Problem Statement
There are a total of numCourses
courses you have to take, labeled from 0
to numCourses-1
.
Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]
Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?
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:
- The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
- You may assume that there are no duplicate edges in the input prerequisites.
1 <= numCourses <= 10^5
Video Tutorial
You can find the detailed video tutorial hereThought Process
It is a classic dependency graph problem. We can translate this problem to direct if there is a cycle in a directed graph or not. A text book solution is Kahn's algorithm for topological sorting. We can have a simple way to represent the graph or use a more proper adjacency lists (a little bit overkill for this problem though)Solutions
Use adjacency lists BFS
Time Complexity: O(V), since each vertex is visited only once during BFSSpace Complexity: O(V+E) since we use adjacency lists to represent a directed graph
Use simple hashmap BFS
Time Complexity: O(V), since each vertex is visited only once during BFS
Space Complexity: O(V) since we are using a hashmap
Use recursion DFS
Time Complexity: O(V), since each vertex is visited only once during BFS
Space Complexity: O(V) since we used a lookup hashmap for memorization purpose (not considering function stack space)
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