207. Course Schedule

Medium
Depth-First Search
Breadth-First Search
Graph
Topological Sort

Description

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.

 

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

Hints

Hint 1
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.
Hint 2
<a href="https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/03Graphs.pdf" target="_blank">Topological Sort via DFS</a> - A great tutorial explaining the basic concepts of Topological Sort.
Hint 3
Topological sort could also be done via <a href="http://en.wikipedia.org/wiki/Topological_sorting#Algorithms" target="_blank">BFS</a>.

Statistics

Acceptance
50.5%
Submissions
4,772,212
Accepted
2,412,188