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 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.
You are given an undirected, weighted graph of n nodes, represented by an edge list, where each edge connects two nodes with a given success probability. Given two nodes, start and end, find the path with the maximum probability of success to go from start to end.
You are given a list of points on a 2D plane, represented as coordinates [x, y]. The cost of connecting two points is defined by the Manhattan distance, which is calculated as |xi - xj| + |yi - yj|. Your task is to return the minimum total cost required to connect all the points. A valid connection between points must form a connected graph, where there is exactly one simple path between any two points.
You are given a network of cities, where some cities are directly connected by bidirectional roads. The network rank between two cities is defined as the total number of roads connected to either of the cities. If a road connects both cities, it is only counted once. The task is to find the maximal network rank for any pair of distinct cities in the infrastructure.