Digital Root

Published: May 24, 2016

What is digital root? Suppose you are given some digits, say 123456, the digital root will be calculated like this:

1 + 2 + 3 + 4 + 5 + 6 = 21
2 + 1 = 3

Summing each digit repeatedly to get a single digit is how we get the digital root.

How to effectively find the digital root

An intuitive solution would be to recurse steps: 1. get singles digits from the given number. 2. sum up all. However, if the given number is really big, this is not an effective solution.

Luckily, there’s a formula to calculate the digital root. This wikipedia page explains what the formula and how it works: Digital root.

The formula is:

// n is a given number
int digital_root = n - 9*(int)Math.floor((double)(n-1)/9);

Why this is the answer? The digital root sees how many numbers are there after the closest of multiple of 9 which is less than the given number. If the given number is 123456, its closest, multiple of 9 is 123453. So, the digital root of 123456 is 3.

The previous two blog posts introduced WebSocket and how to implement a WebSocket application on Ruby on Rails. This blog post digs deeper. It is a memo on creating a more realistic application by Action Cable.

The previous blog post, WebSocket on Rails by Action Cable, focused on WebSocket as a protocol. As in the previous post, by default, Rails app responds to WebSocket connection requests without any hassle. However, other than connecting and sending ping frames, it doesn’t do anything. This blog post focuses on an application side and explains how we can create a full-duplex, bidirectional app.

In the web application domain, we hear some protocol names. Absolutely, HTTP or HTTPS is the most famous protocol that all web developers know. Although there’s a mechanism of Keep-Alive, a single request/response sequence with a single client/server is all done by HTTP. The client initiates the HTTP request to the server. Once the client receives the HTTP response from the server, communication finishes. As far as HTTP is used, the server just waits and waits. Only when the request comes in, the server can send back some data to the client. This communication style is surprisingly capable of doing many things, so most web applications are satisfied with HTTP.