Initialize set with source in DFS (TheAlgorithms#1872)

* Update dfs.py

* Add type hints, rearrange doc-strings and comments

* fixup! Format Python code with psf/black push

* dfs -> depth_first_search

Co-Authored-By: Christian Clauss <cclauss@me.com>

* dfs -> depth_first_search

* Add doctest for DFS

* fixup! Format Python code with psf/black push

* Rename dfs.py to depth_first_search_dictionary.py

* updating DIRECTORY.md

* Rename depth_first_search_dictionary.py to depth_first_search_dfs.py

* updating DIRECTORY.md

* Rename depth_first_search.py to depth_first_search_2.py

* updating DIRECTORY.md

* Rename depth_first_search_dfs.py to depth_first_search.py

* updating DIRECTORY.md

Co-authored-by: John Law <johnlaw.po@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 4 people

DIRECTORY.md

@@ -212,7 +212,7 @@
   * [Check Bipartite Graph Bfs](https://github.com/TheAlgorithms/Python/blob/master/graphs/check_bipartite_graph_bfs.py)
   * [Check Bipartite Graph Dfs](https://github.com/TheAlgorithms/Python/blob/master/graphs/check_bipartite_graph_dfs.py)
   * [Depth First Search](https://github.com/TheAlgorithms/Python/blob/master/graphs/depth_first_search.py)
-  * [Dfs](https://github.com/TheAlgorithms/Python/blob/master/graphs/dfs.py)
+  * [Depth First Search 2](https://github.com/TheAlgorithms/Python/blob/master/graphs/depth_first_search_2.py)
   * [Dijkstra](https://github.com/TheAlgorithms/Python/blob/master/graphs/dijkstra.py)
   * [Dijkstra 2](https://github.com/TheAlgorithms/Python/blob/master/graphs/dijkstra_2.py)
   * [Dijkstra Algorithm](https://github.com/TheAlgorithms/Python/blob/master/graphs/dijkstra_algorithm.py)

graphs/depth_first_search.py

@@ -1,65 +1,59 @@
-#!/usr/bin/python
-
-""" Author: OMKAR PATHAK """
-
-
-class Graph:
-    def __init__(self):
-        self.vertex = {}
-
-    # for printing the Graph vertices
-    def printGraph(self):
-        print(self.vertex)
-        for i in self.vertex.keys():
-            print(i, " -> ", " -> ".join([str(j) for j in self.vertex[i]]))
-
-    # for adding the edge between two vertices
-    def addEdge(self, fromVertex, toVertex):
-        # check if vertex is already present,
-        if fromVertex in self.vertex.keys():
-            self.vertex[fromVertex].append(toVertex)
-        else:
-            # else make a new vertex
-            self.vertex[fromVertex] = [toVertex]
-
-    def DFS(self):
-        # visited array for storing already visited nodes
-        visited = [False] * len(self.vertex)
-
-        # call the recursive helper function
-        for i in range(len(self.vertex)):
-            if visited[i] == False:
-                self.DFSRec(i, visited)
-
-    def DFSRec(self, startVertex, visited):
-        # mark start vertex as visited
-        visited[startVertex] = True
-
-        print(startVertex, end=" ")
-
-        # Recur for all the vertices that are adjacent to this node
-        for i in self.vertex.keys():
-            if visited[i] == False:
-                self.DFSRec(i, visited)
-
+"""The DFS function simply calls itself recursively for every unvisited child of 
+its argument. We can emulate that behaviour precisely using a stack of iterators. 
+Instead of recursively calling with a node, we'll push an iterator to the node's 
+children onto the iterator stack. When the iterator at the top of the stack
+terminates, we'll pop it off the stack.
+
+Pseudocode:
+    all nodes initially unexplored
+    mark s as explored
+    for every edge (s, v):
+        if v unexplored:
+            DFS(G, v)
+"""
+
+from typing import Set, Dict
+
+
+def depth_first_search(graph: Dict, start: str) -> Set[int]:
+    """Depth First Search on Graph
+
+       :param graph: directed graph in dictionary format
+       :param vertex: starting vectex as a string
+       :returns: the trace of the search
+       >>> G = { "A": ["B", "C", "D"], "B": ["A", "D", "E"], 
+       ... "C": ["A", "F"], "D": ["B", "D"], "E": ["B", "F"],
+       ... "F": ["C", "E", "G"], "G": ["F"] }
+       >>> start = "A"
+       >>> output_G = list({'A', 'B', 'C', 'D', 'E', 'F', 'G'})
+       >>> all(x in output_G for x in list(depth_first_search(G, "A")))
+       True
+       >>> all(x in output_G for x in list(depth_first_search(G, "G")))
+       True
+    """
+    explored, stack = set(start), [start]
+    while stack:
+        v = stack.pop()
+        # one difference from BFS is to pop last element here instead of first one
+        for w in graph[v]:
+            if w not in explored:
+                explored.add(w)
+                stack.append(w)
+    return explored
+
+
+G = {
+    "A": ["B", "C", "D"],
+    "B": ["A", "D", "E"],
+    "C": ["A", "F"],
+    "D": ["B", "D"],
+    "E": ["B", "F"],
+    "F": ["C", "E", "G"],
+    "G": ["F"],
+}
 
