This documentation is automatically generated by online-judge-tools/verification-helper
#include "flow/b-flow.hpp"
#pragma once
#include "maxflow.hpp"
#include "mcf_costscaling.hpp"
#include <algorithm>
#include <vector>
// CUT begin
template <typename CAP, typename COST> struct B_Flow {
int N, E;
COST cost_bias;
bool infeasible;
mf_graph<CAP> mf;
mcf_costscaling<CAP, COST> mcf;
std::vector<CAP> b;
std::vector<CAP> fbias;
std::vector<int> fdir;
std::vector<CAP> f;
std::vector<COST> potential;
B_Flow(int N = 0) : N(N), E(0), cost_bias(0), infeasible(false), mf(N + 2), mcf(N + 2), b(N) {}
void add_supply(int v, CAP supply) { b[v] += supply; }
void add_demand(int v, CAP demand) { b[v] -= demand; }
void add_edge(int s, int t, CAP lower_cap, CAP upper_cap, COST cost) {
assert(s >= 0 and s < N);
assert(t >= 0 and t < N);
if (lower_cap > upper_cap) {
infeasible = true;
return;
}
E++;
if (s == t) {
if (cost > 0) {
upper_cap = lower_cap;
} else {
lower_cap = upper_cap;
}
}
if (cost < 0) {
fbias.emplace_back(lower_cap);
fdir.emplace_back(-1);
cost_bias += cost * upper_cap;
b[s] -= upper_cap;
b[t] += upper_cap;
mf.add_edge(t, s, upper_cap - lower_cap);
mcf.add_edge(t, s, upper_cap - lower_cap, -cost);
} else {
fbias.emplace_back(upper_cap);
fdir.emplace_back(1);
if (lower_cap < 0) {
cost_bias += cost * lower_cap, b[s] -= lower_cap, b[t] += lower_cap;
upper_cap -= lower_cap, lower_cap = 0;
}
if (lower_cap > 0) {
cost_bias += cost * lower_cap;
b[s] -= lower_cap;
b[t] += lower_cap;
upper_cap -= lower_cap;
}
mf.add_edge(s, t, upper_cap);
mcf.add_edge(s, t, upper_cap, cost);
}
}
std::pair<bool, COST> solve() {
if (infeasible) return std::make_pair(false, 0);
CAP bsum = 0, bsum_negative = 0;
for (int i = 0; i < N; i++) {
if (b[i] > 0) {
mf.add_edge(N, i, b[i]), mcf.add_edge(N, i, b[i], 0), bsum += b[i];
} else {
mf.add_edge(i, N + 1, -b[i]), mcf.add_edge(i, N + 1, -b[i], 0),
bsum_negative -= b[i];
}
}
if (bsum != bsum_negative or mf.flow(N, N + 1) < bsum) return std::make_pair(false, 0);
std::fill(b.begin(), b.end(), 0);
mcf.add_supply(N, bsum);
mcf.add_demand(N + 1, bsum);
COST ret = mcf.solve();
potential = mcf.potential(), potential.resize(N);
COST cost_ret = cost_bias + ret;
cost_bias = 0;
f = fbias;
auto edges = mcf.edges();
for (int e = 0; e < E; e++) f[e] -= fdir[e] * (edges[e].cap - edges[e].flow);
return std::make_pair(true, cost_ret);
}
};
#line 2 "flow/maxflow.hpp"
#include <algorithm>
#include <cassert>
#include <fstream>
#include <limits>
#include <string>
#include <vector>
// CUT begin
// MaxFlow based and AtCoder Library, single class, no namespace, no private variables, compatible
// with C++11 Reference: <https://atcoder.github.io/ac-library/production/document_ja/maxflow.html>
template <class Cap> struct mf_graph {
struct simple_queue_int {
std::vector<int> payload;
int pos = 0;
void reserve(int n) { payload.reserve(n); }
int size() const { return int(payload.size()) - pos; }
