Merge pull request #1607 from charlie219/Issue_#1479E

SCC_Kosaraju.py added under Graphs

Python/README.md

@@ -135,6 +135,7 @@
 - [Topological Sort/Ordering](graphs/Topological_Sort.py)
 - [Hamiltonian Path](graphs/Hamiltonian_Path.py)
 - [Articulation Point](graphs/Articulation_Point.py)
+- [Strongly Connected Components - Kosaraju's Algorithm](graphs/SCC_Kosaraju.py)
 - [Strongly Connected Components - Tarjan's Algorithm](graphs/SCC_Tarjan.py)
 - [Bipartite Graph](graphs/Bipartite_Graph.py)
 

Python/graphs/SCC_Kosaraju.py

@@ -0,0 +1,159 @@
+"""
+Strongly Connected Components : A directed graph is strongly connected
+        if there is a path between all pairs of vertices. A strongly
+        connected component (SCC) of a directed graph is a maximal
+        strongly connected subgraph.
+
+Purpose: To find all the Strongly Connected Components (SCC) in the
+        given directed graph.
+
+Method: Kosaraju's Algorithms / Double DFS
+Intution: We can find all strongly connected components in O(N+M) time
+        using Kosaraju’s algorithm. Following is detailed Kosaraju’s algorithm.
+
+        1) Create an empty stack ‘S’ and do DFS traversal of a graph.
+            In DFS traversal, after calling recursive DFS for adjacent
+            vertices of a vertex, push the vertex to stack.
+        2) Reverse directions of all arcs to obtain the transpose graph.
+        3) One by one pop a vertex from S while S is not empty. Let the
+        popped vertex be ‘v’. Take v as source and do DFS (call DFSU(node)).
+        The DFS starting from v prints strongly connected component of v.
+
+Time Complexity:  O(N+M)
+Space Complexity: O(N)
+
+Argument: Dictionary ( Graph with each node numbered from 1 to N)
+Return  : List       ( List of diffrent Strongly Connected Components)
+
+"""
+from collections import defaultdict
+
+
+def DFS(graph, node, visited, stack, display):
+
+    # Mark the node Visited
+    visited[node] = True
+
+    for i in graph[node]:
+
+        # Recursively call all DFS() function to all its unvisited adjacent
+        # nodes
+        if not visited[i]:
+            DFS(graph, i, visited, stack, display)
+
+    # If the display is True, then Display the SCC
+    if display:
+        print(node, end=" ")
+    else:
+        stack.append(node)
+
+# Reverse_Graph() function reverse all the directed edges of the graph
+
+
+def Reverse_Graph(graph):
+
+    rev_graph = defaultdict(list)
+    for i in graph.keys():
+        for j in graph[i]:
+            rev_graph[j].append(i)
+
+    # Return the reversed graph
+    return rev_graph
+
+
+def SCC_Kosaraju(n, graph):
+
+    # Initilize the Stack
+    stack = []
+
+    # To keep a track of all the visited nodes
+    visited = [False] * (n + 1)
+
+    for i in range(1, n + 1):
+
+        # (1) Recursively call DFS() to push the unvisited nodes into the stack
+        if not visited[i]:
+            DFS(graph, i, visited, stack, False)
+
+    # (2) Reverse the Graph
+    rev_graph = Reverse_Graph(graph)
+
+    # Mark all the nodes Unvisited
+    visited = [False] * (n + 1)
+
+    while stack:
+        node = stack.pop()
+
+        # (3) For each unvisited node in the stack, call DFS()
+        if not visited[node]:
+
+            # Print the SCC in formated way
+            print("[ ", end="")
+            DFS(rev_graph, node, visited, stack, True)
+            print("]")
+
+
+if __name__ == "__main__":
+
+    n, m = map(int, input("Enter the number of vertex and edges: ").split())
+    print("Enter the edges: ")
+
+    # Store the graph in the form of Dictionary
+    graph = defaultdict(list)
+
+    for i in range(m):
+        a, b = map(int, input().split())
+        # Directed Graph
+        graph[a] += [b]
+
+    print("The Strongly Connected Componentes in the given Directed Graph :")
+    SCC_Kosaraju(n, graph)
+
+"""
+
+Sample Input / Output
+
+        1--------->5        4
+         ^        / \       ^
+          \      /   \     /
+           \    /     \   /
+            \  /       \ /
+             \V         3
+              2
+
+Enter the number of vertex and edges: 5 5
+Enter the edges:
+1 5
+5 2
+2 1
+5 3
+3 4
+The Strongly Connected Componentes in the given Directed Graph are :
+[ 5 2 1 ]
+[ 3 ]
+[ 4 ]
+
+
+        1-------->4----------->5
+        ^         |           /^
+        |         |          /  \
+        |         |         /    \
+        |         |        V      \
+        |         V        6------>7
+        2<--------3
+
+Enter the number of vertex and edges: 7 8
+Enter the edges:
+1 4
+2 1
+3 2
+4 3
+4 5
+5 6
+6 7
+7 5
+The Strongly Connected Componentes in the given Directed Graph are :
+[ 4 3 2 1 ]
+[ 6 7 5 ]
+
+"""