Create kosaraju_algo.py

Provide code for issue #11677

Author: techyshiv

data_structures/graph/kosaraju_algo.py

@@ -0,0 +1,80 @@
+from collections import defaultdict
+
+class Graph:
+    def __init__(self, vertices):
+        self.V = vertices  # Number of vertices
+        self.graph = defaultdict(list)  # Default dictionary to store the graph
+    
+    def add_edge(self, u, v):
+        """Function to add an edge from vertex u to vertex v."""
+        self.graph[u].append(v)
+    
+    def _dfs(self, v, visited, stack=None):
+        """
+        A recursive function to perform DFS from vertex v.
+        If stack is provided, it pushes the vertices in the order of their finish time.
+        """
+        visited[v] = True
+        # Recur for all vertices adjacent to this vertex
+        for neighbor in self.graph[v]:
+            if not visited[neighbor]:
+                self._dfs(neighbor, visited, stack)
+        
+        # Push the vertex to stack if it's not None (used in first DFS pass)
+        if stack is not None:
+            stack.append(v)
+    
+    def _transpose(self):
+        """
+        Function to transpose (reverse) the graph.
+        Returns the transposed graph.
+        """
+        transposed = Graph(self.V)
+        for vertex in self.graph:
+            for neighbor in self.graph[vertex]:
+                transposed.add_edge(neighbor, vertex)
+        return transposed
+    
+    def kosaraju_scc(self):
+        """
+        Function to find and print all Strongly Connected Components (SCCs) using Kosaraju's Algorithm.
+        Returns a list of SCCs, where each SCC is a list of vertices.
+        """
+        # Step 1: Perform DFS to get the finishing times of vertices
+        stack = []
+        visited = [False] * self.V
+        
+        for i in range(self.V):
+            if not visited[i]:
+                self._dfs(i, visited, stack)
+        
+        # Step 2: Transpose the graph
+        transposed_graph = self._transpose()
+        
+        # Step 3: Process vertices in the order defined by the stack
+        visited = [False] * self.V
+        sccs = []  # List to store SCCs
+        
+        while stack:
+            v = stack.pop()
+            if not visited[v]:
+                # Collect all vertices in the current SCC
+                scc_stack = []
+                transposed_graph._dfs(v, visited, scc_stack)
+                sccs.append(scc_stack)
+        
+        return sccs
+
+# Example usage
+if __name__ == "__main__":
+    g = Graph(5)
+    g.add_edge(1, 0)
+    g.add_edge(0, 2)
+    g.add_edge(2, 1)
+    g.add_edge(0, 3)
+    g.add_edge(3, 4)
+    
+    print("Strongly Connected Components:")
+    sccs = g.kosaraju_scc()
+    for i, scc in enumerate(sccs, 1):
+        print(f"SCC {i}: {scc}")