結果
| 問題 | No.3668 Minimum Cut |
| コンテスト | |
| ユーザー |
👑  みうね
|
| 提出日時 | 2026-08-21 15:07:13 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0) |
| 結果 |
AC
|
| 実行時間 | 69 ms / 2,000 ms |
| + 769µs | |
| コード長 | 14,942 bytes |
| 記録 | |
| コンパイル時間 | 3,063 ms |
| コンパイル使用メモリ | 371,744 KB |
| 実行使用メモリ | 6,272 KB |
| 最終ジャッジ日時 | 2026-09-04 22:29:34 |
| 合計ジャッジ時間 | 6,651 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
ソースコード
// https://github.com/drken1215/algorithm/blob/master/NetworkFlow/max_flow_push_relabel.cpp
//
// max-flow (by Push-Relabel), in O(V^2√E)
//
// reference;
// hitonanode: Maxflow (push-relabel, Goldberg & Tarjan) （Push-relabel による最大流）
// https://hitonanode.github.io/cplib-cpp/flow/maxflow_pushrelabel.hpp
//
// verified:
// 典型アルゴリズム問題集 上級〜エキスパート編 E - 最大流
// https://atcoder.jp/contests/pastbook2022/tasks/pastbook2022_e
// https://atcoder.jp/contests/tessoku-book/tasks/tessoku_book_bp
//
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#include <cassert>
// 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 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);
};
// 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;
}
// 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;
}
};
// 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
//------------------------------//
// 典型アルゴリズム問題集 上級〜エキスパート編 E - 最大流
void PAST_Max_Flow() {
int V, E, s, t;
cin >> V >> E >> s >> t;
--s, --t;
// int s = 0, t = V - 1;
FlowGraph<long long> G(V);
for (int i = 0; i < E; ++i) {
long long u, v, c;
cin >> u >> v >> c, u--, v--;
G.add_edge(u, v, c);
}
long long res = PushRelabel(G, s, t, false);
cout << res << endl;
}
int main() {
PAST_Max_Flow();
}