C++ Library for Competitive Programming
/*
* @title グラフ/フロー/最大流/最小流量制約付き最大流
*
* verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1615
*/
#include <iostream>
#include <vector>
#include "emthrm/graph/flow/maximum_flow/dinic.hpp"
#include "emthrm/graph/flow/maximum_flow/maximum_flow_with_lower_bound_constraint.hpp"
int main() {
while (true) {
int n, m;
std::cin >> n >> m;
if (n == 0 && m == 0) [[unlikely]] break;
std::vector<int> u(m), v(m);
for (int i = 0; i < m; ++i) {
std::cin >> u[i] >> v[i];
--u[i]; --v[i];
}
const int s = m + n, t = m + n + 1;
const auto solve =
[m, n, s, t, &u, &v](const int lb, const int ub) -> bool {
emthrm::MaximumFlowWithLowerBoundConstraint<emthrm::Dinic, int>
lower_bound_constraint(m + n + 2);
for (int i = 0; i < m; ++i) {
lower_bound_constraint.add_edge(s, i, 1, 1);
}
for (int i = 0; i < n; ++i) {
lower_bound_constraint.add_edge(m + i, t, lb, ub);
}
for (int i = 0; i < m; ++i) {
lower_bound_constraint.add_edge(i, m + u[i], 0, 1);
lower_bound_constraint.add_edge(i, m + v[i], 0, 1);
}
return lower_bound_constraint.solve(s, t) != -1;
};
int lb = 0, ub = n;
for (int i = 0, j = 1; i < n; ++i) {
while (j <= n && !solve(i, j)) ++j;
if (j > n) break;
if (ub - lb >= j - i) {
lb = i;
ub = j;
}
if (i == j) ++j;
}
std::cout << lb << ' ' << ub << '\n';
}
return 0;
}
#line 1 "test/graph/flow/maximum_flow/maximum_flow_with_lower_bound_constraint.test.cpp"
/*
* @title グラフ/フロー/最大流/最小流量制約付き最大流
*
* verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1615
*/
#include <iostream>
#include <vector>
#line 1 "include/emthrm/graph/flow/maximum_flow/dinic.hpp"
#include <algorithm>
#include <limits>
#include <queue>
#include <utility>
#line 9 "include/emthrm/graph/flow/maximum_flow/dinic.hpp"
namespace emthrm {
template <typename T>
struct Dinic {
struct Edge {
int dst, rev;
T cap;
explicit Edge(const int dst, const T cap, const int rev)
: dst(dst), rev(rev), cap(cap) {}
};
std::vector<std::vector<Edge>> graph;
explicit Dinic(const int n) : graph(n), level(n), itr(n) {}
void add_edge(const int src, const int dst, const T cap) {
graph[src].emplace_back(dst, cap, graph[dst].size());
graph[dst].emplace_back(src, 0, graph[src].size() - 1);
}
T maximum_flow(const int s, const int t,
T limit = std::numeric_limits<T>::max()) {
T res = 0;
while (limit > 0) {
std::fill(level.begin(), level.end(), -1);
level[s] = 0;
std::queue<int> que;
que.emplace(s);
while (!que.empty()) {
const int ver = que.front();
que.pop();
for (const Edge& e : graph[ver]) {
if (level[e.dst] == -1 && e.cap > 0) {
level[e.dst] = level[ver] + 1;
que.emplace(e.dst);
}
}
}
if (level[t] == -1) break;
std::fill(itr.begin(), itr.end(), 0);
while (limit > 0) {
const T f = dfs(s, t, limit);
if (f == 0) break;
limit -= f;
res += f;
}
}
return res;
}
private:
std::vector<int> level, itr;
T dfs(const int ver, const int t, const T flow) {
if (ver == t) return flow;
for (; std::cmp_less(itr[ver], graph[ver].size()); ++itr[ver]) {
