二部グラフのフロー
(flow/flow-on-bipartite-graph.hpp)
二部グラフのフロー
使い方
BipartiteGraph(int N, int M)add_edge(int n, int m, long long cap = 1)flow()MaximumMatching()MinimumVertexCover()MaximumIndependentSet()
Verified with
Code
#pragma once
#include "../atcoder/maxflow.hpp"
namespace BipartiteGraphImpl {
using namespace atcoder;
struct BipartiteGraph : mf_graph<long long> {
int L, R, s, t;
bool is_flow;
explicit BipartiteGraph(int N, int M)
: mf_graph<long long>(N + M + 2),
L(N),
R(M),
s(N + M),
t(N + M + 1),
is_flow(false) {
for (int i = 0; i < L; i++) mf_graph<long long>::add_edge(s, i, 1);
for (int i = 0; i < R; i++) mf_graph<long long>::add_edge(i + L, t, 1);
}
int add_edge(int n, int m, long long cap = 1) override {
assert(0 <= n && n < L);
assert(0 <= m && m < R);
return mf_graph<long long>::add_edge(n, m + L, cap);
}
long long flow() {
is_flow = true;
return mf_graph<long long>::flow(s, t);
}
vector<pair<int, int>> MaximumMatching() {
if (!is_flow) flow();
auto es = mf_graph<long long>::edges();
vector<pair<int, int>> ret;
for (auto &e : es) {
if (e.flow > 0 && e.from != s && e.to != t) {
ret.emplace_back(e.from, e.to - L);
}
}
return ret;
}
// call after calclating flow !
pair<vector<int>, vector<int>> MinimumVertexCover() {
if (!is_flow) flow();
auto colored = PreCalc();
vector<int> nl, nr;
for (int i = 0; i < L; i++)
if (!colored[i]) nl.push_back(i);
for (int i = 0; i < R; i++)
if (colored[i + L]) nr.push_back(i);
return make_pair(nl, nr);
}
// call after calclating flow !
pair<vector<int>, vector<int>> MaximumIndependentSet() {
if (!is_flow) flow();
auto colored = PreCalc();
vector<int> nl, nr;
for (int i = 0; i < L; i++)
if (colored[i]) nl.push_back(i);
for (int i = 0; i < R; i++)
if (!colored[i + L]) nr.push_back(i);
return make_pair(nl, nr);
}
vector<pair<int, int>> MinimumEdgeCover() {
if (!is_flow) flow();
auto es = MaximumMatching();
vector<bool> useL(L), useR(R);
for (auto &p : es) {
useL[p.first] = true;
useR[p.second] = true;
}
for (auto &e : mf_graph<long long>::edges()) {
if (e.flow > 0 || e.from == s || e.to == t) continue;
if (useL[e.from] == false || useR[e.to - L] == false) {
es.emplace_back(e.from, e.to - L);
useL[e.from] = useR[e.to - L] = true;
}
}
return es;
}
private:
vector<bool> PreCalc() {
vector<vector<int>> ag(L + R);
vector<bool> used(L, false);
for (auto &e : mf_graph<long long>::edges()) {
if (e.from == s || e.to == t) continue;
if (e.flow > 0) {
ag[e.to].push_back(e.from);
used[e.from] = true;
} else {
ag[e.from].push_back(e.to);
}
}
vector<bool> colored(L + R, false);
auto dfs = [&](auto rc, int cur) -> void {
for (auto &d : ag[cur]) {
if (!colored[d]) colored[d] = true, rc(rc, d);
}
};
for (int i = 0; i < L; i++)
if (!used[i]) colored[i] = true, dfs(dfs, i);
return colored;
}
};
} // namespace BipartiteGraphImpl
using BipartiteGraphImpl::BipartiteGraph;
/**
* @brief 二部グラフのフロー
* @docs docs/flow/flow-on-bipartite-graph.md
*/
#line 2 "flow/flow-on-bipartite-graph.hpp"
#line 1 "atcoder/maxflow.hpp"
#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
#line 1 "atcoder/internal_queue.hpp"
#line 5 "atcoder/internal_queue.hpp"
namespace atcoder {
namespace internal {
template <class T> struct simple_queue {
std::vector<T> 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 T& t) { payload.push_back(t); }
T& front() { return payload[pos]; }
void clear() {
payload.clear();
pos = 0;
}
void pop() { pos++; }
};
} // namespace internal
} // namespace atcoder
#line 11 "atcoder/maxflow.hpp"
namespace atcoder {
template <class Cap> struct mf_graph {
public:
mf_graph() : _n(0) {}
mf_graph(int n) : _n(n), g(n) {}
