結果
| 問題 | No.3097 Azuki Kurai |
| コンテスト | |
| ユーザー |
 drken1215
|
| 提出日時 | 2026-09-28 20:00:26 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
TLE
不安定
|
| 実行時間 | - |
| コード長 | 54,460 bytes |
| 記録 | |
| コンパイル時間 | 2,415 ms |
| コンパイル使用メモリ | 358,428 KB |
| 実行使用メモリ | 10,608 KB |
| 最終ジャッジ日時 | 2026-09-28 20:00:44 |
| 合計ジャッジ時間 | 17,575 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / judge2_1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | TLE * 1 -- * 31 |
ソースコード
//
// フローアルゴリズム ほぼ全集
//
#include <bits/stdc++.h>
using namespace std;
// output stream
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
template<class S, class T> ostream& operator << (ostream &s, const pair<S, T> &P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 2> &P)
{ return s << '<' << P[0] << "," << P[1] << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 3> &P)
{ return s << '<' << P[0] << "," << P[1] << "," << P[2] << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 4> &P)
{ return s << '<' << P[0] << "," << P[1] << "," << P[2] << "," << P[3] << '>'; }
template<class T> ostream& operator << (ostream &s, const vector<string> &P)
{ for (int i = 0; i < P.size(); ++i) { s << P[i] << endl; } return s; }
template<class T> ostream& operator << (ostream &s, const vector<T> &P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, const deque<T> &P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, const vector<vector<T>> &P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, const set<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, const multiset<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, const unordered_set<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class S, class T> ostream& operator << (ostream &s, const map<S, T> &P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
template<class S, class T> ostream& operator << (ostream &s, const unordered_map<S, T> &P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
//------------------------------//
// Flow
//------------------------------//
// edge class (for max-flow)
template<class FLOW> struct FlowEdge {
// core members
int rev, from, to;
FLOW cap, icap, flow;
// constructor
constexpr FlowEdge() noexcept = default;
constexpr FlowEdge(int rev, int from, int to, FLOW cap, FLOW rcap = 0)
: rev(rev), from(from), to(to), cap(cap), icap(cap), flow(rcap) {
}
void reset() {
flow -= icap - cap;
cap = icap;
}
// debug
friend ostream& operator << (ostream& s, const FlowEdge& e) {
return s << e.from << " -> " << e.to << " (" << e.cap << ", " << e.flow << ")";
}
};
// graph class (for max-flow)
template<class FLOW> struct FlowGraph {
// core members
vector<vector<FlowEdge<FLOW>>> list;
vector<pair<int,int>> pos; // pos[i] := {vertex, order of list[vertex]} of i-th edge
// constructor
FlowGraph(int n = 0) : list(n) { }
void init(int n = 0) {
list.clear(), list.resize(n);
pos.clear();
}
void resize(int n) {
list.resize(n);
}
void clear() {
list.clear(), pos.clear();
}
// getter
vector<FlowEdge<FLOW>> &operator [] (int i) {
assert(0 <= i && i < (int)list.size());
return list[i];
}
const vector<FlowEdge<FLOW>> &operator [] (int i) const {
assert(0 <= i && i < (int)list.size());
return list[i];
}
size_t size() const noexcept {
return list.size();
}
size_t size_edegs() const noexcept {
return pos.size();
}
FlowEdge<FLOW> &get_rev_edge(const FlowEdge<FLOW> &e) {
return list[e.to][e.rev];
}
const FlowEdge<FLOW> &get_rev_edge(const FlowEdge<FLOW> &e) const {
return list[e.to][e.rev];
}
FlowEdge<FLOW> &get_edge(int i) {
return list[pos[i].first][pos[i].second];
}
const FlowEdge<FLOW> &get_edge(int i) const {
return list[pos[i].first][pos[i].second];
}
vector<FlowEdge<FLOW>> get_edges() const {
vector<FlowEdge<FLOW>> edges;
for (int i = 0; i < (int)pos.size(); ++i) {
edges.push_back(get_edge(i));
}
return edges;
}
// change edges
void reset() const {
for (int i = 0; i < (int)list.size(); ++i) {
for (FlowEdge<FLOW> &e : list[i]) e.reset();
}
}
void change_edge(FlowEdge<FLOW> &e, FLOW new_cap, FLOW new_rcap) {
assert(new_cap >= 0 && new_rcap >= 0);
FlowEdge<FLOW> &re = get_rev_edge(e);
e.cap = new_cap, e.icap = new_cap + new_rcap, e.flow = new_rcap;
re.cap = new_rcap, re.icap = new_cap + new_rcap, re.flow = new_cap;
}
// add_edge
void add_edge(int from, int to, FLOW cap, FLOW rcap = 0) {
assert(0 <= from && from < (int)list.size() && 0 <= to && to < (int)list.size());
assert(cap >= 0);
int from_id = int(list[from].size()), to_id = int(list[to].size());
if (from == to) to_id++;
pos.emplace_back(from, from_id);
list[from].push_back(FlowEdge<FLOW>(to_id, from, to, cap, rcap));
list[to].push_back(FlowEdge<FLOW>(from_id, to, from, rcap, cap));
}
void add_bidirected_edge(int from, int to, FLOW cap) {
assert(0 <= from && from < (int)list.size() && 0 <= to && to < (int)list.size());
assert(cap >= 0);
add_edge(from, to, cap, cap);
}
// augment
FLOW augment(int s, int t, FLOW up_flow = numeric_limits<FLOW>::max()) {
vector<bool> seen(size(), false);
auto dfs = [&](auto &&dfs, int v, FLOW up_flow) -> FLOW {
if (v == t) return up_flow;
seen[v] = true;
for (int i = 0; i < (int)list[v].size(); i++) {
FlowEdge<FLOW> &e = list[v][i], &re = get_rev_edge(e);
