Created Prims.py

Competitive Coding/Tree/Minimum Spanning Tree/Prims/Prims.py

@@ -0,0 +1,79 @@
+# 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();