Add Graph Algorithm - Kruskal's Minimum Spanning Tree

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

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+# 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
+
+		# An index variable, used for sorted edges
+		i = 0
+
+		# An index variable, used for result[]
+		e = 0
+
+		# 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 indexof 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
+
+		minimumCost = 0
+		print ("Edges in the constructed MST")
+		for u, v, weight in result:
+			minimumCost += weight
+			print("%d -- %d = %d" % (u, v, weight))
+		print("Minimum Spanning Tree" , minimumCost)
+
+# 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)
+
+# Function call
+g.KruskalMST()

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

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+# 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()