if (seen[e.to] || e.cap <= 0) continue;
FLOW flow = dfs(dfs, e.to, min(up_flow, e.cap));
if (flow > 0) {
e.cap -= flow, e.flow += flow;
re.cap += flow, re.flow -= flow;
return flow;
}
}
return FLOW(0);
};
return dfs(dfs, s, up_flow);
};
FLOW augment(int s, int t, vector<FlowEdge<FLOW>> &path, FLOW up_flow = numeric_limits<FLOW>::max()) {
vector<bool> seen(size(), false);
auto dfs = [&](auto &&dfs, int v, vector<FlowEdge<FLOW>> &path, FLOW up_flow) -> FLOW {
if (v == t) return up_flow;
seen[v] = true;
for (int i = 0; i < (int)list[v].size(); i++) {
FlowEdge<FLOW> &e = list[v][i], &re = get_rev_edge(e);
if (seen[e.to] || e.cap <= 0) continue;
FLOW flow = dfs(dfs, e.to, path, min(up_flow, e.cap));
if (flow > 0) {
e.cap -= flow, e.flow += flow;
re.cap += flow, re.flow -= flow;
path.emplace_back(e);
return flow;
}
}
return FLOW(0);
};
path.clear();
FLOW res = dfs(dfs, s, path, up_flow);
reverse(path.begin(), path.end());
return res;
};
// find reachable nodes from node s (1: s-domain, -1: t-domain, 0: no reach)
vector<int> find_cut(int s, int t) const {
vector<int> res(size(), 0);
auto dfs_s = [&](auto &&dfs_s, int v) -> void {
res[v] = 1;
for (const auto &e : list[v]) {
if (res[e.to] || e.cap <= 0) continue;
dfs_s(dfs_s, e.to);
}
};
auto dfs_t = [&](auto &&dfs_t, int v) -> void {
res[v] = -1;
for (const auto &e : list[v]) {
auto re = get_rev_edge(e);
if (res[e.to] || re.cap <= 0) continue;
dfs_t(dfs_t, e.to);
}
};
dfs_s(dfs_s, s), dfs_t(dfs_t, t);
return res;
}
// finc cutset
vector<FlowEdge<FLOW>> find_cutset(int s, int t) const {
vector<int> cut = find_cut(s, t);
vector<FlowEdge<FLOW>> res;
const auto &edges = get_edges();
for (const auto &e : edges) {
if (cut[e.from] == 1 && cut[e.to] != 1) {
res.emplace_back(e);
}
}
return res;
}
// check if the s-t flow is feasible
bool is_feasible(int s, int t) const {
vector<FLOW> b(list.size(), FLOW(0));
for (int v = 0; v < (int)list.size(); v++) {
for (const auto &e : list[v]) {
b[v] += (e.flow - get_rev_edge(e).flow) / 2;
}
}
if (b[s] + b[t] != 0) return false;
for (int v = 0; v < (int)list.size(); v++) {
if (v != s && v != t && b[v] != FLOW(0)) return false;
}
return true;
}
bool is_feasible(int s, int t, FLOW flow) const {
vector<FLOW> b(list.size(), FLOW(0));
for (int v = 0; v < (int)list.size(); v++) {
for (const auto &e : list[v]) {
b[v] += (e.flow - get_rev_edge(e).flow) / 2;
}
}
if (b[s] != flow) return false;
if (b[t] != -flow) return false;
for (int v = 0; v < (int)list.size(); v++) {
if (v != s && v != t && b[v] != FLOW(0)) return false;
}
return true;
}
// decompose flow into s-t simple paths and cycles
using Path = vector<FlowEdge<FLOW>>;
pair<vector<Path>, vector<Path>> decompose(int s, int t) const {
struct Arc {
int to;
FLOW rem;
int eidx;
};
assert(is_feasible(s, t));
vector<vector<Arc>> fg(list.size());
for (int v = 0; v < (int)list.size(); v++) {
for (int j = 0; j < (int)list[v].size(); j++) {
FLOW f = list[v][j].icap - list[v][j].cap;
if (f > 0) fg[v].push_back({list[v][j].to, f, j});
}
}
vector<int> ptr(list.size(), 0), onpath(list.size(), -1);
vector<pair<int, int>> route;
vector<int> used;
vector<Path> paths, cycles;
auto next_arc = [&](int v) -> int {
while (ptr[v] < (int)fg[v].size() && fg[v][ptr[v]].rem <= 0) ptr[v]++;
return (ptr[v] < (int)fg[v].size() ? ptr[v] : -1);
};
auto extract = [&](int begin, bool is_cycle) {
FLOW mi = numeric_limits<FLOW>::max();
for (int k = begin; k < (int)route.size(); k++) {
auto [v, i] = route[k];
mi = min(mi, fg[v][i].rem);
}
vector<FlowEdge<FLOW>> seq;
for (int k = begin; k < (int)route.size(); k++) {
auto [v, i] = route[k];
fg[v][i].rem -= mi;
FlowEdge<FLOW> e = list[v][fg[v][i].eidx];
e.flow = mi;
seq.push_back(e);
}
if (is_cycle) cycles.push_back(std::move(seq));
else paths.push_back(std::move(seq));
};
auto walk = [&](int start, bool stop_at_t) {
route.clear();
int v = start;
onpath[v] = 0;
used.push_back(v);
while (true) {
int i = next_arc(v), u = fg[v][i].to;
route.push_back({v, i});
if (stop_at_t && u == t) {
extract(0, false);
break;
}
if (onpath[u] != -1) {
extract(onpath[u], true);
break;
}
onpath[u] = (int)route.size();
used.push_back(u);
v = u;
}
for (int w : used) onpath[w] = -1;
used.clear();
};
// extract all s-t paths
while (next_arc(s) != -1) walk(s, true);
// decompose remained circulation into cycles
for (int v = 0; v < (int)list.size(); v++) while (next_arc(v) != -1) walk(v, false);
return {paths, cycles};
}
// debug
friend ostream& operator << (ostream& s, const FlowGraph &G) {
const auto &edges = G.get_edges();
for (const auto &e : edges) s << e << endl;
return s;
}
};
// Dinic
template<class FLOW> FLOW Dinic(FlowGraph<FLOW> &G, int s, int t, FLOW limit_flow) {
assert(0 <= s && s < G.size() && 0 <= t && t < G.size() && s != t);
FLOW current_flow = 0;
vector<int> level((int)G.size(), -1), iter((int)G.size(), 0);
// Dinic BFS
auto bfs = [&]() -> void {
level.assign((int)G.size(), -1);
level[s] = 0;
queue<int> que;
que.push(s);
while (!que.empty()) {
int v = que.front();
que.pop();
for (const FlowEdge<FLOW> &e : G[v]) {
if (level[e.to] < 0 && e.cap > 0) {
level[e.to] = level[v] + 1;
if (e.to == t) return;
que.push(e.to);
}
}
}
};
// Dinic DFS
auto dfs = [&](auto self, int v, FLOW up_flow) {
