Merge pull request TheAlgorithms#161 from arpanjain97/master

Add shortest path algorithms

Author: harshildarji

Diff for: data_structures/Graph/BellmanFord.py

@@ -0,0 +1,52 @@
+def printDist(dist, V):
+	print("\nVertex Distance")
+	for i in range(V):
+		if dist[i] != float('inf') :
+			print(i,"\t",int(dist[i]),end = "\t")
+		else:
+			print(i,"\t","INF",end="\t")
+		print();
+
+def BellmanFord(graph, V, E, src):
+	mdist=[float('inf') for i in range(V)]
+	mdist[src] = 0.0;
+	
+	for i in range(V-1):
+		for j in range(V):
+			u = graph[j]["src"]
+			v = graph[j]["dst"]
+			w = graph[j]["weight"]
+
+			if mdist[u] != float('inf') and mdist[u] + w < mdist[v]:
+				mdist[v] = mdist[u] + w 
+	for j in range(V):
+			u = graph[j]["src"]
+			v = graph[j]["dst"]
+			w = graph[j]["weight"]
+
+			if mdist[u] != float('inf') and mdist[u] + w < mdist[v]:
+				print("Negative cycle found. Solution not possible.")
+				return
+	
+	printDist(mdist, V)	
+
+			
+
+#MAIN
+V = int(input("Enter number of vertices: "));
+E = int(input("Enter number of edges: "));
+
+graph = [dict() for j in range(E)]
+
+for i in range(V):
+	graph[i][i] = 0.0;
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(input("Enter source:"))
+	dst = int(input("Enter destination:"))
+	weight = float(input("Enter weight:"))
+	graph[i] = {"src": src,"dst": dst, "weight": weight}
+	
+gsrc = int(input("\nEnter shortest path source:"))
+BellmanFord(graph, V, E, gsrc)

Diff for: data_structures/Graph/Dijkstra.py

@@ -0,0 +1,56 @@
+
+def printDist(dist, V):
+	print("\nVertex Distance")
+	for i in range(V):
+		if dist[i] != float('inf') :
+			print(i,"\t",int(dist[i]),end = "\t")
+		else:
+			print(i,"\t","INF",end="\t")
+		print();
+
+def minDist(mdist, vset, V):
+	minVal = float('inf')
+	minInd = -1
+	for i in range(V):
+		if (not vset[i]) and mdist[i] < minVal :
+			minInd = i
+			minVal = mdist[i]
+	return minInd
+
+def Dijkstra(graph, V, src):
+	mdist=[float('inf') for i in range(V)]
+	vset = [False for i in range(V)]
+	mdist[src] = 0.0;
+	
+	for i in range(V-1):
+		u = minDist(mdist, vset, V)
+		vset[u] = True;
+		
+		for v in range(V):
+			if (not vset[v]) and graph[u][v]!=float('inf') and mdist[u] + graph[u][v] < mdist[v]:
+				mdist[v] = mdist[u] + graph[u][v] 
+
+	
+
+	printDist(mdist, V)	
+
+			
+
+#MAIN
+V = int(input("Enter number of vertices: "));
+E = int(input("Enter number of edges: "));
+
+graph = [[float('inf') for i in range(V)] for j in range(V)]
+
+for i in range(V):
+	graph[i][i] = 0.0;
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(input("Enter source:"))
+	dst = int(input("Enter destination:"))
+	weight = float(input("Enter weight:"))
+	graph[src][dst] = weight;
+
+gsrc = int(input("\nEnter shortest path source:"))
+Dijkstra(graph, V, gsrc)

Diff for: data_structures/Graph/FloydWarshall.py

@@ -0,0 +1,47 @@
+
+def printDist(dist, V):
+	print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
+	for i in range(V):
+		for j in range(V):
+			if dist[i][j] != float('inf') :
+				print(int(dist[i][j]),end = "\t")
+			else:
+				print("INF",end="\t")
+		print();
+
+
+
+def FloydWarshall(graph, V):
+	dist=[[float('inf') for i in range(V)] for j in range(V)]
+	
+	for i in range(V):
+		for j in range(V):
+			dist[i][j] = graph[i][j]
+
+	for k in range(V):
+		for i in range(V):
+			for j in range(V):
+				if dist[i][k]!=float('inf') and dist[k][j]!=float('inf') and dist[i][k]+dist[k][j] < dist[i][j]:
+					dist[i][j] = dist[i][k] + dist[k][j]
+
+	printDist(dist, V)	
+
+			
+
+#MAIN
+V = int(input("Enter number of vertices: "));
+E = int(input("Enter number of edges: "));
+
+graph = [[float('inf') for i in range(V)] for j in range(V)]
+
+for i in range(V):
+	graph[i][i] = 0.0;
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(input("Enter source:"))
+	dst = int(input("Enter destination:"))
+	weight = float(input("Enter weight:"))
+	graph[src][dst] = weight;
+
+FloydWarshall(graph, V)