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Video Problem

Problem belonging to the post-classroom Mock Interview Question Repository.

Problem Statement

We are interested in analyzing how a video gets shared with group of friends.

We will work with a dictionary that shows us who is friends with whom. In this dictionary, a person will be the key, and the value will be a set containing all the people they are friends with. For example:

friend_data = {
    "Sebastian": {"Kevin", "Lewis", "Fernando"},
    "Max": {"Fernando"},
    "Lewis": {"Sebastian"},
    "Yuki": {"Pierre"},
    "Pierre": {"Yuki"},
    "Fernando": {"Sebastian", "Max"},
    "Carlos": {"Charles", "Lando"},
    "Lando": {"Carlos"},
    "Charles": {"Carlos"},
    "Kevin": {"Sebastian"},
}

In this example, we see that Sebastian has three friends: Kevin, Lewis, and Fernando. Conversely, Lewis only has a single friend: Sebastian.

We choose a random person to show a viral video to, and after watching it they share it with all their friends who share it with all their friends and so on. For example, if we showed Lewis our video, it would travel like this:

  • Lewis watches the video
  • Lewis shares the video with Sebastian
  • Sebastian shares the video with Kevin and Fernando
  • Fernando shares the video with Max

In this scenario, five people will end up seeing the video (Lewis, Sebastian, Kevin, Fernando, and Max).

Write a function that accepts a friend dictionary and an initial person to show it to. The function should return the overall number of people that end up watching to movie as a result.

Neither the dictionary nor the sets inside should be modified.

Examples

For the following friend data:

friend_data = {
    "Sebastian": {"Kevin", "Lewis", "Fernando"},
    "Max": {"Fernando"},
    "Lewis": {"Sebastian"},
    "Yuki": {"Pierre"},
    "Pierre": {"Yuki"},
    "Fernando": {"Sebastian", "Max"},
    "Carlos": {"Charles", "Lando"},
    "Lando": {"Carlos"},
    "Charles": {"Carlos"},
    "Kevin": {"Sebastian"},
}

The following table shows a selection of people, and the group size that would result from showing the video to them:

Person Group Size
Sebastian 5
Max 2
Lewis 5
Yuki 2
Carlos 3
Charles 3