if (v == t) return up_flow;
FLOW res_flow = 0;
for (int &i = iter[v]; i < (int)G[v].size(); ++i) {
FlowEdge<FLOW> &e = G[v][i], &re = G.get_rev_edge(e);
if (level[v] >= level[e.to] || e.cap <= 0) continue;
FLOW flow = self(self, e.to, min(up_flow - res_flow, e.cap));
if (flow <= 0) continue;
res_flow += flow;
e.cap -= flow, e.flow += flow;
re.cap += flow, re.flow -= flow;
if (res_flow == up_flow) break;
}
return res_flow;
};
// flow
while (current_flow < limit_flow) {
bfs();
if (level[t] < 0) break;
iter.assign((int)iter.size(), 0);
while (current_flow < limit_flow) {
FLOW flow = dfs(dfs, s, limit_flow - current_flow);
if (flow <= 0) break;
current_flow += flow;
}
}
return current_flow;
};
template<class FLOW> FLOW Dinic(FlowGraph<FLOW> &G, int s, int t) {
return Dinic(G, s, t, numeric_limits<FLOW>::max());
}
// edge class (for min-cost flow)
template<class FLOW, class COST> struct FlowCostEdge {
// core members
int rev, from, to;
FLOW cap, icap, flow;
COST cost;
// constructor
constexpr FlowCostEdge() noexcept = default;
constexpr FlowCostEdge(int rev, int from, int to, FLOW cap, COST cost)
: rev(rev), from(from), to(to), cap(cap), icap(cap), flow(0), cost(cost) {
}
constexpr FlowCostEdge(int rev, int from, int to, FLOW cap, FLOW rcap, COST cost)
: rev(rev), from(from), to(to), cap(cap), icap(cap), flow(rcap), cost(cost) {
}
void reset() {
flow -= icap - cap;
cap = icap;
}
// debug
friend ostream& operator << (ostream& s, const FlowCostEdge& e) {
return s << e.from << " -> " << e.to << " (" << e.cap << ", " << e.flow << ", " << e.cost << ")";
}
};
// graph class (for min-cost flow)
template<class FLOW, class COST> struct FlowCostGraph {
// core members
vector<vector<FlowCostEdge<FLOW, COST>>> list;
vector<pair<int,int>> pos; // pos[i] := {vertex, order of list[vertex]} of i-th edge
vector<COST> pot; // pot[v] := potential (e.cost + pot[e.from] - pos[e.to] >= 0)
bool include_negative_edge = false;
// constructor
FlowCostGraph(int n = 0) : list(n), pot(n), include_negative_edge(false) { }
void init(int n = 0) {
list.clear(), list.resize(n);
pos.clear();
pot.assign(n, 0);
include_negative_edge = false;
}
// getter
vector<FlowCostEdge<FLOW, COST>> &operator [] (int i) {
assert(0 <= i && i < (int)list.size());
return list[i];
}
const vector<FlowCostEdge<FLOW, COST>> &operator [] (int i) const {
assert(0 <= i && i < (int)list.size());
return list[i];
}
size_t size() const noexcept {
return list.size();
}
size_t size_edegs() const noexcept {
return pos.size();
}
FlowCostEdge<FLOW, COST> &get_rev_edge(const FlowCostEdge<FLOW, COST> &e) {
return list[e.to][e.rev];
}
const FlowCostEdge<FLOW, COST> &get_rev_edge(const FlowCostEdge<FLOW, COST> &e) const {
return list[e.to][e.rev];
}
FlowCostEdge<FLOW, COST> &get_edge(int i) {
return list[pos[i].first][pos[i].second];
}
const FlowCostEdge<FLOW, COST> &get_edge(int i) const {
return list[pos[i].first][pos[i].second];
}
vector<FlowCostEdge<FLOW, COST>> get_edges() const {
vector<FlowCostEdge<FLOW, COST>> edges;
for (int i = 0; i < (int)pos.size(); ++i) {
edges.push_back(get_edge(i));
}
return edges;
}
// change edges
void reset() {
for (int i = 0; i < (int)list.size(); ++i) {
for (FlowCostEdge<FLOW, COST> &e : list[i]) e.reset();
}
}
// add_edge
void add_edge(int from, int to, FLOW cap, COST cost) {
assert(0 <= from && from < (int)list.size() && 0 <= to && to < (int)list.size());
assert(cap >= 0);
int from_id = (int)list[from].size(), to_id = (int)list[to].size();
if (from == to) to_id++;
pos.emplace_back(from, from_id);
list[from].push_back(FlowCostEdge<FLOW, COST>(to_id, from, to, cap, 0, cost));
list[to].push_back(FlowCostEdge<FLOW, COST>(from_id, to, from, 0, cap, -cost));
if (cost < 0) include_negative_edge = true;
}
void add_edge(int from, int to, FLOW cap, FLOW rcap, COST cost) {
assert(0 <= from && from < (int)list.size() && 0 <= to && to < (int)list.size());
assert(cap >= 0);
int from_id = (int)list[from].size(), to_id = (int)list[to].size();
if (from == to) to_id++;
pos.emplace_back(from, from_id);
list[from].push_back(FlowCostEdge<FLOW, COST>(to_id, from, to, cap, rcap, cost));
list[to].push_back(FlowCostEdge<FLOW, COST>(from_id, to, from, rcap, cap, -cost));
if (cost < 0) include_negative_edge = true;
}
void add_bidirected_edge(int from, int to, FLOW cap, COST cost) {
assert(0 <= from && from < (int)list.size() && 0 <= to && to < (int)list.size());
assert(cap >= 0);
add_edge(from, to, cap, cap, cost);
}
// find initial potential (to resolve initial negative-edge)
// pot[v] := potential (e.cost + pot[e.from] - pos[e.to] >= 0)
bool calc_potential_dag() {
pot.assign(size(), 0);
vector<int> deg(size(), 0), st;
for (int v = 0; v < (int)size(); v++) for (const auto &e : list[v]) deg[e.to] += (e.cap > 0);
st.reserve(size());
for (int v = 0; v < (int)size(); v++) if (!deg[v]) st.emplace_back(v);
for (int i = 0; i < (int)size(); i++) {
if ((int)st.size() == i) return false; // not DAG
int cur = st[i];
for (const auto &e : list[cur]) {
if (e.cap <= 0) continue;
deg[e.to]--;
if (deg[e.to] == 0) st.emplace_back(e.to);
if (pot[e.to] >= pot[cur] + e.cost) pot[e.to] = pot[cur] + e.cost;
}
}
return true;
}
bool calc_potential_spfa() {
