursion elixir Rob Baruch

Recursion, from more than one point-of-view.

A common programming idiom in computer science is solving a problem by self-reference, also known as recursion. In this post, we look at two different implementations of the same problem.

Solve a recursive problem in two different programming language paradigms

Let’s look at the solution to a simple problem, compute $f(x)=e^{x}$.

We will illustrate two separate solutions - one in a procedural language (python), and the other in a functional language (elixir).

Let’s start off with the functional language. Were does recursion come into play?

We define the function $f(x)=e^x$ as the infinite sum, $\text{ }f(x) = \sum_{n=0}^\infty{\frac{x^n}{n!}}$

In our solution below, we define two separate recursive functions, exp/2 and fac/1. What’s interesting to note here is how each of these functions has two separate definitions. This is an aspect of programming in elixir that elegantly uses pattern-matching to return different results depending upon the input. Our two functions nicely dovetail into the base-case and recursive case of a recursive algorithm.

For example, looking at exp/2, the first function definition returns 1 for any value of x (as indicated by the _ preceding the variable) and returns 1. This is the mathematical equivalent of $x^0=1\text{ for any }x$.

The second definition of exp/2 is the recursive case. for any value of $n\gt0$. Moreover, we define exp(x, n) as $\frac{e^x}{n!}$ + exp(x, n-1).

Similarly for the definition of fac/1 we see two definitions; one for $n=0$ and another for all values of $n\gt0$.

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Visualizing the News: Grab your PILlow

2017-11-12 5 minute read python programming
A Picture’s Worth a Gazillion Bits newsapi This weekend, I tripped over a neat news REST-ful api called newsapi. Grab an API key and you’re off to the races. There are tons of live headlines - News API can provide headlines from 70 worldwide sources. There are basically two api endpoints: GET GET Register for an account and generate an api-key and let’s get started. Continue reading

Making Heads or Tails out of Recursion and Combinatorial Math

2017-11-09 4 minute read programming math python
GNU — GNU’s Not Unix I thought I’d take a look at two topics at once and make some fun by mashing them together. Today’s topic is recursion. In computer science (and in math, although we call the equation a recurrence relation) recursion is an often misunderstood concept causing lots of panic and anxiety. In reality - it’s pretty easy once you wrap you head around the idiom. What is recursion? Continue reading

Do the Numpy

2017-11-07 3 minute read programming python
Do the Numpy Dance, Is your Chance to do the Nump! Sir Numpy says: The Numpy Dance is your chance to do the nump Do the Numpy Nump, come on and do the Numpty Nump Do the Numpy Nump, just watch me do the Numpty Nump Do ya know what I’m doin’, doin’ the Numpty Nump Do the Numpy Nump, do the Numpty Nump Start at the beginning: NumPy The first library that we will investigate is numpy. Continue reading