Python Program for Topological Sorting
Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG.
For example, a topological sorting of the following graph is “5 4 2 3 1 0”. There can be more than one topological sorting for a graph. For example, another topological sorting of the following graph is “4 5 2 3 1 0”. The first vertex in topological sorting is always a vertex with in-degree as 0 (a vertex with no in-coming edges).
#Python program to print topological sorting of a DAG from collections import defaultdict #Class to represent a graph class Graph: def __init__(self,vertices): self.graph = defaultdict(list) #dictionary containing adjacency List self.V = vertices #No. of vertices # function to add an edge to graph def addEdge(self,u,v): self.graph[u].append(v) # A recursive function used by topologicalSort def topologicalSortUtil(self,v,visited,stack): # Mark the current node as visited. visited[v] = True # Recur for all the vertices adjacent to this vertex for i in self.graph[v]: if visited[i] == False: self.topologicalSortUtil(i,visited,stack) # Push current vertex to stack which stores result stack.insert(0,v) # The function to do Topological Sort. It uses recursive # topologicalSortUtil() def topologicalSort(self): # Mark all the vertices as not visited visited = [False]*self.V stack =[] # Call the recursive helper function to store Topological # Sort starting from all vertices one by one for i in range(self.V): if visited[i] == False: self.topologicalSortUtil(i,visited,stack) # Print contents of stack print stack g= Graph(6) g.addEdge(5, 2); g.addEdge(5, 0); g.addEdge(4, 0); g.addEdge(4, 1); g.addEdge(2, 3); g.addEdge(3, 1); print "Following is a Topological Sort of the given graph"g.topologicalSort() # |
Output:
Following is a Topological Sort of the given graph 5 4 2 3 1 0