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Course Schedule IV

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1.

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.

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 array answer, where answer[j] is the answer to the jth query.

Course Schedule IV diagram

Example 1

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.

Example 2

Input: numCourses = 2, prerequisites = [], queries = [[1,0],[0,1]]

Output: [false,false]

Explanation: There are no prerequisites, and each course is independent.

Example 3

Input: numCourses = 3, prerequisites = [[1,2],[1,0],[2,0]], queries = [[1,0],[1,2]]

Output: [true,true]

Constraints

  • 2 <= numCourses <= 100
  • 0 <= prerequisites.length <= (numCourses * (numCourses - 1) / 2)
  • prerequisites[i].length == 2
  • 0 <= ai, bi <= numCourses - 1
  • ai != bi
  • All the pairs [ai, bi] are unique.
  • The prerequisites graph has no cycles.
  • 1 <= queries.length <= 10^4
  • 0 <= ui, vi <= numCourses - 1
  • ui != vi

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