207. Course Schedule

depth first search , topological sort 
class Solution(object):
    def canFinish(self, numCourses, prerequisites):
        """
        :type numCourses: int
        :type prerequisites: List[List[int]]
        :rtype: bool
        """
        #graph[y] is a list of nodes with an edge from y, y's children nodes 
        graph=[[]for _ in range(numCourses)]
        #visit 0:unvisited -1:being visited 1:visited
        visit=[0]*numCourses
        for x,y in prerequisites:
            graph[y].append(x)
            
        #print graph
        def dfs(i):
            #print 'visiting node',i
            if visit[i]==-1:return False
            if visit[i]==1:return True 
            elif visit[i]==0:
                visit[i]=-1
                for node in graph[i]:
                    if not dfs(node):
                        return False
                visit[i]=1
                return True 

        for i in range(numCourses):
            if not dfs(i):
                return False
        return True
       

breadth first search, Kahn's algorithm 

class Solution(object):
    def canFinish(self, numCourses, prerequisites):
        """
        :type numCourses: int
        :type prerequisites: List[List[int]]
        :rtype: bool
        """
        #graph_in store the incoming edges of all nodes, the prerequisites for each course 
        #graph_out store the outgoing edges of all nodes, courses that needs the particular prerequisite 
        graph_in,graph_out=collections.defaultdict(set),collections.defaultdict(set)
        for x,y in prerequisites:
            graph_in[x].add(y) 
            graph_out[y].add(x)
        #store nodes without any incoming edges 
        s=set([i for i in range(numCourses) if i not in graph_in])
       
        while s:
            n=s.pop()
            #traverse all the children node of n
            for node in graph_out[n]:
                graph_in[node].discard(n)
                if not graph_in[node]:#if the last incoming edge has been deleted, then delete the node from graph_in 
                    del graph_in[node]
                    s.add(node)
                    
        #if there is still edges left in the graph, then its cyclic 
        if graph_in:
            return False
        return True