Merge pull request #630 from PranathiNagisetti/toposort_algo

Add Topological Sorting algorithm to Python graph algorithms

Author: Karanjot786

Python/algorithms/graph_algorithms/toposort_algorithm.py

@@ -0,0 +1,65 @@
+'''Purpose: Orders vertices of a Directed Acyclic Graph (DAG) such that for every directed edge u → v, vertex u comes before v in the ordering.
+
+Type: Graph Algorithm
+
+Use Cases: Task scheduling, course prerequisite ordering, build systems, etc.
+
+Approach: We can implement Toposort using DFS:
+
+For each unvisited node, perform a DFS.
+
+After visiting all neighbors, push the node to a stack.
+
+At the end, pop nodes from the stack to get the topological order.
+
+Time Complexity: O(V + E)
+
+Space Complexity: O(V)'''
+
+# Topological Sorting using DFS in Python
+
+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)
+
+    # Recursive helper function for DFS
+    def _dfs(self, v, visited, stack):
+        visited[v] = True
+        for neighbor in self.graph[v]:
+            if not visited[neighbor]:
+                self._dfs(neighbor, visited, stack)
+        stack.append(v)  # Push vertex after visiting neighbors
+
+    # Topological Sort
+    def topological_sort(self):
+        visited = [False] * self.V
+        stack = []
+
+        for i in range(self.V):
+            if not visited[i]:
+                self._dfs(i, visited, stack)
+
+        # Return in reverse order
+        return stack[::-1]
+
+# Main function
+if __name__ == "__main__":
+    # Example graph
+    g = Graph(6)
+    g.add_edge(5, 2)
+    g.add_edge(5, 0)
+    g.add_edge(4, 0)
+    g.add_edge(4, 1)
+    g.add_edge(2, 3)
+    g.add_edge(3, 1)
+
+    print("Topological Sort of the given graph:")
+    order = g.topological_sort()
+    print(order)