You are given a list of rooms and their visiting order for each day based on a set of rules. On each day, you either revisit a room based on the number of visits or proceed to the next room in a cyclic manner. Your task is to find the first day when all rooms have been visited.
You are given a list of rectangles, each represented by its width and height. Two rectangles are interchangeable if their width-to-height ratios are the same. Your task is to return the number of interchangeable rectangle pairs in the list.
You are given an array changed, which may have been created by doubling each element of an original array and then shuffling the elements. Your task is to determine if changed can be converted back into the original array, where each element in the original array has its double present in changed. If changed is not a valid doubled array, return an empty array. If it is valid, return the original array.
You are driving a taxi along a road with n points. Each point represents a location on the road. Passengers request rides from one point to another, and for each ride, you earn the distance traveled plus a tip. Your goal is to maximize your earnings by picking up passengers optimally. You can only carry one passenger at a time, and may pick up a new passenger at any point after dropping off the previous one.
In a simplified programming language, there are only four operations: incrementing or decrementing a variable X by 1. You are given a list of operations that can either increment or decrement the value of X. Your task is to determine the final value of X after applying all the operations.