bool empty() const { return pos == int(payload.size()); }
void push(const int &t) { payload.push_back(t); }
int &front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
mf_graph() : _n(0) {}
mf_graph(int n) : _n(n), g(n) {}
int add_edge(int from, int to, Cap cap) {
assert(0 <= from && from < _n);
assert(0 <= to && to < _n);
assert(0 <= cap);
int m = int(pos.size());
pos.push_back({from, int(g[from].size())});
int from_id = int(g[from].size());
int to_id = int(g[to].size());
if (from == to) to_id++;
g[from].push_back(_edge{to, to_id, cap});
g[to].push_back(_edge{from, from_id, 0});
return m;
}
struct edge {
int from, to;
Cap cap, flow;
};
edge get_edge(int i) {
int m = int(pos.size());
assert(0 <= i && i < m);
auto _e = g[pos[i].first][pos[i].second];
auto _re = g[_e.to][_e.rev];
return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
}
std::vector<edge> edges() {
int m = int(pos.size());
std::vector<edge> result;
for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); }
return result;
}
void change_edge(int i, Cap new_cap, Cap new_flow) {
int m = int(pos.size());
assert(0 <= i && i < m);
assert(0 <= new_flow && new_flow <= new_cap);
auto &_e = g[pos[i].first][pos[i].second];
auto &_re = g[_e.to][_e.rev];
_e.cap = new_cap - new_flow;
_re.cap = new_flow;
}
std::vector<int> level, iter;
simple_queue_int que;
void _bfs(int s, int t) {
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
que.clear();
que.push(s);
while (!que.empty()) {
int v = que.front();
que.pop();
for (auto e : g[v]) {
if (e.cap == 0 || level[e.to] >= 0) continue;
level[e.to] = level[v] + 1;
if (e.to == t) return;
que.push(e.to);
}
}
}
Cap _dfs(int v, int s, Cap up) {
if (v == s) return up;
Cap res = 0;
int level_v = level[v];
for (int &i = iter[v]; i < int(g[v].size()); i++) {
_edge &e = g[v][i];
if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
Cap d = _dfs(e.to, s, std::min(up - res, g[e.to][e.rev].cap));
if (d <= 0) continue;
g[v][i].cap += d;
g[e.to][e.rev].cap -= d;
res += d;
if (res == up) return res;
}
level[v] = _n;
return res;
}
Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
Cap flow(int s, int t, Cap flow_limit) {
assert(0 <= s && s < _n);
assert(0 <= t && t < _n);
assert(s != t);
level.assign(_n, 0), iter.assign(_n, 0);
que.clear();
Cap flow = 0;
while (flow < flow_limit) {
_bfs(s, t);
if (level[t] == -1) break;
std::fill(iter.begin(), iter.end(), 0);
Cap f = _dfs(t, s, flow_limit - flow);
if (!f) break;
flow += f;
}
return flow;
}
std::vector<bool> min_cut(int s) {
std::vector<bool> visited(_n);
simple_queue_int que;
que.push(s);
while (!que.empty()) {
int p = que.front();
que.pop();
visited[p] = true;
for (auto e : g[p]) {
if (e.cap && !visited[e.to]) {
visited[e.to] = true;
que.push(e.to);
}
}
}
return visited;
}
void dump_graphviz(std::string filename = "maxflow") const {
std::ofstream ss(filename + ".DOT");
ss << "digraph{\n";
for (int i = 0; i < _n; i++) {
for (const auto &e : g[i]) {