 if __name__ == "__main__":
-    g = Graph()
-    g.addEdge(0, 1)
-    g.addEdge(0, 2)
-    g.addEdge(1, 2)
-    g.addEdge(2, 0)
-    g.addEdge(2, 3)
-    g.addEdge(3, 3)
-
-    g.printGraph()
-    print("DFS:")
-    g.DFS()
+    import doctest
 
-    # OUTPUT:
-    # 0  ->  1 -> 2
-    # 1  ->  2
-    # 2  ->  0 -> 3
-    # 3  ->  3
-    # DFS:
-    #  0 1 2 3
+    doctest.testmod()
+    print(depth_first_search(G, "A"))

graphs/depth_first_search_2.py

@@ -0,0 +1,65 @@
+#!/usr/bin/python
+
+""" Author: OMKAR PATHAK """
+
+
+class Graph:
+    def __init__(self):
+        self.vertex = {}
+
+    # for printing the Graph vertices
+    def printGraph(self):
+        print(self.vertex)
+        for i in self.vertex.keys():
+            print(i, " -> ", " -> ".join([str(j) for j in self.vertex[i]]))
+
+    # for adding the edge between two vertices
+    def addEdge(self, fromVertex, toVertex):
+        # check if vertex is already present,
+        if fromVertex in self.vertex.keys():
+            self.vertex[fromVertex].append(toVertex)
+        else:
+            # else make a new vertex
+            self.vertex[fromVertex] = [toVertex]
+
+    def DFS(self):
+        # visited array for storing already visited nodes
+        visited = [False] * len(self.vertex)
+
+        # call the recursive helper function
+        for i in range(len(self.vertex)):
+            if visited[i] == False:
+                self.DFSRec(i, visited)
+
+    def DFSRec(self, startVertex, visited):
+        # mark start vertex as visited
+        visited[startVertex] = True
+
+        print(startVertex, end=" ")
+
+        # Recur for all the vertices that are adjacent to this node
+        for i in self.vertex.keys():
+            if visited[i] == False:
+                self.DFSRec(i, visited)
+
+
+if __name__ == "__main__":
+    g = Graph()
+    g.addEdge(0, 1)
+    g.addEdge(0, 2)
+    g.addEdge(1, 2)
+    g.addEdge(2, 0)
+    g.addEdge(2, 3)
+    g.addEdge(3, 3)
+
+    g.printGraph()
+    print("DFS:")
+    g.DFS()
+
+    # OUTPUT:
+    # 0  ->  1 -> 2
+    # 1  ->  2
+    # 2  ->  0 -> 3
+    # 3  ->  3
+    # DFS:
+    #  0 1 2 3