You are given a set of courses numbered from 0 to numCourses - 1 and a list of prerequisites. Each prerequisite is a pair [ai, bi], indicating that you must complete course ai before course bi. For a series of queries, where each query asks whether a specific course is a prerequisite for another, you are tasked with determining whether each query is true or false.
You are given a rectangular cake of size h x w. There are two arrays of integers, horizontalCuts and verticalCuts. Each element in horizontalCuts represents a horizontal cut, and each element in verticalCuts represents a vertical cut. Your task is to find the maximum area of a piece of cake that can be obtained after making all the cuts specified in the arrays. Since the result can be a large number, return it modulo 10^9 + 7.
You are given n cities and n - 1 roads, forming a tree structure. The roads have been directed, and some roads may need to be reoriented to ensure all cities can reach the capital city (city 0). Your task is to determine the minimum number of road reorientations required to make it possible for each city to reach city 0.
Given an array of integers and an integer k, you need to find the strongest k elements in the array. The strength of each element is determined by how far it is from the median of the array. If two elements are equidistant from the median, the larger element is considered stronger. Return the k strongest elements in any order.
You are tasked with simulating the history of web page visits in a browser. Implement the BrowserHistory class to manage visit, back, and forward actions.
You are tasked with implementing the SubrectangleQueries class which operates on a matrix representing a rectangle with integer values. The class should support two key operations: updateSubrectangle and getValue.