The purpose of this problem is to help the railroad provide its customers with information about the routes. In particular, you will compute the distance along a certain route, the number of different routes between two towns, and the shortest route between two towns.
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If your local machine has Ruby 1.9.3 available, you can run bundle install to retrieve all required gems.




  1. After installing Vagrant and VirtualBox, run vagrant up on the terminal from the project directory.
  2. Once the box has been provisioned, run vagrant ssh on the terminal from the project directory.
  3. You can run the application tests by running rspec from the virtual machine's /vagrant directory.



  • the application will be invoked programmatically; the input data text file is passed in to the Application class as a parameter
  • the string Graph: isn't included in the input file

Change Management

  • new queries might be requested by the local commuter railroad


I'm relatively inexperienced with Ruby as a programming language and have been using JavaScript (and some Clojure) much more extensively as of late. If I've made any grievous style mistakes, I apologize in advance. I chose Ruby because I admire the focus on expressiveness and readability. I wanted to implement some functional programming paradigms and they are relatively cumbersome to implement in Java (the language I have the most experience in of the three requested) and I'm not familiar at all with C# beyond a few introductory tutorials.


I made use of RSpec and a BDD process to solve most of the tasks. I would create a specification and attempt to create the API I would like to satisfy the specification. Once the API was designed, I work work out to implementing the actual code to satisfy the desired API.


I'm using Rake to run the RSpec specifications. Not much more was required as the project was assumed to be used programmatically.


I wanted to create a data-centric and functional DSL to implement the graph search algorithm. I borrowed from my beginner's experience in artificial intelligence to create a generalized graph search algorithm.

Graph Data Structure

In the process of creating tests, I implemented a simple graph data structure to maintain neighbours and implemented a generalized graph search algorithm. The adjacency list seemed optimal for the required use, as neighbour lookup (read: set search) was O(1) in average case and O(n) in the worst case (if Ruby's hash algorithm avoids clustering this is unlikely to be reached). Since this was the primary operation used in the problem, this seems to be the best implementation (to my understanding).

Graph search is performed with the following parameters:

  • root: The required root of the graph for the purposes of the query
  • select: The selection criteria for a goal path. This query is satisfied when a trip that has been selected from the fringe is passed into the select Proc and select returns true. Functionality, select acts in a nature similar to the Array#select method (but on the current path selected from the fringe, instead of on an array instance). See first for details on how to select more than one path.
  • reject: If an optional reject Proc is provided, the search allows cycles and will remove any paths from the fringe that do not satisfy reject constraints. Functionality, reject acts in a nature similar to the Array#reject method (but on the fringe, instead of on an array instance).
  • first: If this parameter is defined, the search will return the first path found that satisfies select criteria. Otherwise, it will accumulate satisfactory paths until the fringe is empty.

I am using uniform cost search, a special case of the A* algorithm as the default search strategy. This is ideal for the problem since uniform cost search is:

  • Complete: The strategy is proven to find a solution in a finite state space (with cycle protection or a fringe filter)
  • Optimal: The strategy is proven to find the best solution based on cost

And since this is a special case of the A* search algorithm (with the trivial heuristic of 0), the strategy is:

  • Admissible: The heuristic will "slow down" costly paths, but will not impede expanding paths with low actual costs.
  • Consistent: The heuristic ensures optimality since each path is proven to be consistent. In other words, the relative cost of the heuristic is always lower than the actual path cost per edge.


The distance function allows questions of distance to be answered with an intuitive input parameter: the route desired to be measured. The function itself reduces the provided route down to the associated distance, or returns NO SUCH ROUTE if, at any point in the reduction, the required neighbour cannot be found.

Find All Trips

Delegates to WeighedDirectedGraph#search.

Find Trip

Delegates to WeightedDirectedGraph#search with the first parameter defined.


I had created a few visualizations to as an aid for me to understand the problem and have included them for convenience:

Input Question 6 Question 7 Question 8 Question 9 Question 10