Pin Similarity and Themed Boards

Frequency: Reported

Pinterest boards contain collections of pins. Given a mapping from board IDs to their pins, compute a similarity score between one requested pin and every other pin that appears on a board with it.

Similarity is the number of boards on which the two pins co-occur.

boards = {
    "board_1": ["a", "c", "d", "e", "f"],
    "board_2": ["a", "c", "g", "i"],
    "board_3": ["b", "d", "e", "j"],
    "board_4": ["a", "c", "e"],
    "board_5": ["b", "d"],
}

For pin a, the expected scores are:

c=3, d=1, e=2, f=1, g=1, i=1

Follow-up 1: top N

Update the function to return the top N pins in descending order of similarity. The source does not visibly specify how ties should be ordered.

Follow-up 2: single-theme boards

If the data instead includes meaningful board names, how might you find boards that are about a single theme?

boards = {
    "dream vacations": ["a", "c", "d", "e", "f"],
    "dinner ideas": ["r", "t", "p", "q"],
    "bucket list": ["a", "c", "g", "i"],
    "vacation destinations": ["b", "d", "e", "j"],
    "vacations": ["a", "c", "e"],
    "my likes": ["f", "s"],
    "travel ideas": ["b", "d"],
    "recipes": ["s", "r", "q"],
    "favorites": ["a", "t", "d", "q"],
}

No required algorithm, output format, or definition of "single theme" was supplied for this discussion follow-up.