Course Schedule

The key idea

Model the courses as a directed graph where an edge b -> a means b is a prerequisite of a. You can finish every course if and only if this graph has no cycle. A cycle is a circular dependency that can never be satisfied.

Problem

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] means that you must take course bi first if you want to take course ai.

For example, the pair [0, 1] means that to take course 0 you have to first take course 1.

Return true if you can finish all courses. Otherwise, return false.

Constraints

1 <= numCourses <= 2000
0 <= prerequisites.length <= 5000
prerequisites[i].length == 2
0 <= ai, bi < numCourses
All the pairs prerequisites[i] are distinct.

Examples

Input: numCourses = 2, prerequisites = [[1,0]] Output: true

Input: numCourses = 2, prerequisites = [[1,0],[0,1]] Output: false

Complexity

Time: O(V + E) Space: O(V + E)

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