From 298d616521ca35b612e5c0c6d49074c7db97b19f Mon Sep 17 00:00:00 2001
From: Dhruvajit Ghosh <ghoshg401@gmail.com>
Date: Mon, 14 Oct 2019 19:57:34 +0530
Subject: [PATCH] prims algorithm in python

---
 GreedyAlgorithms/Prims_Algorithm.py | 81 +++++++++++++++++++++++++++++
 1 file changed, 81 insertions(+)
 create mode 100644 GreedyAlgorithms/Prims_Algorithm.py

diff --git a/GreedyAlgorithms/Prims_Algorithm.py b/GreedyAlgorithms/Prims_Algorithm.py
new file mode 100644
index 00000000..4e136332
--- /dev/null
+++ b/GreedyAlgorithms/Prims_Algorithm.py
@@ -0,0 +1,81 @@
+# A Python program for Prim's Minimum Spanning Tree (MST) algorithm. 
+# The program is for adjacency matrix representation of the graph 
+
+import sys # Library for INT_MAX 
+
+class Graph(): 
+
+	def __init__(self, vertices): 
+		self.V = vertices 
+		self.graph = [[0 for column in range(vertices)] 
+					for row in range(vertices)] 
+
+	# A utility function to print the constructed MST stored in parent[] 
+	def printMST(self, parent): 
+		print "Edge \tWeight"
+		for i in range(1, self.V): 
+			print parent[i], "-", i, "\t", self.graph[i][ parent[i] ] 
+
+	# A utility function to find the vertex with 
+	# minimum distance value, from the set of vertices 
+	# not yet included in shortest path tree 
+	def minKey(self, key, mstSet): 
+
+		# Initilaize min value 
+		min = sys.maxint 
+
+		for v in range(self.V): 
+			if key[v] < min and mstSet[v] == False: 
+				min = key[v] 
+				min_index = v 
+
+		return min_index 
+
+	# Function to construct and print MST for a graph 
+	# represented using adjacency matrix representation 
+	def primMST(self): 
+
+		# Key values used to pick minimum weight edge in cut 
+		key = [sys.maxint] * self.V 
+		parent = [None] * self.V # Array to store constructed MST 
+		# Make key 0 so that this vertex is picked as first vertex 
+		key[0] = 0
+		mstSet = [False] * self.V 
+
+		parent[0] = -1 # First node is always the root of 
+
+		for cout in range(self.V): 
+
+			# Pick the minimum distance vertex from 
+			# the set of vertices not yet processed. 
+			# u is always equal to src in first iteration 
+			u = self.minKey(key, mstSet) 
+
+			# Put the minimum distance vertex in 
+			# the shortest path tree 
+			mstSet[u] = True
+
+			# Update dist value of the adjacent vertices 
+			# of the picked vertex only if the current 
+			# distance is greater than new distance and 
+			# the vertex in not in the shotest path tree 
+			for v in range(self.V): 
+				# graph[u][v] is non zero only for adjacent vertices of m 
+				# mstSet[v] is false for vertices not yet included in MST 
+				# Update the key only if graph[u][v] is smaller than key[v] 
+				if self.graph[u][v] > 0 and mstSet[v] == False and key[v] > self.graph[u][v]: 
+						key[v] = self.graph[u][v] 
+						parent[v] = u 
+
+		self.printMST(parent) 
+
+g = Graph(5) 
+g.graph = [ [0, 2, 0, 6, 0], 
+			[2, 0, 3, 8, 5], 
+			[0, 3, 0, 0, 7], 
+			[6, 8, 0, 0, 9], 
+			[0, 5, 7, 9, 0]] 
+
+g.primMST(); 
+
+# Contributed by Divyanshu Mehta