You are given a set of courses and a list of prerequisites. Each prerequisite is a pair of courses where the second course must be taken before the first one. Determine if it is possible to complete all courses based on these prerequisites. If there are cycles in the dependencies, it would be impossible to finish all courses.
You are given a tree with ’n’ nodes labeled from 0 to n-1, represented by ’n-1’ edges. Your task is to find all roots that minimize the height of the tree. The height of a tree is defined as the number of edges in the longest downward path from the root to any leaf.
You are given a directed graph where each node represents a point, and edges represent possible transitions between nodes. A node is considered terminal if it has no outgoing edges. A node is deemed safe if every path starting from it leads either to a terminal node or another safe node. Your task is to identify all the safe nodes in the graph and return them in ascending order.
You are given a group of n people, each with a unique amount of money and quietness. An array richer specifies the relationships between people where richer[i] = [ai, bi] indicates that person ai has more money than person bi. You are also given an array quiet where quiet[i] represents the quietness of person i. Your task is to return an array answer where answer[x] is the person y who has the least quietness among all people who have equal or more money than person x.
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.
