Adds Doc test in depth_first_search_2.py (#10094)

* Adds Doc test in depth_first_search_2.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Fixes depth_first_search_2.py formatting

* Cleanup

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

graphs/depth_first_search_2.py

@@ -9,12 +9,44 @@ class Graph:
 
     # for printing the Graph vertices
     def print_graph(self) -> None:
+        """
+        Print the graph vertices.
+
+        Example:
+        >>> g = Graph()
+        >>> g.add_edge(0, 1)
+        >>> g.add_edge(0, 2)
+        >>> g.add_edge(1, 2)
+        >>> g.add_edge(2, 0)
+        >>> g.add_edge(2, 3)
+        >>> g.add_edge(3, 3)
+        >>> g.print_graph()
+        {0: [1, 2], 1: [2], 2: [0, 3], 3: [3]}
+        0  ->  1 -> 2
+        1  ->  2
+        2  ->  0 -> 3
+        3  ->  3
+        """
         print(self.vertex)
         for i in self.vertex:
             print(i, " -> ", " -> ".join([str(j) for j in self.vertex[i]]))
 
     # for adding the edge between two vertices
     def add_edge(self, from_vertex: int, to_vertex: int) -> None:
+        """
+        Add an edge between two vertices.
+
+        :param from_vertex: The source vertex.
+        :param to_vertex: The destination vertex.
+
+        Example:
+        >>> g = Graph()
+        >>> g.add_edge(0, 1)
+        >>> g.add_edge(0, 2)
+        >>> g.print_graph()
+        {0: [1, 2]}
+        0  ->  1 -> 2
+        """
         # check if vertex is already present,
         if from_vertex in self.vertex:
             self.vertex[from_vertex].append(to_vertex)
@@ -23,6 +55,21 @@ class Graph:
             self.vertex[from_vertex] = [to_vertex]
 
     def dfs(self) -> None:
+        """
+        Perform depth-first search (DFS) traversal on the graph
+        and print the visited vertices.
+
+        Example:
+        >>> g = Graph()
+        >>> g.add_edge(0, 1)
+        >>> g.add_edge(0, 2)
+        >>> g.add_edge(1, 2)
+        >>> g.add_edge(2, 0)
+        >>> g.add_edge(2, 3)
+        >>> g.add_edge(3, 3)
+        >>> g.dfs()
+        0 1 2 3
+        """
         # visited array for storing already visited nodes
         visited = [False] * len(self.vertex)
 
@@ -32,6 +79,24 @@ class Graph:
                 self.dfs_recursive(i, visited)
 
     def dfs_recursive(self, start_vertex: int, visited: list) -> None:
+        """
+        Perform a recursive depth-first search (DFS) traversal on the graph.
+
+        :param start_vertex: The starting vertex for the traversal.
+        :param visited: A list to track visited vertices.
+
+        Example:
+        >>> g = Graph()
+        >>> g.add_edge(0, 1)
+        >>> g.add_edge(0, 2)
+        >>> g.add_edge(1, 2)
+        >>> g.add_edge(2, 0)
+        >>> g.add_edge(2, 3)
+        >>> g.add_edge(3, 3)
+        >>> visited = [False] * len(g.vertex)
+        >>> g.dfs_recursive(0, visited)
+        0 1 2 3
+        """
         # mark start vertex as visited
         visited[start_vertex] = True
 
@@ -40,10 +105,15 @@ class Graph:
         # Recur for all the vertices that are adjacent to this node
         for i in self.vertex:
             if not visited[i]:
+                print(" ", end="")
                 self.dfs_recursive(i, visited)
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
     g = Graph()
     g.add_edge(0, 1)
     g.add_edge(0, 2)
@@ -55,11 +125,3 @@ if __name__ == "__main__":
     g.print_graph()
     print("DFS:")
     g.dfs()
-
-    # OUTPUT:
-    # 0  ->  1 -> 2
-    # 1  ->  2
-    # 2  ->  0 -> 3
-    # 3  ->  3
-    # DFS:
-    #  0 1 2 3