added brief description,complexity and applications of the algorithm.…

python/kruskal.py

@@ -1,12 +1,23 @@
 #kruskal's algorithm for minimum spanning tree
-parent = dict()
-rank = dict()
 
-def make_set(vertice):
+"""
+  **Brief** :Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest.It is a greedy algorithm in graph theory as it finds a minimum spanning tree for a connected weighted graph adding increasing cost arcs at each step. The algorithm is implemented using disjoint-set data structure here.
+
+
+  **Complexity** :O(ElogE) OR O(ElogV) where E and V are the number of edges and vertices respectively
+
+  **Applications** :Most of the cable network companies use the Disjoint Set Union data structure in Kruskal’s algorithm to find the shortest path to lay cables across a city or group of cities.
+
+"""
+
+parent = dict()                     #intializing a new empty dictionary named parent. This will contain the parent vertices of each vertice
+rank = dict()                       #intitializing a new empty dictionary named rank. This will hold the rank of each vertice
+
+def make_set(vertice):              #this function will create a set out of a single vertice
     parent[vertice] = vertice
     rank[vertice] = 0
 
-def find(vertice):
+def find(vertice):                  #this function returns the parent of the given vertice in the argument. It is a recursive function.
     if parent[vertice] != vertice:
         parent[vertice] = find(parent[vertice])
     return parent[vertice]
@@ -22,11 +33,12 @@ def union(vertice1, vertice2):
             if rank[root1] == rank[root2]: rank[root2] += 1
 
 def kruskal(graph):
-    for vertice in graph['vertices']:
+    for vertice in graph['vertices']:           #creating an entry for each vertice of the graph in the the parent and rank dictionaries using the make_set function
         make_set(vertice)
 
-    minimum_spanning_tree = set()
-    edges = list(graph['edges'])
+    minimum_spanning_tree = set()               #initializing the minimum spanning tree as a set data structure. This set will keep expanding until we get the final set at the end of this function.
+
+    edges = list(graph['edges'])                #edges is the list of all the edges of the graph. each edge is represented as a dictionary with the following keys: (weight,vertice1,vertice2)
     edges.sort()
     for edge in edges:
         weight, vertice1, vertice2 = edge