virtual 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;
}
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);
std::vector<int> level(_n), iter(_n);
internal::simple_queue<int> que;
auto bfs = [&]() {
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);
}
}
};
auto dfs = [&](auto self, int v, 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 =
self(self, e.to, 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 = 0;
while (flow < flow_limit) {
bfs();
if (level[t] == -1) break;
std::fill(iter.begin(), iter.end(), 0);
Cap f = dfs(dfs, t, flow_limit - flow);
if (!f) break;
flow += f;
}
return flow;
}
std::vector<bool> min_cut(int s) {
std::vector<bool> visited(_n);
internal::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;
}
private:
int _n;
struct _edge {
int to, rev;
Cap cap;
};
std::vector<std::pair<int, int>> pos;
std::vector<std::vector<_edge>> g;
};
} // namespace atcoder
#line 4 "flow/flow-on-bipartite-graph.hpp"
namespace BipartiteGraphImpl {
using namespace atcoder;
struct BipartiteGraph : mf_graph<long long> {
int L, R, s, t;
bool is_flow;
explicit BipartiteGraph(int N, int M)
: mf_graph<long long>(N + M + 2),
L(N),
R(M),
s(N + M),
t(N + M + 1),
is_flow(false) {
for (int i = 0; i < L; i++) mf_graph<long long>::add_edge(s, i, 1);
for (int i = 0; i < R; i++) mf_graph<long long>::add_edge(i + L, t, 1);
}
int add_edge(int n, int m, long long cap = 1) override {
assert(0 <= n && n < L);
assert(0 <= m && m < R);
return mf_graph<long long>::add_edge(n, m + L, cap);
}
long long flow() {
is_flow = true;
return mf_graph<long long>::flow(s, t);
}
vector<pair<int, int>> MaximumMatching() {
if (!is_flow) flow();
auto es = mf_graph<long long>::edges();
vector<pair<int, int>> ret;
for (auto &e : es) {
if (e.flow > 0 && e.from != s && e.to != t) {
ret.emplace_back(e.from, e.to - L);
}
}
return ret;
}
// call after calclating flow !
pair<vector<int>, vector<int>> MinimumVertexCover() {
if (!is_flow) flow();
auto colored = PreCalc();
vector<int> nl, nr;
for (int i = 0; i < L; i++)
if (!colored[i]) nl.push_back(i);
for (int i = 0; i < R; i++)
if (colored[i + L]) nr.push_back(i);
return make_pair(nl, nr);
}
// call after calclating flow !
pair<vector<int>, vector<int>> MaximumIndependentSet() {
if (!is_flow) flow();
auto colored = PreCalc();
vector<int> nl, nr;
for (int i = 0; i < L; i++)
if (colored[i]) nl.push_back(i);
for (int i = 0; i < R; i++)
if (!colored[i + L]) nr.push_back(i);
return make_pair(nl, nr);
}
vector<pair<int, int>> MinimumEdgeCover() {
if (!is_flow) flow();
auto es = MaximumMatching();
vector<bool> useL(L), useR(R);
for (auto &p : es) {
useL[p.first] = true;
useR[p.second] = true;
}
for (auto &e : mf_graph<long long>::edges()) {
if (e.flow > 0 || e.from == s || e.to == t) continue;
if (useL[e.from] == false || useR[e.to - L] == false) {
es.emplace_back(e.from, e.to - L);
useL[e.from] = useR[e.to - L] = true;
}
}
return es;
}
private:
vector<bool> PreCalc() {
vector<vector<int>> ag(L + R);
vector<bool> used(L, false);
for (auto &e : mf_graph<long long>::edges()) {
if (e.from == s || e.to == t) continue;
if (e.flow > 0) {
ag[e.to].push_back(e.from);
used[e.from] = true;
} else {
ag[e.from].push_back(e.to);
}
}
vector<bool> colored(L + R, false);
auto dfs = [&](auto rc, int cur) -> void {
for (auto &d : ag[cur]) {
if (!colored[d]) colored[d] = true, rc(rc, d);
}
};
for (int i = 0; i < L; i++)
if (!used[i]) colored[i] = true, dfs(dfs, i);
return colored;
}
};
} // namespace BipartiteGraphImpl
using BipartiteGraphImpl::BipartiteGraph;
/**
* @brief 二部グラフのフロー
* @docs docs/flow/flow-on-bipartite-graph.md
*/
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