Add Prim's MST algorithm

Prims_algorithm.py

@@ -0,0 +1,96 @@
+# A Python implementation of
+# Prim's Minimum Spanning Tree (MST) algorithm.
+# The program is for an adjacency matrix
+# representation of the graph. Time
+# Time complexity is O(V^2). If the input
+# graph is represented as an adjacency list
+# rather than a matrix, time complexity
+# can be reduced O(E * logV) with the help of
+# a binary heap. Space complexity: O(V).
+
+
+import sys
+
+
+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):
+
+		# Initialize min value
+		min = sys.maxsize
+
+		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.maxsize] * 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 shortest 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)
+
+
+# Driver's code
+if __name__ == '__main__':
+	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()
+
+
+