Merge pull request #239 from Mohitkumar6122/patch-2

Create topological_sort.py

Author: master-fury

Arrays-Sorting/src/Topological Sort/topological_sort.py

@@ -0,0 +1,56 @@
+''' 
+     TOPOLOGICAL SORT :
+     Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge u v, 
+     vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG.
+     
+     For more Information about Topological Sort visit : https://cp-algorithms.com/graph/topological-sort.html
+
+     You are given a directed graph with n vertices and m edges. 
+     You have to number the vertices so that every edge leads from the vertex with a smaller number assigned to the vertex with a larger one.     
+'''
+
+from __future__ import print_function
+
+'''
+     a
+    / \
+   b  c
+  / \
+  d  e
+'''
+
+edges = {'a': ['c', 'b'], 'b': ['d', 'e'], 'c': [], 'd': [], 'e': []}
+vertices = ['a', 'b', 'c', 'd', 'e']
+
+
+def topological_sort(start, visited, sort):
+   #Perform topolical sort on a directed acyclic graph.
+    current = start
+    # add current to visited
+    visited.append(current)
+    neighbors = edges[current]
+    for neighbor in neighbors:
+        # if neighbor not in visited, visit
+        if neighbor not in visited:
+            sort = topological_sort(neighbor, visited, sort)
+    # if all neighbors visited add current to sort
+    sort.append(current)
+    # if all vertices haven't been visited select a new one to visit
+    if len(visited) != len(vertices):
+        for vertice in vertices:
+            if vertice not in visited:
+                sort = topological_sort(vertice, visited, sort)
+    # return sort
+    return sort
+
+
+sort = topological_sort('a', [], [])
+print(sort) # prints the sorted array
+
+''' 
+     OUTPUT : ['c', 'd', 'e', 'b', 'a']
+     
+     Time Complexity: O(V+E). 
+     The above algorithm is simply DFS so time complexity is the same as DFS which is. O(V+E).
+
+'''