added Johnson’s algorithm for shortest path

Author: prasannathapa

Johnson’s algorithm for shortest path

@@ -0,0 +1,90 @@
+from collections import defaultdict 
+MAX_INT = float('Inf') 
+
+def minDistance(dist, visited): 
+
+	(minimum, minVertex) = (MAX_INT, 0) 
+	for vertex in range(len(dist)): 
+		if minimum > dist[vertex] and visited[vertex] == False: 
+			(minimum, minVertex) = (dist[vertex], vertex) 
+
+	return minVertex 
+
+def Dijkstra(graph, modifiedGraph, src): 
+
+	num_vertices = len(graph) 
+
+	sptSet = defaultdict(lambda : False) 
+
+	dist = [MAX_INT] * num_vertices 
+
+	dist[src] = 0
+
+	for count in range(num_vertices): 
+
+		curVertex = minDistance(dist, sptSet) 
+		sptSet[curVertex] = True
+
+		for vertex in range(num_vertices): 
+			if ((sptSet[vertex] == False) and
+				(dist[vertex] > (dist[curVertex] +
+				modifiedGraph[curVertex][vertex])) and
+				(graph[curVertex][vertex] != 0)): 
+				
+				dist[vertex] = (dist[curVertex] +
+								modifiedGraph[curVertex][vertex]); 
+
+	for vertex in range(num_vertices): 
+		print ('Vertex ' + str(vertex) + ': ' + str(dist[vertex])) 
+
+def BellmanFord(edges, graph, num_vertices): 
+
+	dist = [MAX_INT] * (num_vertices + 1) 
+	dist[num_vertices] = 0
+
+	for i in range(num_vertices): 
+		edges.append([num_vertices, i, 0]) 
+
+	for i in range(num_vertices): 
+		for (src, des, weight) in edges: 
+			if((dist[src] != MAX_INT) and
+					(dist[src] + weight < dist[des])): 
+				dist[des] = dist[src] + weight 
+
+	return dist[0:num_vertices] 
+
+def JohnsonAlgorithm(graph): 
+
+	edges = [] 
+
+	for i in range(len(graph)): 
+		for j in range(len(graph[i])): 
+
+			if graph[i][j] != 0: 
+				edges.append([i, j, graph[i][j]]) 
+
+	modifyWeights = BellmanFord(edges, graph, len(graph)) 
+
+	modifiedGraph = [[0 for x in range(len(graph))] for y in
+					range(len(graph))] 
+
+	for i in range(len(graph)): 
+		for j in range(len(graph[i])): 
+
+			if graph[i][j] != 0: 
+				modifiedGraph[i][j] = (graph[i][j] +
+						modifyWeights[i] - modifyWeights[j]); 
+
+	print ('Modified Graph: ' + str(modifiedGraph)) 
+
+	for src in range(len(graph)): 
+		print ('\nShortest Distance with vertex ' +
+						str(src) + ' as the source:\n') 
+		Dijkstra(graph, modifiedGraph, src) 
+
+graph = [[0, -5, 2, 3], 
+		[0, 0, 4, 0], 
+		[0, 0, 0, 1], 
+		[0, 0, 0, 0]] 
+
+JohnsonAlgorithm(graph)