The Fibonacci sequence

The Fibonacci sequence is a sequence of numbers starting with 0 and 1 and then adding the sum of the two last numbers at the end of the sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The mathematical representation of the Fibonacci sequence is:

F(n) = F(n-1) + F(n-2)
Read More

Routing with angular

Angular’s ngRoute is useful when building single page apps with multiple views. It allows you to easily load a template into the screen and initialize the controller associated with it.

This is not only helpful to keep your code organized by having different controllers for different screens, but also gives your users a way to create bookmarks that associate a URL in the address bar with the current content of your app. This is a piece of functionality that has always been part of the web(links), so it is a good a idea to keep it there so users don’t run into unexpected behavior.

Read More

Unique paths

A robot is located at the top-left corner of a m x n grid (marked ‘S’ in the diagram below). The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘F’ in the diagram below). How many possible unique paths are there?

| S |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   | F |

The first idea that came to my mind after seeing this problem was to find all the combinations for two movements down and six movements to the right(»»»vv). I couldn’t remember of the top of my head the formula but after a little playing with pen and paper it came back to me. The formula is:

Read More

Binary search

I was just going through the basics and I wanted to verify that I still knew how to do a binary search. If I remember correctly these are the steps:

– Set a left pointer at the beginning of the sorted array

– Set a right pointer at the end of the sorted array

– Calculate the middle between those two pointers(If there is no exact middle, truncate the number) and set the a middle pointer there

– Check if the middle is the number you are looking for. If it is return

– If the element at middle is greater than the element you are looking for set the left pointer to middle + 1

– If the element at middle is lower than the element you are looking for set the right pointer to middle – 1

– Repeat until the number is found or left is greater than right (not found)

Read More


Since I started working on big companies I’ve been becoming a little interested in distributed systems. There are some distributed technologies I’ve been wanting to play with, but I don’t have a bunch of machines I can use to test how they work. To avoid having to buy multiple machines I decided to learn how to do it in a single machine using virtualization.

In this post I’m going to try to explain the basics of virtualization so we can build a few virtual machines that can talk to each other.

Types of virtualization

There are a few types of virtualization:

  • Hardware emulation – This is generally very slow because the hardware is emulated with software.
  • Full virtualization – Uses an hypervisor to share hardware with the host machine.
  • Para-virtualization – Shares the process with the guest operating system.
  • Operating System-level virtualization – Partitions a host into insulated guests. This is kind of chroot but with much stronger resource isolation.
Read More

Consuming a Google ID Token from a server

Before your server can trust that a Google ID Token actually comes from a valid user, you need to validate it. Validation of an ID token requires two steps:

  • Verify that the value of the aud field in the ID token is identical to your app’s client ID and that the iss is
  • Verify that the ID token is a JWT which is properly signed with an appropriate Google public key and has not expired

Anatomy of an ID Token

An ID Token consists of three sections separated by dots: header.body.signature. Here is an example taken from Google:

Read More

Using Google+ id tokens from an Android app

I already wrote a post explaining how to sign-in to Google+ from an Android app. Now I want to be able to match all requests my app makes with the user associated with those requests.

Google uses the OpenID protocol and ID Tokens to make this possible. An ID Token consists of two JSON objects, base64 encoded, concatenated and cryptographically signed. This token can be attached to your requests so your server knows who is the user it should associate the request with. This token must be kept secret because anybody using it will be able to identify themselves as the user. To keep the token safe always use HTTPS and transfer it as an HTTP header.

Read More

Google+ sign-in on Android

I’m building a system for which I want to use Google+ as authentication system. This will allow me to focus on my app instead of worrying about building a secure authentication system.

The first step to building this system is to have my Android app allow users to sign in with Google. We are going to build a simple Android app that allows users to Sign In using their Google+ account.

Scaffolding the app

To get started we can use a generator I created with yeoman. Once installed create an empty folder and run:

yo android-minimal

At this point you should be able to build and run a very simple app.

Read More

JavaScript Numbers

The title for this post might sound vague, but the reason I’m writing it is because in JavaScript this is true:

(.1 + .2) !== .3;

This makes my head explode so I want to understand better the reason for this.

IEEE 754

It turns out that JavaScript only has one number type, unlike other programming languages that have many types(int, long, float, etc…). The type JavaScript uses is defined by the IEEE 754 standard for floating point numbers. This format is good because many hardware manufacturers ship they chips with support for this standard which makes operations on these numbers really fast.

Read More

Project scaffolding with Yeoman

Every time I start a new project I go to old projects to review and copy my build steps and linting rules among other things. A good developer would have automated the creation of a new project instead of going back every time. I want to redeem myself so I’m taking a look a Yeoman.

Yeoman is a tool for scaffolding web apps. It basically allows you to create custom reusable app skeletons called generators.


npm install -g yo
Read More