“Knight to E4!…. Yes Hermione, I think this is going to be exactly like wizard’s chess.” — Ronald Weasley

Binary Decomposition

, we were essentially taking 1 step forward at a time until we reach the matrix we need. However, we don’t have to take 1 step at a time; we can take many steps forward with a technique called Binary Decomposition.

The simplest introduction to Binary Decomposition is often the example of multiplication.

Let’s say we have to solve x=3⁸. We could multiply “3” 8 times and we would get our answer. But we know that 3² =9 and we could use substitution and only need to solve x=9⁴. …


“Ron, you don’t suppose this is going to be like . . real wizard’s chess, do you?” — Hermione Granger

A few weeks ago, Alex Golec wrote an awesome walkthrough to , a former interview problem at Google:

Imagine you place a knight chess piece on a phone dial pad. This chess piece moves in an uppercase “L” shape: two steps horizontally followed by one vertically, or one step horizontally then two vertically…

How many distinct numbers can you dial in N hops from a particular starting position?

Alex demonstrated some of the many ways the problem can be solved using recursion and dynamic programming. …


With Paris, ServiceNow has introduced custom GraphQL APIs which enables us to create highly flexible, reusable, and cacheable APIs for integrations or front end engineering.

However, documentation and tutorials for this new technology is sparse for the ServiceNow community. For this tutorial, we will build a GraphQL API for the Automated Test Framework that will be iteratively improved through the tutorial

  • Parts of a GraphQL API
  • A basic example of returning data from a single record
  • how to connect schemas together to return even more data
  • how to return a list of related records

GraphQL has three types of operations…


Slack is a real time messaging platform that makes work entertaining with many ways to integrate third party tools to create powerful and interesting interactions. ServiceNow is a PaaS & SaaS provider for internal service management, automation, & orchestration. Together, they have offer a wide range of opportunities. Today, we will be integrating the two.

ServiceNow boasts a that can be used to integrate external applications with your instance. Each API is very useful, but they all have their own limitations. So, before you head down the path of a processor, please consider these other APIs…

Jeff Manville

I like helping people with Code & Math. I try to make everything I do a version of that.

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