if (e.cap > 0) ss << i << "->" << e.to << "[label=" << e.cap << "];\n";
}
}
ss << "}\n";
ss.close();
return;
}
int _n;
struct _edge {
int to, rev;
Cap cap;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
#line 4 "flow/mcf_costscaling.hpp"
// Cost scaling
// https://people.orie.cornell.edu/dpw/orie633/
template <class Cap, class Cost, int SCALING = 1, int REFINEMENT_ITER = 20>
struct mcf_costscaling {
mcf_costscaling() = default;
mcf_costscaling(int n) : _n(n), to(n), b(n), p(n) {}
int _n;
std::vector<Cap> cap;
std::vector<Cost> cost;
std::vector<int> opposite;
std::vector<std::vector<int>> to;
std::vector<Cap> b;
std::vector<Cost> p;
int add_edge(int from_, int to_, Cap cap_, Cost cost_) {
assert(0 <= from_ and from_ < _n);
assert(0 <= to_ and to_ < _n);
assert(0 <= cap_);
cost_ *= (_n + 1);
const int e = int(cap.size());
to[from_].push_back(e);
cap.push_back(cap_);
cost.push_back(cost_);
opposite.push_back(to_);
to[to_].push_back(e + 1);
cap.push_back(0);
cost.push_back(-cost_);
opposite.push_back(from_);
return e / 2;
}
void add_supply(int v, Cap supply) { b[v] += supply; }
void add_demand(int v, Cap demand) { add_supply(v, -demand); }
template <typename RetCost = Cost> RetCost solve() {
Cost eps = 1;
std::vector<int> que;
for (const auto c : cost) {
while (eps <= -c) eps <<= SCALING;
}
for (; eps >>= SCALING;) {
auto no_admissible_cycle = [&]() -> bool {
for (int i = 0; i < _n; i++) {
if (b[i]) return false;
}
std::vector<Cost> pp = p;
for (int iter = 0; iter < REFINEMENT_ITER; iter++) {
bool flg = false;
for (int e = 0; e < int(cap.size()); e++) {
if (!cap[e]) continue;
int i = opposite[e ^ 1], j = opposite[e];
if (pp[j] > pp[i] + cost[e] + eps)
pp[j] = pp[i] + cost[e] + eps, flg = true;
}
if (!flg) return p = pp, true;
}
return false;
};
if (no_admissible_cycle()) continue; // Refine
for (int e = 0; e < int(cap.size()); e++) {
const int i = opposite[e ^ 1], j = opposite[e];
const Cost cp_ij = cost[e] + p[i] - p[j];
if (cap[e] and cp_ij < 0)
b[i] -= cap[e], b[j] += cap[e], cap[e ^ 1] += cap[e], cap[e] = 0;
}
que.clear();
int qh = 0;
for (int i = 0; i < _n; i++) {
if (b[i] > 0) que.push_back(i);
}
std::vector<int> iters(_n);
while (qh < int(que.size())) {
const int i = que[qh++];
for (; iters[i] < int(to[i].size()) and b[i]; ++iters[i]) { // Push
int e = to[i][iters[i]];
if (!cap[e]) continue;
int j = opposite[e];
Cost cp_ij = cost[e] + p[i] - p[j];
if (cp_ij >= 0) continue;
Cap f = b[i] > cap[e] ? cap[e] : b[i];
if (b[j] <= 0 and b[j] + f > 0) que.push_back(j);
b[i] -= f, b[j] += f, cap[e] -= f, cap[e ^ 1] += f;
}
if (b[i] > 0) { // Relabel
bool flg = false;
for (int e : to[i]) {
if (!cap[e]) continue;
Cost x = p[opposite[e]] - cost[e] - eps;
if (!flg or x > p[i]) flg = true, p[i] = x;
}
que.push_back(i), iters[i] = 0;
}
}
}
RetCost ret = 0;
for (int e = 0; e < int(cap.size()); e += 2) ret += RetCost(cost[e]) * cap[e ^ 1];
return ret / (_n + 1);
}
std::vector<Cost> potential() const {
