def prim(G, root):
MST = weighted_graph.Graph(G.num_nodes())
inMST = [False] * G.num_nodes()
graph_PQ = graph_priority_queue.MinHeap(G.num_nodes())
root_node = NodeData(root, root, 0)
graph_PQ.insert(root_node)
MSTwt = 0
while not graph_PQ.is_empty():
element = graph_PQ.pop()
MST.set_vertex(element.vertex, G.get_node(element.vertex).data)
inMST[element.vertex] = True
if element.vertex != element.MST_vertex:
MST.add_edge(element.vertex, element.MST_vertex, element.weight)
MSTwt = MSTwt + element.weight
adjlist = G.get_node(element.vertex).get_edges()
for MST_vertex, candidate_vertex, wt in adjlist:
if not inMST[candidate_vertex]:
newelt = NodeData(candidate_vertex, MST_vertex, wt)
graph_PQ.insert(newelt)
print('MST weight: ' + str(MSTwt))
return MST
def kruskal(G):
set_roots = initialize_set(G.num_nodes())
MST = weighted_graph.Graph(G.num_nodes())
for i in range(G.num_nodes()):
MST.set_vertex(i, G.get_node(i).data)
E = G.sort_edges()
MSTwt = 0
for i in range(len(E)):
u, v, w = E[i]
rootu = find_root(set_roots, u)
rootv = find_root(set_roots, v)
if rootu != rootv:
union(set_roots, rootu, rootv)
print('Adding edge: ' + str((u, v, w)))
MST.add_edge(u, v, w)
MSTwt = MSTwt + w
print('MST weight: ' + str(MSTwt))
return MST
import weighted_graph
import kruskal
node_numbers = {
'N1': 0,
'N2': 1,
'N3': 2,
'N4': 3,
'N5': 4,
'N6': 5,
'N7': 6,
'N8': 7
}
G = weighted_graph.Graph(len(node_numbers))
for node in node_numbers:
G.set_vertex(node_numbers[node], node)
G.add_edge(node_numbers['N1'], node_numbers['N2'], 3)
G.add_edge(node_numbers['N1'], node_numbers['N4'], 2)
G.add_edge(node_numbers['N1'], node_numbers['N3'], 3)
G.add_edge(node_numbers['N2'], node_numbers['N4'], 9)
G.add_edge(node_numbers['N2'], node_numbers['N5'], 4)
G.add_edge(node_numbers['N2'], node_numbers['N7'], 2)
G.add_edge(node_numbers['N3'], node_numbers['N4'], 4)
G.add_edge(node_numbers['N3'], node_numbers['N5'], 1)
G.add_edge(node_numbers['N3'], node_numbers['N7'], 6)
G.add_edge(node_numbers['N3'], node_numbers['N8'], 6)
def dijkstra(G,s):
span_tree = weighted_graph.Graph(G.num_nodes())
in_span_tree = [False]*G.num_nodes()
distances = [float('inf')]*G.num_nodes()
distances[s] = 0
predecessors = [-1]*G.num_nodes()
E = []
graph_PQ = graph_priority_queue.MinHeap(G.num_nodes())
for v in range(G.num_nodes()):
E.extend(G.get_node(v).get_edges())
source = NodeData(s,-1,0)
graph_PQ.insert(source)
while not graph_PQ.is_empty():
element = graph_PQ.pop()
span_tree.set_vertex(element.vertex,
G.get_node(element.vertex).data)
in_span_tree[element.vertex] = True
if element.Svertex != -1:
span_tree.add_edge(element.vertex,
element.Svertex,
element.weight)
adjlist = G.get_node(element.vertex).get_edges()
for Svertex, candidate_vertex, wt in adjlist:
if in_span_tree[candidate_vertex] == False:
if (distances[candidate_vertex] >
(distances[Svertex] + wt)):
predecessors[candidate_vertex] = Svertex
distances[candidate_vertex] = distances[Svertex]+wt
newelt = NodeData(candidate_vertex,
Svertex,
distances[candidate_vertex])
graph_PQ.insert(newelt)
for v in range(G.num_nodes()):
if v == s:
continue
if (predecessors[v]==-1 or
distances[v] == float('inf')):
print('NO PATH from node '+ str(s) +
' to node '+ str(v))
continue
else:
print('Shortest path (cost = '+ str(distances[v])+
') from node '+str(s)+' to node '+str(v)+': ')
stack = [v]
done = False
current_node = v
while not done:
current_node = predecessors[current_node]
if current_node != -1:
stack.append(current_node)
else:
done = True
stack.reverse()
print(stack)
import weighted_graph
g = weighted_graph.Graph()
g.add_edge("A", "B", 2)
g.add_edge("A", "C", 2)
g.add_edge("A", "E", 0)
g.add_edge("B", "D", 0)
g.add_edge("B", "F", 0)
g.add_edge("C", "G", 2)
g.add_edge("G", "B", 1)
g.add_edge("F", "E")
g.add_edge("E", "A", 0)
g.add_node("I")
pathFW = g.FloydWarshall('A', 'I')
pathD = g.dijkstra('A', 'I')
print(pathFW)
print(pathD)