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# Course Schedule Leetcode Solution

Written by: Tushar Sharma

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.

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

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:

• 1 <= numCourses <= 105
• 0 <= prerequisites.length <= 5000
• prerequisites[i].length == 2
• 0 <= ai, bi < numCourses
• All the pairs prereq

# Explanation

Lets take a good test case like

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

Here

• 4 is prerequisite for both 1 and 2
• 1 is a prerequisite for 3
• 2 is a prerequisite for 3.

We can visuallize it as a directed graph.

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.

# Complexity

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

V : numCourses & E : prerequisites

### Footnotes

1. 207. Course Schedule