I was given the following question:

Given a list of Pesrons, and two arbitrary Persons out of that list, we need to find the minimum n-degree relationship between them.

Here are the definitions of Person and a "relationship":

• A Person is defined as having 2 properties: Name and Age:

  class Person
  {
      public string Name { get; set; }
      public int Age { get; set; }
  }

• A relationship between two Persons is defined as follows:

  1. Two Persons are considered to be in a first-degree relationship if they have either the same name or the same age.
  2. Two Persons are considered to be in a n-degree relationship if they have n people of first-degree connecting them.

Example input:

Given the following list of Persons:

persons = [{ Name = "John", Age = 60 }, ( Name = "John", Age = 50 }, { Name = "Ted", Age = 50 }]

Then:

1. The two Johns have a 1st degree relationship (because they have the same name).
2. The second John and Ted have a 1st degree relationship (because they have the same age).
3. Hence, the first John and Ted have a 2nd degree relationship (because the second John connects them).

Now, I understand that it's a simple Dijkstra's algorithm question, but what I don't know is how should we build the graph of Persons?