def FloydWarshall_itr(a_graph, k, subsol_kminus1): num_of_vertices = a_graph.num_vertices subsol_k = DenseMatrix(num_of_vertices, num_of_vertices) for vertex_a_id in a_graph.vertex_dic: for vertex_b_id in a_graph.vertex_dic: path_ab_kminus1_cost = subsol_kminus1.read_val(vertex_a_id, vertex_b_id) path_akb_cost = subsol_kminus1.read_val(vertex_a_id, k) + subsol_kminus1.read_val(k, vertex_b_id) path_ab_k_cost = min(path_ab_kminus1_cost, path_akb_cost) subsol_k.set_val(vertex_a_id, vertex_b_id, path_ab_k_cost) return subsol_k
def FloydWarshall(a_graph):
num_of_vertices = a_graph.num_vertices
#Initialize the subsolution of the shortest paths between every pair of vertices in G that contains 0 internal vertices
subsol_0 = DenseMatrix(num_of_vertices, num_of_vertices)
for vertex_a_id in a_graph.vertex_dic:
for vertex_b_id in a_graph.vertex_dic:
if vertex_a_id == vertex_b_id:
subsol_0.set_val(vertex_a_id, vertex_b_id, 0)
else:
edge_ab = a_graph.find_edge(vertex_a_id, vertex_b_id)
if edge_ab != None:
subsol_0.set_val(vertex_a_id, vertex_b_id, edge_ab.edge_cost)
else:
subsol_0.set_val(vertex_a_id, vertex_b_id, float('inf'))
subsol_k = subsol_0
#Iteratively, using the subsolution of the shortest paths between every pair of vertices in G that contains only v1, v2, ... vk-1,
#find the subsolution of the shortest paths between very pair of vertices in G that contains only v1, v2, ... vk-1, vk
for k in range(1, len(a_graph.vertex_dic)):
subsol_kminus1 = subsol_k
subsol_k = FloydWarshall_itr(a_graph, k, subsol_kminus1)
print(k)
return subsol_k