There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course ai first if you want to take course bi.
For example, the pair [0, 1] indicates that you have to take course 0 before you can take course 1.
Prerequisites can also be indirect. If course a is a prerequisite of course b, and course b is a prerequisite of course c, then course a is a prerequisite of course c.You are also given an array queries where queries[j] = [uj, vj]. For the jth query, you should answer whether course uj is a prerequisite of course vj or not.Return a boolean arrayanswer, whereanswer[j]is the answer to thejthquery.
Input: numCourses = 2, prerequisites = [[1,0]], queries = [[0,1],[1,0]]Output: [false,true]Explanation: The pair [1, 0] indicates that you have to take course 1 before you can take course 0.Course 0 is not a prerequisite of course 1, but the opposite is true.
Input: numCourses = 2, prerequisites = [], queries = [[1,0],[0,1]]Output: [false,false]Explanation: There are no prerequisites, and each course is independent.
class Solution: # Time: O(n^3) Floyd-Warshall transitive closure (n <= 100) # Space: O(n^2) def check_if_prerequisite( self, num_courses: int, prerequisites: list[list[int]], queries: list[list[int]] ) -> list[bool]: # reach[a][b] = True if a is a (direct or indirect) prerequisite of b. reach = [[False] * num_courses for _ in range(num_courses)] for a, b in prerequisites: reach[a][b] = True for k in range(num_courses): for i in range(num_courses): if reach[i][k]: for j in range(num_courses): if reach[k][j]: reach[i][j] = True return [reach[u][v] for u, v in queries]
