Add Graph Algorithm - Prim's Minimum Spanning Tree

src/main/python/algorithms/graph/prim_mst.py

@@ -0,0 +1,77 @@
+# A Python program for Prim's Minimum Spanning Tree (MST) algorithm.
+# The program is for adjacency matrix representation of the graph
+
+class Graph:
+    def __init__(self, vertices):
+        self.V = vertices
+        self.graph = [[0 for column in range(vertices)] for row in range(vertices)]
+
+    # 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]])
+
+    # 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 = 1000000
+
+        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 = [1000000] * self.V
+        parent = [None] * self.V  # Array to store constructed MST
+        key[0] = 0  # Make key 0 so that this vertex is picked as first vertex
+        mstSet = [False] * self.V
+
+        parent[0] = -1  # First node is always the root 
+
+        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()