added kruskal algo in python

GreedyAlgorithms/kruskal.py

@@ -0,0 +1,103 @@
+# Python program for Kruskal's algorithm to find
+# Minimum Spanning Tree of a given connected,
+# undirected and weighted graph
+
+from collections import defaultdict
+
+#Class to represent a graph
+class Graph:
+
+	def __init__(self,vertices):
+		self.V= vertices #No. of vertices
+		self.graph = [] # default dictionary
+								# to store graph
+
+
+	# function to add an edge to graph
+	def addEdge(self,u,v,w):
+		self.graph.append([u,v,w])
+
+	# A utility function to find set of an element i
+	# (uses path compression technique)
+	def find(self, parent, i):
+		if parent[i] == i:
+			return i
+		return self.find(parent, parent[i])
+
+	# A function that does union of two sets of x and y
+	# (uses union by rank)
+	def union(self, parent, rank, x, y):
+		xroot = self.find(parent, x)
+		yroot = self.find(parent, y)
+
+		# Attach smaller rank tree under root of
+		# high rank tree (Union by Rank)
+		if rank[xroot] < rank[yroot]:
+			parent[xroot] = yroot
+		elif rank[xroot] > rank[yroot]:
+			parent[yroot] = xroot
+
+		# If ranks are same, then make one as root
+		# and increment its rank by one
+		else :
+			parent[yroot] = xroot
+			rank[xroot] += 1
+
+	# The main function to construct MST using Kruskal's
+		# algorithm
+	def KruskalMST(self):
+
+		result =[] #This will store the resultant MST
+
+		i = 0 # An index variable, used for sorted edges
+		e = 0 # An index variable, used for result[]
+
+			# Step 1: Sort all the edges in non-decreasing
+				# order of their
+				# weight. If we are not allowed to change the
+				# given graph, we can create a copy of graph
+		self.graph = sorted(self.graph,key=lambda item: item[2])
+
+		parent = [] ; rank = []
+
+		# Create V subsets with single elements
+		for node in range(self.V):
+			parent.append(node)
+			rank.append(0)
+
+		# Number of edges to be taken is equal to V-1
+		while e < self.V -1 :
+
+			# Step 2: Pick the smallest edge and increment
+					# the index for next iteration
+			u,v,w = self.graph[i]
+			i = i + 1
+			x = self.find(parent, u)
+			y = self.find(parent ,v)
+
+			# If including this edge does't cause cycle,
+						# include it in result and increment the index
+						# of result for next edge
+			if x != y:
+				e = e + 1
+				result.append([u,v,w])
+				self.union(parent, rank, x, y)
+			# Else discard the edge
+
+		# print the contents of result[] to display the built MST
+		print "Following are the edges in the constructed MST"
+		for u,v,weight in result:
+			#print str(u) + " -- " + str(v) + " == " + str(weight)
+			print ("%d -- %d == %d" % (u,v,weight))
+
+# Driver code
+g = Graph(4)
+g.addEdge(0, 1, 10)
+g.addEdge(0, 2, 6)
+g.addEdge(0, 3, 5)
+g.addEdge(1, 3, 15)
+g.addEdge(2, 3, 4)
+
+g.KruskalMST()
+
+#This code is contributed by Neelam Yadav