### CyberSpy

Rantings from a guy with way too much free time

# Recursion Revisited

2017-11-28

### 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 $n\gt0$.

# Visualizing the News: Grab your PILlow

2017-11-12
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 https://newsapi.org/v1/articles GET https://newsapi.org/v1/sources Register for an account and generate an api-key and let’s get started. Accessing the API with Python newsapi can easily be accessed using a browser since the REST-ful method used is a GET method. Continue reading

# Making Heads or Tails out of Recursion and Combinatorial Math

2017-11-09
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

# Getting Visual With It

2017-11-08
Time to Get Vizzy With It! Like Will says: Gettin vizzy wit it Na na na na na na na nana Na na na na nana Gettin vizzy wit it… Plot thickens Time to turn on the lights and see what our data objects look like when we turn them into visualized plots. Sure, we can use the print function to see the numbers within our numpy objects. Better yet, let’s turn our objects into pretty graphical images. Continue reading

# Do the Numpy

2017-11-07
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

# Data Science with Python: Let there be Light

2017-11-05
Data-Science - Clueless? No prob. We got you dude. So you’ve likely heard all the hype about “data-science” - and if you’re not among the cool kids, it might be a wee-bit overwhelming to you. Where to even start? What does it all mean? How do you even begin to understand what you need to know to begin learning more and making progress in the field. Let’s start off with a few definitions: Continue reading

# Conway's Game of Life

2017-11-03
Conway’s Game of Life In 1970, British mathematician John Horton Conway invented a cellular automaton called The Game of Life. This simple game is governed by its initial cellular state and four simple rules: Any live cell with fewer than two live neighbors dies, as if caused by underpopulation. Any live cell with two or three live neighbors lives on to the next generation. Any live cell with more than three live neighbors dies, as if by overpopulation. Continue reading