Edge& e = graph[ver][itr[ver]];
if (level[ver] < level[e.dst] && e.cap > 0) {
const T tmp = dfs(e.dst, t, std::min(flow, e.cap));
if (tmp > 0) {
e.cap -= tmp;
graph[e.dst][e.rev].cap += tmp;
return tmp;
}
}
}
return 0;
}
};
} // namespace emthrm
#line 1 "include/emthrm/graph/flow/maximum_flow/maximum_flow_with_lower_bound_constraint.hpp"
#line 1 "include/emthrm/graph/flow/maximum_flow/maximum_flow.hpp"
/**
* @title 最大流コンセプト
*/
#ifndef EMTHRM_GRAPH_FLOW_MAXIMUM_FLOW_MAXIMUM_FLOW_HPP_
#define EMTHRM_GRAPH_FLOW_MAXIMUM_FLOW_MAXIMUM_FLOW_HPP_
#include <concepts>
#line 10 "include/emthrm/graph/flow/maximum_flow/maximum_flow.hpp"
namespace emthrm {
template <template <typename> class C, typename T>
concept MaximumFlow = requires (C<T> mf) {
{mf.add_edge(std::declval<int>(), std::declval<int>(), std::declval<T>())}
-> std::same_as<void>;
{mf.maximum_flow(std::declval<int>(), std::declval<int>())}
-> std::same_as<T>;
};
} // namespace emthrm
#endif // EMTHRM_GRAPH_FLOW_MAXIMUM_FLOW_MAXIMUM_FLOW_HPP_
#line 5 "include/emthrm/graph/flow/maximum_flow/maximum_flow_with_lower_bound_constraint.hpp"
namespace emthrm {
template <template <typename> class C, typename T>
requires MaximumFlow<C, T>
struct MaximumFlowWithLowerBoundConstraint {
explicit MaximumFlowWithLowerBoundConstraint(const int n)
: n(n), sum_lb(0), mf(n + 2) {}
void add_edge(const int src, const int dst, const T lb, const T ub) {
mf.add_edge(src, dst, ub - lb);
mf.add_edge(n, dst, lb);
mf.add_edge(src, n + 1, lb);
sum_lb += lb;
}
T solve(const int s, const int t) {
const T a = mf.maximum_flow(n, n + 1);
const T b = mf.maximum_flow(s, n + 1);
const T c = mf.maximum_flow(n, t);
const T d = mf.maximum_flow(s, t);
return a + b == sum_lb && b == c ? b + d : -1;
}
private:
const int n;
T sum_lb;
C<T> mf;
};
} // namespace emthrm
#line 12 "test/graph/flow/maximum_flow/maximum_flow_with_lower_bound_constraint.test.cpp"
int main() {
while (true) {
int n, m;
std::cin >> n >> m;
if (n == 0 && m == 0) [[unlikely]] break;
std::vector<int> u(m), v(m);
for (int i = 0; i < m; ++i) {
std::cin >> u[i] >> v[i];
--u[i]; --v[i];
}
const int s = m + n, t = m + n + 1;
const auto solve =
[m, n, s, t, &u, &v](const int lb, const int ub) -> bool {
emthrm::MaximumFlowWithLowerBoundConstraint<emthrm::Dinic, int>
lower_bound_constraint(m + n + 2);
for (int i = 0; i < m; ++i) {
lower_bound_constraint.add_edge(s, i, 1, 1);
}
for (int i = 0; i < n; ++i) {
lower_bound_constraint.add_edge(m + i, t, lb, ub);
}
for (int i = 0; i < m; ++i) {
lower_bound_constraint.add_edge(i, m + u[i], 0, 1);
lower_bound_constraint.add_edge(i, m + v[i], 0, 1);
}
return lower_bound_constraint.solve(s, t) != -1;
};
int lb = 0, ub = n;
for (int i = 0, j = 1; i < n; ++i) {
while (j <= n && !solve(i, j)) ++j;
if (j > n) break;
if (ub - lb >= j - i) {
lb = i;
ub = j;
}
if (i == j) ++j;
}
std::cout << lb << ' ' << ub << '\n';
}
return 0;
}