std::vector<Cost> ret = p, c0 = cost;
for (auto &x : ret) x /= (_n + 1);
for (auto &x : c0) x /= (_n + 1);
while (true) {
bool flg = false;
for (int i = 0; i < _n; i++) {
for (const auto e : to[i]) {
if (!cap[e]) continue;
int j = opposite[e];
auto y = ret[i] + c0[e];
if (ret[j] > y) ret[j] = y, flg = true;
}
}
if (!flg) break;
}
return ret;
}
struct edge {
int from, to;
Cap cap, flow;
Cost cost;
};
edge get_edge(int e) const {
int m = cap.size() / 2;
assert(e >= 0 and e < m);
return {opposite[e * 2 + 1], opposite[e * 2], cap[e * 2] + cap[e * 2 + 1], cap[e * 2 + 1],
cost[e * 2] / (_n + 1)};
}
std::vector<edge> edges() const {
int m = cap.size() / 2;
std::vector<edge> result(m);
for (int i = 0; i < m; i++) result[i] = get_edge(i);
return result;
}
};
#line 6 "flow/b-flow.hpp"
// CUT begin
template <typename CAP, typename COST> struct B_Flow {
int N, E;
COST cost_bias;
bool infeasible;
mf_graph<CAP> mf;
mcf_costscaling<CAP, COST> mcf;
std::vector<CAP> b;
std::vector<CAP> fbias;
std::vector<int> fdir;
std::vector<CAP> f;
std::vector<COST> potential;
B_Flow(int N = 0) : N(N), E(0), cost_bias(0), infeasible(false), mf(N + 2), mcf(N + 2), b(N) {}
void add_supply(int v, CAP supply) { b[v] += supply; }
void add_demand(int v, CAP demand) { b[v] -= demand; }
void add_edge(int s, int t, CAP lower_cap, CAP upper_cap, COST cost) {
assert(s >= 0 and s < N);
assert(t >= 0 and t < N);
if (lower_cap > upper_cap) {
infeasible = true;
return;
}
E++;
if (s == t) {
if (cost > 0) {
upper_cap = lower_cap;
} else {
lower_cap = upper_cap;
}
}
if (cost < 0) {
fbias.emplace_back(lower_cap);
fdir.emplace_back(-1);
cost_bias += cost * upper_cap;
b[s] -= upper_cap;
b[t] += upper_cap;
mf.add_edge(t, s, upper_cap - lower_cap);
mcf.add_edge(t, s, upper_cap - lower_cap, -cost);
} else {
fbias.emplace_back(upper_cap);
fdir.emplace_back(1);
if (lower_cap < 0) {
cost_bias += cost * lower_cap, b[s] -= lower_cap, b[t] += lower_cap;
upper_cap -= lower_cap, lower_cap = 0;
}
if (lower_cap > 0) {
cost_bias += cost * lower_cap;
b[s] -= lower_cap;
b[t] += lower_cap;
upper_cap -= lower_cap;
}
mf.add_edge(s, t, upper_cap);
mcf.add_edge(s, t, upper_cap, cost);
}
}
std::pair<bool, COST> solve() {
if (infeasible) return std::make_pair(false, 0);
CAP bsum = 0, bsum_negative = 0;
for (int i = 0; i < N; i++) {
if (b[i] > 0) {
mf.add_edge(N, i, b[i]), mcf.add_edge(N, i, b[i], 0), bsum += b[i];
} else {
mf.add_edge(i, N + 1, -b[i]), mcf.add_edge(i, N + 1, -b[i], 0),
bsum_negative -= b[i];
}
}
if (bsum != bsum_negative or mf.flow(N, N + 1) < bsum) return std::make_pair(false, 0);
std::fill(b.begin(), b.end(), 0);
mcf.add_supply(N, bsum);
mcf.add_demand(N + 1, bsum);
COST ret = mcf.solve();
potential = mcf.potential(), potential.resize(N);
COST cost_ret = cost_bias + ret;
cost_bias = 0;
f = fbias;
auto edges = mcf.edges();
for (int e = 0; e < E; e++) f[e] -= fdir[e] * (edges[e].cap - edges[e].flow);
return std::make_pair(true, cost_ret);
}
};