pot.assign(size(), 0);
queue<int> que;
vector<bool> inque(size(), false);
vector<int> cnt(size(), 0);
for (int v = 0; v < (int)size(); v++) que.push(v), inque[v] = true;
while (!que.empty()) {
int cur = que.front();
que.pop();
inque[cur] = false;
if (cnt[cur] > (int)size()) return false; // include negative-cycle
cnt[cur]++;
for (const auto &e : list[cur]) {
if (e.cap <= 0) continue;
if (pot[e.to] > pot[cur] + e.cost) {
pot[e.to] = pot[cur] + e.cost;
if (!inque[e.to]) inque[e.to] = true, que.push(e.to);
}
}
}
return true;
}
bool calc_potential() {
return calc_potential_dag() || calc_potential_spfa();
}
bool init_potential() {
if (!include_negative_edge) return true;
return calc_potential();
}
// decompose flow into s-t simple paths and cycles
using Path = vector<FlowCostEdge<FLOW, COST>>;
pair<vector<Path>, vector<Path>> decompose(int s, int t) const {
struct Arc {
int to;
FLOW rem;
int eidx;
};
vector<vector<Arc>> fg(list.size());
for (int v = 0; v < (int)list.size(); v++) {
for (int j = 0; j < (int)list[v].size(); j++) {
FLOW f = list[v][j].icap - list[v][j].cap;
if (f > 0) fg[v].push_back({list[v][j].to, f, j});
}
}
vector<Path> paths, cycles;
auto build = [&](const vector<pair<int,int>> &route, bool is_cycle) {
FLOW mi = numeric_limits<FLOW>::max();
for (auto [v,i] : route) mi = min(mi, fg[v][i].rem);
vector<FlowCostEdge<FLOW,COST>> seq;
for (auto [v,i] : route) {
fg[v][i].rem -= mi;
FlowCostEdge<FLOW,COST> e = list[v][fg[v][i].eidx];
e.flow = mi;
seq.push_back(e);
}
if (is_cycle) cycles.push_back(std::move(seq));
else paths.push_back(std::move(seq));
};
// Phase 1: extract all cycles and make graph DAG
const int NOTSEEN = 0, INSTACK = 1, FINISH = 2;
vector<int> color(list.size(), NOTSEEN);
vector<int> pos_in_stack(list.size(), -1);
vector<pair<int, int>> stk;
auto dfs = [&](auto &&dfs, int v) -> bool {
color[v] = INSTACK;
pos_in_stack[v] = (int)stk.size();
for (int i = 0; i < (int)fg[v].size(); i++) {
if (fg[v][i].rem <= 0) continue;
int u = fg[v][i].to;
if (color[u] == INSTACK) {
vector<pair<int,int>> route;
for (int k = pos_in_stack[u]; k < (int)stk.size(); k++) {
route.push_back(stk[k]);
}
route.push_back({v, i});
build(route, true);
return true;
}
if (color[u] == NOTSEEN) {
stk.push_back({v, i});
if (dfs(dfs, u)) return true;
stk.pop_back();
}
}
color[v] = FINISH;
pos_in_stack[v] = -1;
return false;
};
while (true) {
fill(color.begin(), color.end(), NOTSEEN);
stk.clear();
bool found = false;
for (int v = 0; v < (int)list.size() && !found; v++) {
if (color[v] == NOTSEEN && dfs(dfs, v)) found = true;
}
if (!found) break;
}
// Phase 2: find all s-t paths
vector<int> ptr(list.size(), 0);
auto next_arc = [&](int v) -> int {
while (ptr[v] < (int)fg[v].size() && fg[v][ptr[v]].rem <= 0) ptr[v]++;
return ptr[v] < (int)fg[v].size() ? ptr[v] : -1;
};
while (next_arc(s) != -1) {
vector<pair<int,int>> route;
int v = s;
while (v != t) {
int i = next_arc(v);
route.push_back({v, i});
v = fg[v][i].to;
}
build(route, false);
}
return {paths, cycles};
}
// debug
friend ostream& operator << (ostream& s, const FlowCostGraph &G) {
const auto &edges = G.get_edges();
for (const auto &e : edges) s << e << endl;
return s;
}
};
// min-cost max-flow (<= limit_flow), slope ver.
template<class FLOW, class COST> vector<pair<FLOW, COST>>
MinCostFlowSlope(FlowCostGraph<FLOW, COST> &G, int S, int T, FLOW limit_flow)
{
// result values
FLOW cur_flow = 0;
COST cur_cost = 0, pre_cost = numeric_limits<COST>::max() / 2;
vector<pair<FLOW, COST>> res;
res.emplace_back(cur_flow, cur_cost);
// intermediate values
vector<COST> dist((int)G.size(), numeric_limits<COST>::max() / 2);
vector<int> prevv((int)G.size(), -1), preve((int)G.size(), -1);
// dual
auto dual_step = [&]() -> bool {
dist.assign((int)G.size(), numeric_limits<COST>::max() / 2);
dist[S] = 0;
priority_queue<pair<COST,int>, vector<pair<COST,int>>, greater<pair<COST,int>>> que;
que.emplace(0, S);
while (!que.empty()) {
auto [cur, v] = que.top();
que.pop();
if (cur > dist[v]) continue;
for (int i = 0; i < (int)G[v].size(); i++) {
const auto &e = G[v][i];
COST add = e.cost + G.pot[v] - G.pot[e.to];
if (e.cap > 0 && dist[e.to] > dist[v] + add) {
dist[e.to] = dist[v] + add;
prevv[e.to] = v;
preve[e.to] = i;
que.emplace(dist[e.to], e.to);
}
}
}
return dist[T] < numeric_limits<COST>::max() / 2;
};
// primal
auto primal_step = [&]() -> void {
for (int v = 0; v < G.size(); v++) {
if (dist[v] < numeric_limits<COST>::max() / 2) G.pot[v] += dist[v];
else G.pot[v] = numeric_limits<COST>::max() / 2;
}
FLOW flow = limit_flow - cur_flow;
COST cost = G.pot[T] - G.pot[S];
for (int v = T; v != S; v = prevv[v]) {
flow = min(flow, G[prevv[v]][preve[v]].cap);
}
for (int v = T; v != S; v = prevv[v]) {
FlowCostEdge<FLOW, COST> &e = G[prevv[v]][preve[v]];
FlowCostEdge<FLOW, COST> &re = G.get_rev_edge(e);
e.cap -= flow, e.flow += flow;
re.cap += flow, re.flow -= flow;
}
cur_flow += flow;
cur_cost += flow * cost;
if (pre_cost == cost) res.pop_back();
res.emplace_back(cur_flow, cur_cost);
pre_cost = cost;
};
// initialize potential
assert(G.init_potential());
// primal-dual
while (cur_flow < limit_flow) {
if (!dual_step()) break;
primal_step();
}
return res;
}
// min-cost max-flow, slope ver.
