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Course Schedule Leetcode Solution

Tags: leetcode graph bfs java python

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 bi first if you want to take course ai.

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

Testcase

Example 1

Input: numCourses = 2, prerequisites = [[1,0]]
Output: true
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0. So it is possible.

Example 2

Input: numCourses = 2, prerequisites = [[1,0],[0,1]]
Output: false
Explanation: There are a total of 2 courses to take. 
To take course 1 you should have finished course 0, 
and to take course 0 you should also have finished course 1. So it is impossible.

Constraints:

Explanation

Lets take a good test case like

numCourses = 5
prerequisites = [[1,4],[2,4],[3,1],[3,2]]

Here

We can visuallize it as a directed graph.

graph directed

This problem is equivalent to finding if a cycle exists in a directed graph. If a cycle exists, no topological ordering exists and therefore it will be impossible to take all courses.

Solution


Complexity

Time complexity: $$\mid V \mid + \mid E \mid$$.

V : numCourses & E : prerequisites


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