Add Kosaraju algorithm (#910)

* added kosaraju's algorithm under /algorithms/graph

* added test case for /algorithms/graph/strongly_connected_component_kosaraju

---------

Co-authored-by: Rubal Singh <nbarubz@gmail.com>

algorithms/graph/strongly_connected_components_kosaraju.py

@@ -0,0 +1,81 @@
+"""
+Implementing strongly connected components in a graph using Kosaraju's algorithm.
+https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm
+"""
+
+
+class Kosaraju:
+    """
+    Kosaraju's algorithm use depth first search approach to find strongly connected components in a directed graph.
+    Approach:
+        1. Make a DFS call to keep track of finish time of each vertex.
+        2. Tranpose the original graph. ie 1->2 transpose is 1<-2
+        3. Make another DFS call to calculate strongly connected components.
+    """
+
+    def dfs(self, i, V, adj, visited, stk):
+        visited[i] = 1
+
+        for x in adj[i]:
+            if visited[x] == -1:
+                self.dfs(x, V, adj, visited, stk)
+
+        stk.append(i)
+
+    def kosaraju(self, V, adj):
+
+        stk, visited = [], [-1]*(V+1)
+
+        for i in range(V):
+            if visited[i] == -1:
+                self.dfs(i, V, adj, visited, stk)
+
+        stk.reverse()
+        res = stk.copy()
+
+        ans, visited1 = 0, [-1]*(V+1)
+
+        adj1 = [[] for x in range(V)]
+
+        for i in range(len(adj)):
+            for x in adj[i]:
+                adj1[x].append(i)
+
+        for i in range(len(res)):
+            if visited1[res[i]] == -1:
+                ans += 1
+                self.dfs(res[i], V, adj1, visited1, stk)
+
+        return ans
+
+
+def main():
+    """
+    Let's look at the sample input.
+
+    6 7  #no of vertex, no of edges
+    0 2  #directed edge 0->2
+    1 0
+    2 3
+    3 1
+    3 4
+    4 5
+    5 4
+
+    calculating no of strongly connected compnenets in a directed graph.
+    answer should be: 2
+    1st strong component: 0->2->3->1->0
+    2nd strongly connected component: 4->5->4
+    """
+    V, E = map(int, input().split())
+    adj = [[] for x in range(V)]
+
+    for i in range(E):
+        u, v = map(int, input().split())
+        adj[u].append(v)
+
+    print(Kosaraju().kosaraju(V, adj))
+
+
+if __name__ == '__main__':
+    main()

tests/test_graph.py

@@ -14,6 +14,7 @@
 from algorithms.graph import cycle_detection
 from algorithms.graph import find_path
 from algorithms.graph import path_between_two_vertices_in_digraph
+from algorithms.graph import strongly_connected_components_kosaraju
 
 import unittest
 
@@ -349,3 +350,19 @@ def test_node_is_reachable(self):
         self.assertTrue(g.is_reachable(1, 3))
         self.assertFalse(g.is_reachable(3, 1))
 
+class TestStronglyConnectedComponentsKosaraju(unittest.TestCase):
+    def test_kosaraju_algorithm(self):
+        V = 6
+        adj = [
+            [2],
+            [0],
+            [3],
+            [1, 4],
+            [5],
+            [4]
+        ]
+
+        result = strongly_connected_components_kosaraju.Kosaraju().kosaraju(V, adj)
+
+        # Expected result: 2 strongly connected components
+        self.assertEqual(result, 2)