Topological Sort
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# 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.append(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 the stack
print(stack[::-1]) # return list in reverse order
# Driver Code
if __name__ == '__main__':
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")
# Function Call
g.topologicalSort()
"""
Time Complexity: O(V+E). The above algorithm is simply DFS with an extra stack. So time complexity is the same as DFS
Auxiliary space: O(V). The extra space is needed for the stack
"""
Python
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