#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2370"
#include <algorithm>
#include <iostream>
#include <map>
#include <vector>
#include "Mylib/Graph/BipartiteGraph/check_bipartite_graph.cpp"
#include "Mylib/Graph/Template/graph.cpp"
#include "Mylib/Typical/subset_sum_limited.cpp"
namespace hl = haar_lib;
int main() {
int V, E;
std::cin >> V >> E;
hl::graph<int> g(V);
g.read<1, false, false>(E);
auto res = hl::check_bipartite_graph(g);
if (std::all_of(res.begin(), res.end(), [](const auto &a) { return (bool) a; })) {
int k = 0;
std::map<int, int> c;
for (auto &x : res) {
int a = (*x).first.size();
int b = (*x).second.size();
k += std::min(a, b);
c[std::abs(a - b)] += 1;
}
std::vector<int> a, m;
for (auto &p : c) {
a.push_back(p.first);
m.push_back(p.second);
}
auto r = hl::subset_sum_limited(c.size(), V, a, m);
int64_t ans = 0;
for (int i = 0; i <= V; ++i) {
if (r[i]) {
int64_t a = k + i;
ans = std::max(ans, a * (V - a));
}
}
ans -= E;
std::cout << ans << "\n";
} else {
std::cout << -1 << "\n";
}
return 0;
}
#line 1 "test/aoj/2370/main.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2370"
#include <algorithm>
#include <iostream>
#include <map>
#include <vector>
#line 2 "Mylib/Graph/BipartiteGraph/check_bipartite_graph.cpp"
#include <optional>
#include <stack>
#include <utility>
#line 4 "Mylib/Graph/Template/graph.cpp"
namespace haar_lib {
template <typename T>
struct edge {
int from, to;
T cost;
int index = -1;
edge() {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
};
template <typename T>
struct graph {
using weight_type = T;
using edge_type = edge<T>;
std::vector<std::vector<edge<T>>> data;
auto& operator[](size_t i) { return data[i]; }
const auto& operator[](size_t i) const { return data[i]; }
auto begin() const { return data.begin(); }
auto end() const { return data.end(); }
graph() {}
graph(int N) : data(N) {}
bool empty() const { return data.empty(); }
int size() const { return data.size(); }
void add_edge(int i, int j, T w, int index = -1) {
data[i].emplace_back(i, j, w, index);
}
void add_undirected(int i, int j, T w, int index = -1) {
add_edge(i, j, w, index);
add_edge(j, i, w, index);
}
template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
void read(int M) {
for (int i = 0; i < M; ++i) {
int u, v;
std::cin >> u >> v;
u -= I;
v -= I;
T w = 1;
if (WEIGHTED) std::cin >> w;
if (DIRECTED)
add_edge(u, v, w, i);
else
add_undirected(u, v, w, i);
}
}
};
template <typename T>
using tree = graph<T>;
} // namespace haar_lib
#line 7 "Mylib/Graph/BipartiteGraph/check_bipartite_graph.cpp"
namespace haar_lib {
template <typename T>
auto check_bipartite_graph(const graph<T> &g) {
std::vector<std::optional<std::pair<std::vector<int>, std::vector<int>>>> ret;
const int N = g.size();
std::vector<int> check(N, -1);
std::vector<bool> visit(N);
for (int i = 0; i < N; ++i) {
if (visit[i]) continue;
std::vector<int> a, b;
bool res =
[&]() {
std::stack<int> st;
st.push(i);
check[i] = 0;
a.push_back(i);
while (not st.empty()) {
auto cur = st.top();
st.pop();
if (visit[cur]) continue;
visit[cur] = true;
for (auto &e : g[cur]) {
if (check[e.to] == check[cur]) return false;
if (check[e.to] == -1) {
if (check[cur] == 0) {
check[e.to] = 1;
b.push_back(e.to);
} else {
check[e.to] = 0;
a.push_back(e.to);
}
st.push(e.to);
}
}
}
return true;
}();
if (res) {
ret.emplace_back(std::make_pair(a, b));
} else {
ret.emplace_back();
}
}
return ret;
}
} // namespace haar_lib
#line 2 "Mylib/Typical/subset_sum_limited.cpp"
#include <cassert>
#line 4 "Mylib/Typical/subset_sum_limited.cpp"
namespace haar_lib {
auto subset_sum_limited(int N, int K, const std::vector<int> &a, const std::vector<int> &m) {
assert((int) a.size() == N and (int) m.size() == N);
std::vector<int> dp(K + 1, -1);
dp[0] = 0;
for (int i = 0; i < N; ++i) {
for (int j = 0; j <= K; ++j) {
if (dp[j] >= 0) {
dp[j] = m[i];
} else if (j < a[i] or dp[j - a[i]] <= 0) {
dp[j] = -1;
} else {
dp[j] = dp[j - a[i]] - 1;
}
}
}
for (int i = 0; i <= K; ++i) dp[i] = dp[i] >= 0;
return dp;
}
} // namespace haar_lib
#line 10 "test/aoj/2370/main.test.cpp"
namespace hl = haar_lib;
int main() {
int V, E;
std::cin >> V >> E;
hl::graph<int> g(V);
g.read<1, false, false>(E);
auto res = hl::check_bipartite_graph(g);
if (std::all_of(res.begin(), res.end(), [](const auto &a) { return (bool) a; })) {
int k = 0;
std::map<int, int> c;
for (auto &x : res) {
int a = (*x).first.size();
int b = (*x).second.size();
k += std::min(a, b);
c[std::abs(a - b)] += 1;
}
std::vector<int> a, m;
for (auto &p : c) {
a.push_back(p.first);
m.push_back(p.second);
}
auto r = hl::subset_sum_limited(c.size(), V, a, m);
int64_t ans = 0;
for (int i = 0; i <= V; ++i) {
if (r[i]) {
int64_t a = k + i;
ans = std::max(ans, a * (V - a));
}
}
ans -= E;
std::cout << ans << "\n";
} else {
std::cout << -1 << "\n";
}
return 0;
}
test/aoj/2370/main.test.cpp
Basic graph
(Mylib/Graph/Template/graph.cpp)