template<class FLOW, class COST> vector<pair<FLOW, COST>>
MinCostFlowSlope(FlowCostGraph<FLOW, COST> &G, int S, int T)
{
return MinCostFlowSlope(G, S, T, numeric_limits<FLOW>::max());
}
// min-cost max-flow (<= limit_flow)
template<class FLOW, class COST> pair<FLOW, COST>
MinCostFlow(FlowCostGraph<FLOW, COST> &G, int S, int T, FLOW limit_flow)
{
return MinCostFlowSlope(G, S, T, limit_flow).back();
}
// min-cost max-flow (<= limit_flow)
template<class FLOW, class COST> pair<FLOW, COST>
MinCostFlow(FlowCostGraph<FLOW, COST> &G, int S, int T)
{
return MinCostFlow(G, S, T, numeric_limits<FLOW>::max());
}
// Min Cost Circulation Flow by Cost-Scaling
template<class FLOW, class COST> COST MinCostCirculation(FlowCostGraph<FLOW, COST> &G) {
const int N = (int)G.size();
const COST SCALE = N + 1;
COST eps = 1;
vector<FLOW> balance(G.size(), 0);
vector<COST> price(G.size(), 0);
auto reduced_cost = [&](const FlowCostEdge<FLOW, COST> &e) -> COST {
return e.cost * SCALE - price[e.from] + price[e.to];
};
auto ConstructGaux = [&]() -> void {
vector<bool> visited(G.size(), false);
vector<int> st;
st.reserve(N);
for (int s = 0; s < N; s++) {
if (balance[s] <= 0 || visited[s]) continue;
visited[s] = true;
st.push_back(s);
while (!st.empty()) {
int v = st.back();
st.pop_back();
for (const auto &e : G[v]) {
if (e.cap <= 0 || reduced_cost(e) >= 0 || visited[e.to]) continue;
visited[e.to] = true;
st.push_back(e.to);
}
}
}
for (int v = 0; v < G.size(); ++v) if (visited[v]) price[v] += eps;
};
auto augment_blocking_flow = [&]() -> bool {
vector<int> iter(N, 0);
auto augment = [&](auto &&augment, int v, FLOW flow) -> FLOW {
if (balance[v] < 0) {
FLOW dif = min(flow, -balance[v]);
balance[v] += dif;
return dif;
}
for (int &i = iter[v]; i < (int)G[v].size(); i++) {
auto &e = G[v][i];
if (e.cap <= 0 || reduced_cost(e) >= 0) continue;
FLOW dif = augment(augment, e.to, min(flow, e.cap));
if (dif <= 0) continue;
auto &re = G.get_rev_edge(e);
e.cap -= dif, e.flow += dif;
re.cap += dif, re.flow -= dif;
return dif;
}
return FLOW(0);
};
bool finish = true;
for (int v = 0; v < N; ++v) {
while (balance[v] > 0) {
FLOW f = augment(augment, v, balance[v]);
if (f <= 0) break;
balance[v] -= f;
}
if (balance[v] > 0) finish = false;
}
return finish;
};
// eps init
COST need = 0;
for (int v = 0; v < N; v++) {
for (const auto &e : G[v]) {
if (e.cap <= 0) continue;
need = max(need, -e.cost * SCALE);
}
}
while (eps < need) eps *= 2;
// cost scaling
while (eps > 1) {
eps /= 2;
for (int v = 0; v < N; v++) {
for (int i = 0; i < (int)G[v].size(); i++) {
auto &e = G[v][i];
if (e.cap <= 0 || reduced_cost(e) >= 0) continue;
auto &re = G.get_rev_edge(e);
FLOW f = e.cap;
balance[e.from] -= f, balance[e.to] += f;
e.cap -= f, e.flow += f;
re.cap += f, re.flow -= f;
}
}
while (true) {
ConstructGaux();
if (augment_blocking_flow()) break;
}
}
COST res = 0;
const auto &edges = G.get_edges();
for (const auto &e : edges) res += e.flow * e.cost;
return res;
}
//--------------------------------//
// Minumum Cost b-flow
//--------------------------------//
// Minimum Cost b-flow (by primal-dual, negative cycle is NG)
template<class FLOW, class COST> struct MinCostBFlowByPrimalDual {
// inner values
int N;
FlowCostGraph<FLOW, COST> G;
vector<FLOW> dss; // demand (< 0) and supply (> 0)
vector<COST> dual;
// constructor
explicit MinCostBFlowByPrimalDual(int n) : N(n), G(n + 2), dss(n, 0) {}
// setter
void add_edge(int from, int to, FLOW cap, COST cost) {
assert(cap >= 0);
G.add_edge(from, to, cap, cost);
}
void set_ds(int v, FLOW ds) {
assert(0 <= v && v < N);
dss[v] = ds;
}
void set_ds(const vector<FLOW> &vds) {
assert((int)vds.size() == N);
dss = vds;
}
// getter
FlowCostEdge<FLOW, COST> &get_edge(int i) {
return G.get_edge(i);
}
const FlowCostEdge<FLOW, COST> &get_edge(int i) const {
return G.get_edge(i);
}
vector<FlowCostEdge<FLOW, COST>> get_edges() const {
return G.get_edges();
}
COST get_dual(int v) const {
return dual[v];
}
vector<COST> get_duals() const {
return dual;
}
// solver
pair<bool, COST> solve(bool calc_potential = false) {
// dss treatment
int s = N, t = N + 1;
FLOW ssum = 0, tsum = 0;
for (int v = 0; v < N; v++) {
if (dss[v] > 0) ssum += dss[v], G.add_edge(s, v, dss[v], COST(0));
else if (dss[v] < 0) tsum -= dss[v], G.add_edge(v, t, -dss[v], COST(0));
}
// feasibility check
if (ssum != tsum) return {false, COST(0)};
// min-cost flow
auto [maxflow, mincost] = MinCostFlow(G, s, t, ssum);
if (maxflow < ssum) return {false, COST(0)};
// find dual
if (calc_potential) {
G.calc_potential();
dual = G.pot;
dual.pop_back(), dual.pop_back(); // eliminate s, t
}
return {true, mincost};
}
};
// Minimum Cost b-flow (by cost-scaling min-cost circulation)
template<class FLOW, class COST> struct MinCostBFlowByCostScaling {
// inner Edge
struct InnerEdge {
int from, to;
FLOW cap;
COST cost;
InnerEdge(int from_, int to_, FLOW cap_, COST cost_) : from(from_), to(to_), cap(cap_), cost(cost_) {}
friend ostream& operator << (ostream& s, const InnerEdge& e) {
return s << e.from << " -> " << e.to << " (" << e.cap << ", " << e.cost << ")";
}
};
// inner values
int N;
FlowCostGraph<FLOW, COST> G;
vector<InnerEdge> edges;
vector<FLOW> dss; // demand (< 0) and supply (> 0)
vector<COST> dual;
// constructor
explicit MinCostBFlowByCostScaling(int n = 0) : N(n), G(n), dss(n, 0) {}
