There are a total of n courses you have to take, labeled from
Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair:
Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses?
Input: 2, [[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.
Input: 2, [[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.
- 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.
Use DFS way of topological sort.
from collections import defaultdict class Solution(object): def canFinish(self, numCourses, prerequisites): """ :type numCourses: int :type prerequisites: List[List[int]] :rtype: bool """ class Graph(object): def __init__(self, vertices): self.graph = defaultdict(list) self.V = vertices def addEdge(self, u, v): self.graph[u].append(v) def tsUtil(self, v, temporary, permanent): if v not in temporary: return False temporary.remove(v) for w in self.graph[v]: if w in permanent: if not self.tsUtil(w, temporary, permanent): return False permanent.remove(v) return True def isTsPossible(self): temporary = set(range(self.V)) permanent = set(range(self.V)) while len(permanent) > 0: if not self.tsUtil(next(iter(permanent)), temporary, permanent): return False return True graph = Graph(numCourses) for p in prerequisites: u, v = p, p graph.addEdge(u, v) return graph.isTsPossible()