Merge pull request #632 from PranathiNagisetti/kosaraju_algo

Add Kosaraju's Algorithm for SCC in Python graph algorithms

Author: Karanjot786

Python/algorithms/graph_algorithms/kosaraju_algorithm.py

@@ -0,0 +1,81 @@
+""""
+Kosaraju’s Algorithm
+Description:Finds all Strongly Connected Components (SCCs) in a directed graph.
+Time Complexity: O(V + E)
+Space Complexity: O(V + E)
+"""
+
+from collections import defaultdict
+
+class Graph:
+    def __init__(self, vertices):
+        self.V = vertices
+        self.graph = defaultdict(list)
+
+    # Add an edge from u to v
+    def add_edge(self, u, v):
+        self.graph[u].append(v)
+
+    # DFS utility
+    def _dfs(self, v, visited, component):
+        visited[v] = True
+        component.append(v)
+        for neighbor in self.graph[v]:
+            if not visited[neighbor]:
+                self._dfs(neighbor, visited, component)
+
+    # Transpose the graph
+    def _transpose(self):
+        g_t = Graph(self.V)
+        for v in self.graph:
+            for u in self.graph[v]:
+                g_t.add_edge(u, v)
+        return g_t
+
+    # Kosaraju's Algorithm to find SCCs
+    def kosaraju_scc(self):
+        visited = [False] * self.V
+        stack = []
+
+        # Step 1: Fill vertices in stack according to finishing times
+        for i in range(self.V):
+            if not visited[i]:
+                self._fill_order(i, visited, stack)
+
+        # Step 2: Transpose the graph
+        transposed = self._transpose()
+
+        # Step 3: Process all vertices in order defined by stack
+        visited = [False] * self.V
+        sccs = []
+        while stack:
+            v = stack.pop()
+            if not visited[v]:
+                component = []
+                transposed._dfs(v, visited, component)
+                sccs.append(component)
+
+        return sccs
+
+    # Helper function for first DFS to fill stack
+    def _fill_order(self, v, visited, stack):
+        visited[v] = True
+        for neighbor in self.graph[v]:
+            if not visited[neighbor]:
+                self._fill_order(neighbor, visited, stack)
+        stack.append(v)
+
+# test Cases
+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, component in enumerate(sccs, 1):
+        print(f"Component {i}: {component}")
+