Create gabows_algorithm.py

Implemented Gabow's algorithm to find all the strongly connected components in a directed graph with a time complexity of O(V+E) as mentioned in the issue TheAlgorithms#12297

Author: Param1304

graphs/gabows_algorithm.py

@@ -0,0 +1,113 @@
+"""
+This is a pure Python implementation of 
+Gabow's algorithm for finding
+strongly connected components (SCCs) 
+in a directed graph.
+
+For doctests run:
+    python -m doctest -v gabow_algorithm.py
+or
+    python3 -m doctest -v gabow_algorithm.py
+For manual testing run:
+    python gabow_algorithm.py
+"""
+
+from collections import defaultdict
+from typing import List, Dict
+class Graph:
+    """
+    Graph data structure to represent 
+    a directed graph and find SCCs
+    using Gabow's algorithm.
+
+    Attributes:
+        vertices (int): Number of 
+        vertices in the graph.
+        graph (Dict[int, List[int]]): 
+        Adjacency list of the graph.
+
+    Methods:
+        add_edge(u, v): Adds an edge 
+        from vertex u to vertex v.
+        find_sccs(): Finds and returns 
+        all SCCs in the graph.
+
+    Examples:
+    >>> g = Graph(5)
+    >>> g.add_edge(0, 2)
+    >>> g.add_edge(2, 1)
+    >>> g.add_edge(1, 0)
+    >>> g.add_edge(0, 3)
+    >>> g.add_edge(3, 4)
+    >>> sorted(g.find_sccs())
+    [[0, 1, 2], [3], [4]]
+    """
+    def __init__(self, vertices: int) -> None:
+        self.vertices = vertices
+        self.graph: Dict[int, List[int]] = defaultdict(list)
+        self.index = 0
+        self.stack_s = []  # Stack S
+        self.stack_p = []  # Stack P
+        self.visited = [False] * vertices
+        self.result = []
+    def add_edge(self, u: int, v: int) -> None:
+        """
+        Adds a directed edge from vertex u to vertex v.
+
+        :param u: Starting vertex of the edge.
+        :param v: Ending vertex of the edge.
+        """
+        self.graph[u].append(v)
+
+    def _dfs(self, v: int) -> None:
+        """
+        Depth-first search helper function to 
+        process each vertex and identify SCCs.
+        :param v: The current vertex to process in DFS.
+        """
+        self.visited[v] = True
+        self.stack_s.append(v)
+        self.stack_p.append(v)
+
+        for neighbor in self.graph[v]:
+            if not self.visited[neighbor]:
+                self._dfs(neighbor)
+            elif neighbor in self.stack_p:
+                while self.stack_p and self.stack_p[-1] != neighbor:
+                    self.stack_p.pop()
+        if self.stack_p and self.stack_p[-1] == v:
+            scc = []
+            while True:
+                node = self.stack_s.pop()
+                scc.append(node)
+                if node == v:
+                    break
+            self.stack_p.pop()
+            self.result.append(scc)
+    def find_sccs(self) -> List[List[int]]:
+        """
+        Finds all strongly connected components 
+        in the directed graph.
+        :return: List of SCCs, where each SCC 
+        is represented as a list of vertices.
+        """
+        for v in range(self.vertices):
+            if not self.visited[v]:
+                self._dfs(v)
+        return self.result
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
+    # Example usage for manual testing
+    try:
+        vertex_count = int(input("Enter the number of vertices: "))
+        g = Graph(vertex_count)
+        edge_count = int(input("Enter the number of edges: "))
+        print("Enter each edge as a pair of vertices (u v):")
+        for _ in range(edge_count):
+            u, v = map(int, input().split())
+            g.add_edge(u, v)
+        sccs = g.find_sccs()
+        print("Strongly Connected Components:", sccs)
+    except ValueError:
+        print("Invalid input. Please enter valid integers.")