def sensitive(G: Graph, s: str, t: str) -> Tuple[str, str]:
"""
Sig: Graph G(V,E), str, str -> Tuple[str, str]
Pre:
Post:
Ex: sensitive(g1, 'a', 'f') = ('b', 'd')
"""
GRes = Graph(is_directed=True)
for (u, v) in G.edges:
# Variant: len(G.edges) - G.edges.index((u, v))
residual = G.capacity(u, v) - G.flow(u, v)
if residual == 0:
GRes.add_edge(v, u, capacity=G.capacity(u, v))
elif residual == G.capacity(u, v):
GRes.add_edge(u, v, capacity=G.capacity(u, v))
else:
GRes.add_edge(u, v, capacity=residual)
GRes.add_edge(v, u, capacity=G.flow(u, v))
reachable = set()
dfs(GRes, s, reachable)
for (u, v) in G.edges:
# Variant: len(G.edges) - G.edges.index((u, v))
if u in reachable and v not in reachable:
return (u, v)
return (None, None)
def dfs_residual(G: Graph, R: Graph, node: str, nodes: Set[str]):
nodes.add(node)
for neighbor in G.neighbors(node):
capacity = G.capacity(node, neighbor)
flow = G.flow(node, neighbor)
R.add_edge(neighbor, node, capacity=flow, flow=0)
if neighbor not in nodes:
dfs_residual(G, R, neighbor, nodes)
def dfs_find_reachable(R: Graph, node: str, reachable: Set[str]):
reachable.add(node)
for neighbor in R.neighbors(node):
avalable_capacity = R.capacity(node, neighbor) - R.flow(node, neighbor)
if (neighbor not in reachable and avalable_capacity != 0):
dfs_find_reachable(R, neighbor, reachable)