def all_pairs_shortest_paths(edges):
# check validity of input
if not isinstance(edges, list):
raise ValueError("input is not a list")
if any(not isinstance(e, tuple) or len(e) != 3
or not isinstance(e[2], int) for e in edges):
raise ValueError("invalid edges")
if not edges:
return []
# check for non-positive weights
if helpers.has_non_positive_weights(edges):
raise ValueError("non-positive weights are not supported")
# check for multiple edges
if helpers.has_multiple_edges_between_nodes(edges):
raise ValueError("multiple edges between nodes are not supported")
# check for loops
if helpers.has_loops(edges):
raise ValueError("loopy edges are not supported")
# check for connectedness
if helpers.is_disconnected(edges):
raise ValueError("disconnected graphs are not supported")
dist = {}
nodes = helpers.get_nodes(edges)
for n1 in nodes:
for n2 in nodes:
dist[(n1, n2)] = 0 if n1 == n2 else sys.maxsize
edge2weight = {}
for n1, n2, d in edges:
dist[(n1, n2)] = d
dist[(n2, n1)] = d
edge2weight[(n1, n2)] = d
edge2weight[(n2, n1)] = d
for k in nodes:
for n1 in nodes:
for n2 in nodes:
if dist[(n1, n2)] > dist[(n1, k)] + dist[(k, n2)]:
dist[(n1, n2)] = dist[(n1, k)] + dist[(k, n2)]
for n1 in nodes:
for n2 in nodes:
if (n2, n1) in dist or n1 == n2:
dist.pop((n1, n2))
s = sum(e[2] for e in edges)
return [(k[0], k[1], s - dist[k] if \
s - dist[k] > edge2weight.get((k[0], k[1]), 0) else dist[k]) \
for k in dist]
def all_pairs_shortest_paths(edges):
# check validity of input
if not isinstance(edges, list):
raise ValueError("input is not a list")
if any(not isinstance(e, tuple) or len(e) != 3 or not isinstance(e[2], int) for e in edges):
raise ValueError("invalid edges")
if not edges:
return []
# check for non-positive weights
if helpers.has_non_positive_weights(edges):
raise ValueError("non-positive weights are not supported")
# check for multiple edges
if helpers.has_multiple_edges_between_nodes(edges):
raise ValueError("multiple edges between nodes are not supported")
# check for loops
if helpers.has_loops(edges):
raise ValueError("loopy edges are not supported")
# check for connectedness
if helpers.is_disconnected(edges):
raise ValueError("disconnected graphs are not supported")
dist = {}
nodes = helpers.get_nodes(edges)
for n1 in nodes:
for n2 in nodes:
dist[(n1, n2)] = 0 if n1 == n2 else sys.maxsize
for n1, n2, d in edges:
dist[(n1, n2)] = d
dist[(n2, n1)] = d
node_2_min = {n:(min(e[2] for e in edges if e[0] == n or e[1] == n))
for n in nodes}
for n1 in nodes:
for n2 in nodes:
dist[(n1, n2)] = node_2_min[n1]
for n1 in nodes:
for n2 in nodes:
if (n2, n1) in dist or n1 == n2:
dist.pop((n1, n2))
return [(k[0], k[1], dist[k]) for k in dist]
def all_pairs_shortest_paths(edges):
# check validity of input
if not isinstance(edges, list):
raise ValueError("input is not a list")
# if empty graph
if not edges:
return []
# check for non-positive weights
if helpers.has_non_positive_weights(edges):
raise ValueError("non-positive weights are not supported")
# check for multiple edges
if helpers.has_multiple_edges_between_nodes(edges):
raise ValueError("multiple edges between nodes are not supported")
# check for loops
if helpers.has_loops(edges):
raise ValueError("loopy edges are not supported")
# check for connectedness
if helpers.is_disconnected(edges):
raise ValueError("disconnected graphs are not supported")
dist = {}
nodes = helpers.get_nodes(edges)
for n1 in nodes:
for n2 in nodes:
dist[(n1, n2)] = 0 if n1 == n2 else sys.maxsize
for n1, n2, d in edges:
dist[(n1, n2)] = d
dist[(n2, n1)] = d
for k in nodes:
for n1 in nodes:
for n2 in nodes:
if dist[(n1, n2)] > dist[(n1, k)] + dist[(k, n2)]:
dist[(n1, n2)] = dist[(n1, k)] + dist[(k, n2)]
for n1 in nodes:
for n2 in nodes:
if (n2, n1) in dist or n1 == n2:
dist.pop((n1, n2))
return [(k[0], k[1], dist[k]) for k in dist]