// setter
void add_edge(int from, int to, FLOW cap, COST cost) {
assert(cap >= 0);
edges.push_back(InnerEdge(from, to, cap, cost));
}
void set_ds(int v, FLOW ds) {
assert(0 <= v && v < N);
dss[v] = ds;
}
void set_ds(const vector<FLOW> &vds) {
assert((int)vds.size() == N);
dss = vds;
}
// getter
FlowCostEdge<FLOW, COST> &get_edge(int i) {
return G.get_edge(i);
}
const FlowCostEdge<FLOW, COST> &get_edge(int i) const {
return G.get_edge(i);
}
vector<FlowCostEdge<FLOW, COST>> get_edges() const {
return G.get_edges();
}
COST get_dual(int v) const {
return dual[v];
}
vector<COST> get_duals() const {
return dual;
}
// solver
pair<bool, COST> solve(bool calc_potential = true) {
// push s-t flow
FlowGraph<FLOW> preG(N + 2);
int s = N, t = N + 1;
for (const auto &e : edges) preG.add_edge(e.from, e.to, e.cap);
FLOW ssum = 0, tsum = 0;
for (int v = 0; v < N; v++) {
if (dss[v] > 0) ssum += dss[v], preG.add_edge(s, v, dss[v]);
else if (dss[v] < 0) tsum -= dss[v], preG.add_edge(v, t, -dss[v]);
}
// feasibility check
if (ssum != tsum) return {false, COST(0)};
if (Dinic(preG, s, t) < ssum) return {false, COST(0)};
// come down to min-cost circulation
for (int i = 0; i < (int)edges.size(); i++) {
const auto &e = edges[i];
const auto &ge = preG.get_edge(i);
G.add_edge(ge.from, ge.to, ge.cap, ge.flow, e.cost);
}
COST mincost = MinCostCirculation(G);
// find dual
if (calc_potential) {
G.calc_potential();
dual = G.pot;
}
return {true, mincost};
}
};
// Network Simplex Method
template<class FLOW, class COST> struct MinCostBFlowByNetworkSimplex {
// inner Edge
struct InnerEdge {
int from, to;
FLOW cap;
COST cost;
InnerEdge(int from_, int to_, FLOW cap_, COST cost_) : from(from_), to(to_), cap(cap_), cost(cost_) {}
};
struct Parent {
int p, e;
FLOW up, down;
};
// inner values
int N, original_edge_size;
vector<InnerEdge> edges;
vector<FLOW> dss; // demand (< 0) and supply (> 0)
bool feasible;
COST total_cost;
vector<COST> dual;
// intermediate results
int BUCKET_SIZE, MINOR_LIMIT;
vector<Parent> parents;
vector<int> depth, nex, pre, candidates;
// constructor
explicit MinCostBFlowByNetworkSimplex(int n = 0) : N(n), dss(n) {}
// setter
void add_edge(int from, int to, FLOW cap, COST cost) {
assert(cap >= 0);
edges.emplace_back(from, to, cap, cost);
edges.emplace_back(to, from, 0, -cost);
}
void set_ds(int v, FLOW ds) {
assert(0 <= v && v < N);
dss[v] = ds;
}
void set_ds(const vector<FLOW> &vds) {
assert((int)vds.size() == N);
dss = vds;
}
// getter
FLOW get_flow(int i) const {
return edges[(i * 2) ^ 1].cap;
}
COST get_dual(int v) const {
return dual[v];
}
vector<COST> get_duals() const {
return dual;
}
// solver
pair<bool, COST> solve() {
BUCKET_SIZE = max(int(sqrt(double(edges.size())) * 0.2), 10);
MINOR_LIMIT = max(int(BUCKET_SIZE * 0.1), 3);
precompute();
candidates.reserve(BUCKET_SIZE);
int ei = 0;
while (true) {
for (int i = 0; i < MINOR_LIMIT; i++) if (!minor()) break;
COST best = 0;
int best_ei = -1;
candidates.clear();
for (int i = 0; i < (int)edges.size(); i++) {
if (edges[ei].cap > 0) {
COST clen = edges[ei].cost + dual[edges[ei ^ 1].to] - dual[edges[ei].to];
if (clen < 0) {
if (clen < best) best = clen, best_ei = ei;
candidates.push_back(ei);
if ((int)candidates.size() == BUCKET_SIZE) break;
}
}
ei++;
if (ei == (int)edges.size()) ei = 0;
}
if (candidates.empty()) break;
push_flow(best_ei);
}
if (!postcompute()) return {false, COST(-1)};
else return {true, total_cost};
}
void connect(int a, int b) {
nex[a] = b, pre[b] = a;
}
void precompute() {
original_edge_size = (int)edges.size();
dual.assign(N + 1, 0);
parents.resize(N), depth.assign(N + 1, 1);
nex.assign((N + 1) * 2, 0), pre.assign((N + 1) * 2, 0);
COST inf_cost = 1;
for (int i = 0; i < (int)edges.size(); i += 2) {
inf_cost += (edges[i].cost >= 0 ? edges[i].cost : -edges[i].cost);
}
edges.reserve((int)edges.size() + N * 2);
for (int i = 0; i < N; i++) {
if (dss[i] >= 0) {
edges.push_back(InnerEdge(i, N, 0, inf_cost));
edges.push_back(InnerEdge(N, i, dss[i], -inf_cost));
dual[i] = -inf_cost;
} else {
edges.push_back(InnerEdge(i, N, -dss[i], -inf_cost));
edges.push_back(InnerEdge(N, i, 0, inf_cost));
dual[i] = inf_cost;
}
int e = (int)edges.size() - 2;
parents[i] = {N, e, edges[e].cap, edges[e ^ 1].cap};
}
depth[N] = 0;
for (int i = 0; i < N + 1; i++) connect(i * 2, i * 2 + 1);
for (int i = 0; i < N; i++) connect(i * 2 + 1, nex[N * 2]), connect(N * 2, i * 2);
}
bool postcompute() {
for (int i = 0; i < N; i++) {
edges[parents[i].e].cap = parents[i].up;
edges[parents[i].e ^ 1].cap = parents[i].down;
}
feasible = true;
for (int i = 0; i < N; i++) {
int e = original_edge_size + i * 2;
if (dss[i] >= 0) {
if (edges[e ^ 1].cap > 0) feasible = false;
} else {
if (edges[e].cap > 0) feasible = false;
}
}
if (!feasible) return false;
total_cost = 0;
for (int i = 0; i < (int)edges.size(); i += 2) {
total_cost += edges[i ^ 1].cap * edges[i].cost;
}
dual.pop_back();
return true;
}
void push_flow(int ei0) {
int u0 = edges[ei0 ^ 1].to, v0 = edges[ei0].to, del_u = v0;
FLOW f = edges[ei0].cap;
COST clen = edges[ei0].cost + dual[u0] - dual[v0];
bool del_u_side = true;
int lca = get_lca(u0, v0, f, del_u_side, del_u);
if (f > 0) {
int u = u0, v = v0;
while (u != lca) parents[u].up += f, parents[u].down -= f, u = parents[u].p;
