/
minimum_cost_cycle.hpp
130 lines (126 loc) · 3.52 KB
/
minimum_cost_cycle.hpp
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#include "graph/base.hpp"
// {wt, vs, es}, O(N * shortest path)
template <typename T, typename GT>
tuple<T, vc<int>, vc<int>> minimum_cost_cycle_directed(GT& G) {
const int N = G.N;
T mi = 0, ma = 0;
for (auto& e: G.edges) chmin(mi, e.cost), chmax(ma, e.cost);
assert(mi >= 0);
T ans = infty<T>;
vc<T> dist(N);
vc<int> vs, es;
vc<int> par_e(N, -1);
pqg<pair<T, int>> que;
deque<int> deq;
FOR(r, N) {
fill(dist.begin() + r, dist.end(), infty<T>);
if (ma <= 1) {
auto push = [&](int v, bool back) -> void {
(back ? deq.eb(v) : deq.emplace_front(v));
};
for (auto& e: G[r]) {
if (r <= e.to && chmin(dist[e.to], e.cost))
par_e[e.to] = e.id, push(e.to, e.cost);
}
while (len(deq)) {
auto v = POP(deq);
for (auto& e: G[v]) {
if (r <= e.to && chmin(dist[e.to], dist[v] + e.cost)) {
par_e[e.to] = e.id, push(e.to, e.cost);
}
}
}
} else {
for (auto& e: G[r]) {
if (r <= e.to && chmin(dist[e.to], e.cost)) {
par_e[e.to] = e.id, que.emplace(e.cost, e.to);
}
}
while (len(que)) {
auto [dv, v] = POP(que);
if (dist[v] != dv) continue;
for (auto& e: G[v]) {
T x = dv + e.cost;
if (r <= e.to && chmin(dist[e.to], x)) {
par_e[e.to] = e.id, que.emplace(x, e.to);
}
}
}
}
if (chmin(ans, dist[r])) {
vs.clear(), es.clear();
vs.eb(r);
while (1) {
int eid = par_e[vs.back()];
es.eb(eid);
vs.eb(G.edges[eid].frm);
if (vs.back() == r) break;
}
reverse(all(vs));
reverse(all(es));
};
}
return {ans, vs, es};
}
// {wt, vs, es}, O(N * shortest path)
template <typename T, typename GT>
tuple<T, vc<int>, vc<int>> minimum_cost_cycle_undirected(GT& G) {
const int N = G.N;
T ans = infty<T>;
vc<T> dist(N);
vc<int> par_e(N);
vc<int> vs, es;
FOR(r, N) {
fill(dist.begin() + r, dist.end(), infty<T>);
pqg<pair<T, int>> que;
dist[r] = 0, que.emplace(0, r);
while (len(que)) {
auto [dv, v] = POP(que);
if (dist[v] != dv) continue;
for (auto& e: G[v]) {
if (e.to < r) continue;
T x = dv + e.cost;
if (chmin(dist[e.to], x)) {
par_e[e.to] = e.id;
que.emplace(x, e.to);
}
}
}
int best_e = -1;
for (auto& e: G.edges) {
int a = e.frm, b = e.to;
if (a < r || b < r || par_e[a] == e.id || par_e[b] == e.id) continue;
if (chmin(ans, dist[a] + dist[b] + e.cost)) best_e = e.id;
}
if (best_e == -1) continue;
vs.clear(), es.clear();
auto& e = G.edges[best_e];
int a = e.frm, b = e.to;
// r -> a
while (a != r) {
int eid = par_e[a];
vs.eb(a), es.eb(eid);
a = G.edges[eid].frm ^ G.edges[eid].to ^ a;
}
vs.eb(a);
reverse(all(vs)), reverse(all(es));
es.eb(best_e);
while (b != r) {
int eid = par_e[b];
vs.eb(b), es.eb(eid);
b = G.edges[eid].frm ^ G.edges[eid].to ^ b;
}
vs.eb(b);
}
return {ans, vs, es};
}
// {wt, vs, es}, O(N * shortest path)
template <typename T, typename GT>
tuple<T, vc<int>, vc<int>> minimum_cost_cycle(GT& G) {
for (auto& e: G.edges) assert(e.cost >= 0);
if constexpr (GT::is_directed) {
return minimum_cost_cycle_directed<T>(G);
} else {
return minimum_cost_cycle_undirected<T>(G);
}
}