visited = True # Check if there is an outgoing edge for a node in the adjacency list if src in self. Since both Stack and Queue can be bounded and unbounded, it makes sense to use an array for bounded stack and queue and may be linked list (it suits problem domain) for an unbounded queue. # The default dictionary would create an empty list as a default (value) # for the nonexistent keys.ĭef AddEdge(self, src : int, dst : int) : 1) Both Stack and Queue are built on top of basic data structures like an array or linked list. For topological sort, any dispenser will do the job. ‘V’ is the number of vertices and ‘E’ is the number of edges in a graph.įrom collections import deque, defaultdict Stacks, with a LIFO policy, and queues, with a FIFO policy, are dispensers so are priority queues. Time complexity of topological sort : O ( V + E ) for an adjacency list implementation of a graph. Pop the vertex V at the stack ( STK ) top.ĭata structure used for storing graph: Adjacency list Data structure used for DFS: Stack.Print the vertex V at the stack ( STK ) top.Push the source vertex S into the stack STK.Topological Sort ( Graph G, Source_Vertex V ).For every vertex V adjacent to the source vertex S.When the DFS ends, the nodes are popped off the stack to get a topologically sorted order.Īlgorithm : Topological Sort ( Graph G, Source_Vertex S ) A node is pushed into the stack only after all the adjacent nodes on its outgoing edges are visited. While doing a DFS, a stack is maintained to store the nodes in a reverse topologically sorted order. A topologically sorted order could be found by doing a DFS on the graph. Example 2 : In the below graph vertex 0 has no incoming edges and can be reached before 5, 2, 1, 3, 6 and 4. Rule for topological sorting : Vertex with no incoming edges is accessed first followed by the vertices on the outgoing paths.Įxample 1 : In the below graph vertex 1 has no incoming edges and can be reached before 3, 6, 0, 5, 2 and 4. Topological sort represents a linear ordering of vertices in a Directed Acyclic Graph (DAG) meeting some prerequisite rules. ![]() Key points of topological sorting algorithm
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