/
bflow.hpp
244 lines (215 loc) · 6.47 KB
/
bflow.hpp
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#pragma once
template <class Flow = ll, class Cost = ll>
struct MinCostFlow {
private:
static constexpr int SCALING_FACTOR = 2;
using V_id = uint32_t;
using E_id = uint32_t;
struct Edge {
friend struct MinCostFlow;
private:
V_id frm, to;
Flow flow, cap;
Cost cost;
E_id rev;
public:
Edge() = default;
Edge(const V_id frm, const V_id to, const Flow cap, const Cost cost,
const E_id rev)
: frm(frm), to(to), flow(0), cap(cap), cost(cost), rev(rev) {}
[[nodiscard]] Flow residual_cap() const { return cap - flow; }
};
public:
struct EdgePtr {
friend struct MinCostFlow;
private:
const MinCostFlow *instance;
const V_id v;
const E_id e;
EdgePtr(const MinCostFlow *instance, const V_id v, const E_id e)
: instance(instance), v(v), e(e) {}
[[nodiscard]] const Edge &edge() const { return instance->g[v][e]; }
[[nodiscard]] const Edge &rev() const {
const Edge &e = edge();
return instance->g[e.to][e.rev];
}
public:
[[nodiscard]] V_id frm() const { return rev().to; }
[[nodiscard]] V_id to() const { return edge().to; }
[[nodiscard]] Flow flow() const { return edge().flow; }
[[nodiscard]] Flow lower() const { return -rev().cap; }
[[nodiscard]] Flow upper() const { return edge().cap; }
[[nodiscard]] Cost cost() const { return edge().cost; }
[[nodiscard]] Cost gain() const { return -edge().cost; }
};
private:
V_id n;
std::vector<std::vector<Edge>> g;
std::vector<Flow> b;
public:
MinCostFlow(int n) : n(n) {
g.resize(n);
b.resize(n);
}
V_id add_vertex() {
++n;
g.resize(n);
b.resize(n);
return n - 1;
}
std::vector<V_id> add_vertices(const size_t size) {
std::vector<V_id> ret;
for (V_id i = 0; i < size; ++i) ret.emplace_back(n + i);
n += size;
g.resize(n);
b.resize(n);
return ret;
}
void add(const V_id frm, const V_id to, const Flow lo, const Flow hi,
const Cost cost) {
const E_id e = g[frm].size(), re = frm == to ? e + 1 : g[to].size();
assert(lo <= hi);
g[frm].emplace_back(Edge{frm, to, hi, cost, re});
g[to].emplace_back(Edge{to, frm, -lo, -cost, e});
edges.eb(EdgePtr{this, frm, e});
}
void add_source(const V_id v, const Flow amount) { b[v] += amount; }
void add_sink(const V_id v, const Flow amount) { b[v] -= amount; }
private:
static Cost constexpr unreachable = std::numeric_limits<Cost>::max();
Cost farthest;
vc<Cost> potential, dist;
vc<Edge *> parent;
pqg<pair<Cost, int>> pq;
vc<V_id> excess_vs, deficit_vs;
vc<EdgePtr> edges;
Edge &rev(const Edge &e) { return g[e.to][e.rev]; }
void push(Edge &e, const Flow amount) {
e.flow += amount;
g[e.to][e.rev].flow -= amount;
}
Cost residual_cost(const V_id frm, const V_id to, const Edge &e) {
return e.cost + potential[frm] - potential[to];
}
bool dual(const Flow delta) {
dist.assign(n, unreachable);
parent.assign(n, nullptr);
excess_vs.erase(
remove_if(all(excess_vs), [&](const V_id v) { return b[v] < delta; }),
end(excess_vs));
deficit_vs.erase(
remove_if(all(deficit_vs), [&](const V_id v) { return b[v] > -delta; }),
end(deficit_vs));
for (const auto v: excess_vs) pq.emplace(dist[v] = 0, v);
farthest = 0;
size_t deficit_count = 0;
while (!pq.empty()) {
const auto [d, u] = pq.top();
pq.pop();
if (dist[u] < d) continue;
farthest = d;
if (b[u] <= -delta) ++deficit_count;
if (deficit_count >= deficit_vs.size()) break;
for (auto &e: g[u]) {
if (e.residual_cap() < delta) continue;
const auto v = e.to;
const auto new_dist = d + residual_cost(u, v, e);
if (new_dist >= dist[v]) continue;
pq.emplace(dist[v] = new_dist, v);
parent[v] = &e;
}
}
pq = decltype(pq)();
for (V_id v = 0; v < n; ++v) {
potential[v] += std::min(dist[v], farthest);
}
return deficit_count > 0;
}
void primal(const Flow delta) {
for (const auto t: deficit_vs) {
if (dist[t] > farthest) continue;
Flow f = -b[t];
V_id v;
for (v = t; parent[v] != nullptr && f >= delta; v = parent[v]->frm) {
f = std::min(f, parent[v]->residual_cap());
}
f = std::min(f, b[v]);
if (f < delta) continue;
for (v = t; parent[v] != nullptr;) {
auto &e = *parent[v];
push(e, f);
const size_t u = parent[v]->frm;
parent[v] = nullptr;
v = u;
}
b[t] += f;
b[v] -= f;
}
}
void saturate_negative(const Flow delta) {
excess_vs.clear();
deficit_vs.clear();
for (auto &es: g)
for (auto &e: es) {
const Flow rcap = e.residual_cap();
const Cost rcost = residual_cost(e.frm, e.to, e);
if (rcost < 0 && rcap >= delta) {
push(e, rcap);
b[e.frm] -= rcap;
b[e.to] += rcap;
}
}
for (V_id v = 0; v < n; ++v)
if (b[v] != 0) { (b[v] > 0 ? excess_vs : deficit_vs).emplace_back(v); }
}
public:
std::pair<bool, i128> solve() {
potential.resize(n);
for (auto &es: g)
for (auto &e: es) {
const Flow rcap = e.residual_cap();
if (rcap < 0) {
push(e, rcap);
b[e.frm] -= rcap;
b[e.to] += rcap;
}
}
Flow inf_flow = 1;
for (const auto &es: g)
for (const auto &e: es) inf_flow = std::max(inf_flow, e.residual_cap());
Flow delta = 1;
while (delta <= inf_flow) delta *= SCALING_FACTOR;
for (delta /= SCALING_FACTOR; delta; delta /= SCALING_FACTOR) {
saturate_negative(delta);
while (dual(delta)) primal(delta);
}
i128 value = 0;
for (const auto &es: g)
for (const auto &e: es) { value += i128(e.flow) * e.cost; }
value /= 2;
if (excess_vs.empty() && deficit_vs.empty()) {
return {true, value};
} else {
return {false, value};
}
}
template <class T>
T get_result_value() {
T value = 0;
for (const auto &es: g)
for (const auto &e: es) { value += (T)(e.flow) * (T)(e.cost); }
value /= (T)2;
return value;
}
std::vector<Cost> get_potential() {
std::fill(potential.begin(), potential.end(), 0);
for (int i = 0; i < (int)n; i++)
for (const auto &es: g)
for (const auto &e: es)
if (e.residual_cap() > 0)
potential[e.to]
= std::min(potential[e.to], potential[e.frm] + e.cost);
return potential;
}
std::vector<EdgePtr> get_edges() { return edges; }
};