while (v != lca) parents[v].up -= f, parents[v].down += f, v = parents[v].p;
}
int u = u0, par = v0;
auto p_caps = make_pair(edges[ei0].cap - f, edges[ei0 ^ 1].cap + f);
COST p_diff = -clen;
if (!del_u_side) {
swap(u, par);
swap(p_caps.first, p_caps.second);
p_diff *= -1;
}
int par_e = ei0 ^ (del_u_side ? 0 : 1);
while (par != del_u) {
int d = depth[par], idx = u * 2;
while (idx != u * 2 + 1) {
if (idx % 2 == 0) d++, dual[idx / 2] += p_diff, depth[idx / 2] = d;
else d--;
idx = nex[idx];
}
connect(pre[u * 2], nex[u * 2 + 1]);
connect(u * 2 + 1, nex[par * 2]);
connect(par * 2, u * 2);
swap(parents[u].e, par_e);
par_e ^= 1;
swap(parents[u].up, p_caps.first);
swap(parents[u].down, p_caps.second);
swap(p_caps.first, p_caps.second);
int next_u = parents[u].p;
parents[u].p = par;
par = u;
u = next_u;
}
edges[par_e].cap = p_caps.first;
edges[par_e ^ 1].cap = p_caps.second;
}
bool minor() {
if (candidates.empty()) return false;
COST best = 0;
int best_ei = -1;
int i = 0;
while (i < int(candidates.size())) {
int ei = candidates[i];
if (edges[ei].cap <= 0) {
swap(candidates[i], candidates.back());
candidates.pop_back();
continue;
}
COST clen = edges[ei].cost + dual[edges[ei ^ 1].to] - dual[edges[ei].to];
if (clen >= 0) {
swap(candidates[i], candidates.back());
candidates.pop_back();
continue;
}
if (clen < best) best = clen, best_ei = ei;
i++;
}
if (best_ei == -1) return false;
push_flow(best_ei);
return true;
}
int get_lca(int u, int v, FLOW &flow, bool &del_u_side, int &del_u) {
auto up_u = [&]() {
if (parents[u].down < flow) flow = parents[u].down, del_u = u, del_u_side = true;
u = parents[u].p;
};
auto up_v = [&]() {
if (parents[v].up <= flow) flow = parents[v].up, del_u = v, del_u_side = false;
v = parents[v].p;
};
if (depth[u] >= depth[v]) {
int num = depth[u] - depth[v];
for (int i = 0; i < num; i++) up_u();
} else {
int num = depth[v] - depth[u];
for (int i = 0; i < num; i++) up_v();
}
while (u != v) up_u(), up_v();
return u;
}
};
// b-flow manager
template<class FLOW, class COST> struct MinCostBFlow {
// Edge
struct InnerEdge {
int from, to;
FLOW lower_cap, upper_cap, flow;
COST cost;
InnerEdge(int from_, int to_, FLOW lower_, FLOW upper_, COST cost_)
: from(from_), to(to_), lower_cap(lower_), upper_cap(upper_), flow(0), cost(cost_) {}
friend ostream& operator << (ostream& s, const InnerEdge& e) {
return s << e.from << "->" << e.to
<< " (" << e.flow << "/" << e.lower_cap << "~" << e.upper_cap << ", " << e.cost << ")";
}
};
// inner values
int N;
vector<InnerEdge> edges;
vector<FLOW> lower_dss, upper_dss, dss; // demand (< 0) and supply (> 0)
vector<COST> dual;
// constructor
explicit MinCostBFlow(int n = 0) : N(n), lower_dss(n, 0), upper_dss(n, 0), dss(n, 0) {}
// setter
void add_edge(int from, int to, FLOW cap, COST cost) {
assert(cap >= 0);
edges.push_back(InnerEdge(from, to, 0, cap, cost));
}
void add_edge(int from, int to, FLOW lower_cap, FLOW upper_cap, COST cost) {
assert(lower_cap <= upper_cap);
edges.push_back(InnerEdge(from, to, lower_cap, upper_cap, cost));
}
void set_ds(int v, FLOW ds) {
assert(0 <= v && v < N);
lower_dss[v] = ds, upper_dss[v] = ds;
}
void set_ds(int v, FLOW lower_ds, FLOW upper_ds) {
assert(0 <= v && v < N);
assert(lower_ds <= upper_ds);
lower_dss[v] = lower_ds, upper_dss[v] = upper_ds;
}
// getter
InnerEdge &get_edge(int i) {
return edges[i];
}
const InnerEdge &get_edge(int i) const {
return edges[i];
}
vector<InnerEdge> get_edges() const {
return edges;
}
COST get_dual(int v) const {
return dual[v];
}
vector<COST> get_duals() const {
return dual;
}
// solver
bool pre_compute() {
bool need_super_node = false;
for (int v = 0; v < N; v++) {
if (lower_dss[v] == upper_dss[v]) dss[v] = lower_dss[v];
else need_super_node = true;
}
// lower_ds, upper_ds -> strict ds
if (need_super_node) {
int super = N;
dss.assign(N + 1, 0);
for (int v = 0; v < N; v++) {
if (lower_dss[v] >= 0) {
add_edge(super, v, lower_dss[v], upper_dss[v], 0);
} else if (upper_dss[v] < 0) {
add_edge(v, super, -upper_dss[v], -lower_dss[v], 0);
} else {
add_edge(super, v, upper_dss[v], 0);
add_edge(v, super, -lower_dss[v], 0);
}
}
}
// push lower_cap
for (const auto &e : edges) {
dss[e.to] += e.lower_cap, dss[e.from] -= e.lower_cap;
}
return need_super_node;
}
pair<bool, COST> solve(const string solver = "network_simplex", bool calc_potential = false) {
bool need_super_node = pre_compute();
COST res = 0;
if (solver == "primal_dual") {
MinCostBFlowByPrimalDual<FLOW, COST> G(N + (int)need_super_node);
G.set_ds(dss);
for (const auto &e : edges) G.add_edge(e.from, e.to, e.upper_cap - e.lower_cap, e.cost);
auto [feasible, mincost] = G.solve(calc_potential);
if (!feasible) return {false, COST(0)};
for (int i = 0; i < (int)edges.size(); i++) {
auto &e = edges[i];
const auto &ge = G.get_edge(i);
e.flow = e.upper_cap - ge.cap;
res += e.flow * e.cost;
}
if (calc_potential) {
dual = G.get_duals();
if (need_super_node) dual.pop_back();
}
} else if (solver == "cost_scaling") {
MinCostBFlowByCostScaling<FLOW, COST> G(N + (int)need_super_node);
G.set_ds(dss);
for (const auto &e : edges) G.add_edge(e.from, e.to, e.upper_cap - e.lower_cap, e.cost);
auto [feasible, mincost] = G.solve(calc_potential);
if (!feasible) return {false, COST(0)};
for (int i = 0; i < (int)edges.size(); i++) {
auto &e = edges[i];
const auto &ge = G.get_edge(i);
