Determine Relatedness and Shortest Distance Between Pins

Given a system composed of boards and pins, where each board contains several pins. Pins might have direct distances between them. Implement the following features: Given two pins, determine if they are related. Related means they are in the same or connected boards. Given two pins, calculate the shortest distance between them. Return -1 if no path exists. Given two boards, calculate the shortest distance using any pins. Return -1 if no path exists. Input format: Data structure for boards and pins Distances between pins Output format: For function 1, return a boolean value For functions 2 and 3, return an integer Provide a time and space complexity explanation. Example case: Board 1: Travel, contains pins: Mountain, Lake, Inn Board 2: Decoration, contains pins: House, Stone Pond, Inn Board 3: Graffiti, contains pins: Picasso, Lake Board 4: Car, contains pins: BYD, Xiaopeng Determine if pins "Mountain" and "Lake" are related. Calculate the shortest distance between pins "Mountain" and "House". Calculate the shortest distance between boards "Travel" and "Car". Example Input Create a board system with boards and pins and test are_related and shortest distance functions.