src/jiangly/graph/07B-Min-Cost-Flow.hpp
Code
/** MinCostFlow 新版
* 2023-11-09: https://qoj.ac/submission/244680
**/
template<class T>
struct MinCostFlow {
struct _Edge {
int to;
T cap;
T cost;
_Edge(int to_, T cap_, T cost_) : to(to_), cap(cap_), cost(cost_) {}
};
int n;
std::vector<_Edge> e;
std::vector<std::vector<int>> g;
std::vector<T> h, dis;
std::vector<int> pre;
bool dijkstra(int s, int t) {
dis.assign(n, std::numeric_limits<T>::max());
pre.assign(n, -1);
std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>> que;
dis[s] = 0;
que.emplace(0, s);
while (!que.empty()) {
T d = que.top().first;
int u = que.top().second;
que.pop();
if (dis[u] != d) {
continue;
}
for (int i : g[u]) {
int v = e[i].to;
T cap = e[i].cap;
T cost = e[i].cost;
if (cap > 0 && dis[v] > d + h[u] - h[v] + cost) {
dis[v] = d + h[u] - h[v] + cost;
pre[v] = i;
que.emplace(dis[v], v);
}
}
}
return dis[t] != std::numeric_limits<T>::max();
}
MinCostFlow() {}
MinCostFlow(int n_) {
init(n_);
}
void init(int n_) {
n = n_;
e.clear();
g.assign(n, {});
}
void addEdge(int u, int v, T cap, T cost) {
g[u].push_back(e.size());
e.emplace_back(v, cap, cost);
g[v].push_back(e.size());
e.emplace_back(u, 0, -cost);
}
std::pair<T, T> flow(int s, int t) {
T flow = 0;
T cost = 0;
h.assign(n, 0);
while (dijkstra(s, t)) {
for (int i = 0; i < n; ++i) {
h[i] += dis[i];
}
T aug = std::numeric_limits<int>::max();
for (int i = t; i != s; i = e[pre[i] ^ 1].to) {
aug = std::min(aug, e[pre[i]].cap);
}
for (int i = t; i != s; i = e[pre[i] ^ 1].to) {
e[pre[i]].cap -= aug;
e[pre[i] ^ 1].cap += aug;
}
flow += aug;
cost += aug * h[t];
}
return std::make_pair(flow, cost);
}
struct Edge {
int from;
int to;
T cap;
T cost;
T flow;
};
std::vector<Edge> edges() {
std::vector<Edge> a;
for (int i = 0; i < e.size(); i += 2) {
Edge x;
x.from = e[i + 1].to;
x.to = e[i].to;
x.cap = e[i].cap + e[i + 1].cap;
x.cost = e[i].cost;
x.flow = e[i + 1].cap;
a.push_back(x);
}
return a;
}
};
#line 1 "src/jiangly/graph/07B-Min-Cost-Flow.hpp"
/** MinCostFlow 新版
* 2023-11-09: https://qoj.ac/submission/244680
**/
template<class T>
struct MinCostFlow {
struct _Edge {
int to;
T cap;
T cost;
_Edge(int to_, T cap_, T cost_) : to(to_), cap(cap_), cost(cost_) {}
};
int n;
std::vector<_Edge> e;
std::vector<std::vector<int>> g;
std::vector<T> h, dis;
std::vector<int> pre;
bool dijkstra(int s, int t) {
dis.assign(n, std::numeric_limits<T>::max());
pre.assign(n, -1);
std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>> que;
dis[s] = 0;
que.emplace(0, s);
while (!que.empty()) {
T d = que.top().first;
int u = que.top().second;
que.pop();
if (dis[u] != d) {
continue;
}
for (int i : g[u]) {
int v = e[i].to;
T cap = e[i].cap;
T cost = e[i].cost;
if (cap > 0 && dis[v] > d + h[u] - h[v] + cost) {
dis[v] = d + h[u] - h[v] + cost;
pre[v] = i;
que.emplace(dis[v], v);
}
}
}
return dis[t] != std::numeric_limits<T>::max();
}
MinCostFlow() {}
MinCostFlow(int n_) {
init(n_);
}
void init(int n_) {
n = n_;
e.clear();
g.assign(n, {});
}
void addEdge(int u, int v, T cap, T cost) {
g[u].push_back(e.size());
e.emplace_back(v, cap, cost);
g[v].push_back(e.size());
e.emplace_back(u, 0, -cost);
}
std::pair<T, T> flow(int s, int t) {
T flow = 0;
T cost = 0;
h.assign(n, 0);
while (dijkstra(s, t)) {
for (int i = 0; i < n; ++i) {
h[i] += dis[i];
}
T aug = std::numeric_limits<int>::max();
for (int i = t; i != s; i = e[pre[i] ^ 1].to) {
aug = std::min(aug, e[pre[i]].cap);
}
for (int i = t; i != s; i = e[pre[i] ^ 1].to) {
e[pre[i]].cap -= aug;
e[pre[i] ^ 1].cap += aug;
}
flow += aug;
cost += aug * h[t];
}
return std::make_pair(flow, cost);
}
struct Edge {
int from;
int to;
T cap;
T cost;
T flow;
};
std::vector<Edge> edges() {
std::vector<Edge> a;
for (int i = 0; i < e.size(); i += 2) {
Edge x;
x.from = e[i + 1].to;
x.to = e[i].to;
x.cap = e[i].cap + e[i + 1].cap;
x.cost = e[i].cost;
x.flow = e[i + 1].cap;
a.push_back(x);
}
return a;
}
};
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