e.flow = e.upper_cap - ge.cap;
res += e.flow * e.cost;
}
if (calc_potential) {
dual = G.get_duals();
if (need_super_node) dual.pop_back();
}
} else if (solver == "network_simplex") {
MinCostBFlowByNetworkSimplex<FLOW, COST> G(N + (int)need_super_node);
G.set_ds(dss);
for (const auto &e : edges) G.add_edge(e.from, e.to, e.upper_cap - e.lower_cap, e.cost);
auto [feasible, mincost] = G.solve();
if (!feasible) return {false, COST(0)};
for (int i = 0; i < (int)edges.size(); i++) {
auto &e = edges[i];
e.flow = e.lower_cap + G.get_flow(i);
res += e.flow * e.cost;
}
if (calc_potential) {
dual = G.get_duals();
if (need_super_node) dual.pop_back();
}
}
return {true, res};
}
};
// Push-Relabel
// we can skip 2nd phase if we should know only about maxflow and residual graph
template<class FLOW> FLOW PushRelabel
(FlowGraph<FLOW> &G, int s, int t, FLOW limit_flow, bool do_2nd_phase = false) {
assert(0 <= s && s < (int)G.size());
assert(0 <= t && t < (int)G.size());
assert(s != t);
const int GlobalRelabelRreq = 5;
const bool UseGapRelabeling = true;
struct PushQueue {
vector<pair<int, int>> even, odd;
int num_even, num_odd;
void init(int N) { even.resize(N), odd.resize(N), num_even = num_odd = 0; }
void clear() { num_even = num_odd = 0; }
int size() const { return num_even + num_odd; }
bool empty() const { return size() == 0; }
int highest() const {
int a = (num_even > 0 ? even[num_even - 1].second : -1);
int b = (num_odd > 0 ? odd[num_odd - 1].second : -1);
return (a > b ? a : b);
}
void push(int v, int h) {
if (h & 1) odd[num_odd++] = {v, h};
else even[num_even++] = {v, h};
}
int pop() {
if (num_even == 0 || (num_odd > 0 && odd[num_odd - 1].second > even[num_even - 1].second)) {
return odd[--num_odd].first;
} else {
return even[--num_even].first;
}
}
} push_que;
int gap, N = (int)G.size();
vector<int> dist, dcnt;
vector<FLOW> excess;
// heuristics
auto global_relabeling = [&](int t) -> void {
push_que.clear();
if (UseGapRelabeling) gap = 1, dcnt.assign(N + 1, 0);
dist.assign(N, N);
dist[t] = 0;
static vector<int> que;
if (que.empty()) que.resize(N);
que[0] = t;
int qb = 0, qe = 1;
while (qb < qe) {
int now = que[qb++];
if (UseGapRelabeling) gap = dist[now] + 1, dcnt[dist[now]]++;
if (excess[now] > 0) push_que.push(now, dist[now]);
for (const auto &e : G[now]) {
if (G.get_rev_edge(e).cap > 0 && dist[e.to] == N) {
dist[e.to] = dist[now] + 1;
while ((int)que.size() <= qe) que.emplace_back(0);
que[qe++] = e.to;
}
}
}
};
// push
auto push = [&](int v, FlowEdge<FLOW> &e) -> void {
auto &re = G.get_rev_edge(e);
FLOW delta = e.cap < excess[v] ? e.cap : excess[v];
excess[v] -= delta, e.cap -= delta, e.flow += delta;
excess[e.to] += delta, re.cap += delta, re.flow -= delta;
if (excess[e.to] > 0 && excess[e.to] <= delta) {
if (!UseGapRelabeling || dist[e.to] <= gap) push_que.push(e.to, dist[e.to]);
}
};
// run
auto run = [&](int t) -> void {
global_relabeling(t);
int tick = (int)G.pos.size() * GlobalRelabelRreq;
while (!push_que.empty()) {
int v = push_que.pop();
if (UseGapRelabeling && dist[v] > gap) continue;
int dnex = N * 2 - 1;
for (auto &e : G[v]) {
if (e.cap <= 0) continue;
if (dist[e.to] == dist[v] - 1) {
push(v, e);
if (excess[v] <= 0) break;
} else {
if (dist[e.to] + 1 < dnex) dnex = dist[e.to] + 1;
}
}
if (excess[v] > 0) {
if (UseGapRelabeling) {
if (dnex != dist[v] && dcnt[dist[v]] == 1 && dist[v] < gap) gap = dist[v];
if (dnex == gap) gap++;
while (push_que.highest() > gap) push_que.pop();
if (dnex > gap) dnex = N;
if (dist[v] != dnex) dcnt[dist[v]]--, dcnt[dnex]++;
}
dist[v] = dnex;
if (!UseGapRelabeling || dist[v] < gap) push_que.push(v, dist[v]);
}
if (GlobalRelabelRreq && --tick == 0) {
tick = (int)G.pos.size() * GlobalRelabelRreq;
global_relabeling(t);
}
}
};
// 1st phase: find preflow
excess.assign(N, 0), dist.assign(N, 0);
excess[s] += limit_flow, excess[t] -= limit_flow;
dist[s] = N;
if (UseGapRelabeling) gap = 1, dcnt.assign(N + 1, 0), dcnt[0] = N - 1;
push_que.init(N);
for (auto &e : G[s]) push(s, e);
run(t);
FLOW res = excess[t] + limit_flow;
// 2nd phase: convert preflow into flow
if (do_2nd_phase) {
excess[s] += excess[t], excess[t] = 0;
global_relabeling(s);
run(s);
assert(excess == vector<FLOW>(N, 0));
}
return res;
}
template<class FLOW> FLOW PushRelabel
(FlowGraph<FLOW> &G, int s, int t, bool do_2nd_phase = false) {
return PushRelabel(G, s, t, numeric_limits<FLOW>::max(), do_2nd_phase);
}
//------------------------------//
// Examples
//------------------------------//
int main() {
int N, M, K;
long long INF = 1LL << 40;
cin >> N >> M >> K;
vector<long long> A(N), B(M);
for (int i = 0; i < N; i++) cin >> A[i];
for (int i = 0; i < M; i++) cin >> B[i], B[i]--;
for (int D = 1; D <= M; D++) {
int s = (D * 2 + 1) * N, t = s + 1;
FlowGraph<long long> G(t + 1);
for (int i = 0; i < N; i++) {
G.add_edge(s, i, A[i]);
if (i != B[D-1]) G.add_edge(i + D * 2 * N, t, INF);
}
for (int d = 0; d < D; d++) {
for (int i = 0; i < N; i++) {
if (d == 0 || i != B[d-1]) G.add_edge(i + d * 2 * N, i + (d * 2 + 1) * N, K);
if (d == 0 || i != B[d-1]) G.add_edge(i + d * 2 * N, i + (d * 2 + 2) * N, INF);
for (int di = -1; di <= 1; di += 2) {
int i2 = (i + di + N) % N;
G.add_edge(i + (d * 2 + 1) * N, i2 + (d * 2 + 2) * N, INF);
}
}
}
long long maxflow = PushRelabel(G, s, t);
cout << maxflow << endl;
}
}