test/atcoder/agc011_c.UFPU.test.cpp

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• Last update: 2025-08-08 18:52:16+09:00
• Problem: https://atcoder.jp/contests/agc011/tasks/agc011_c

Depends on

• Union-Find (ポテンシャル, undo可能) (src/DataStructure/UnionFind_Potentialized_Undoable.hpp)

Code

// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/agc011/tasks/agc011_c
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
// ポテンシャルUF (2部グラフ判定+連結成分)
#include <iostream>
#include "src/DataStructure/UnionFind_Potentialized_Undoable.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 UnionFind_Potentialized_Undoable<bool> uf(N);
 vector<int> b(N, 1);
 for (int i= 0; i < M; ++i) {
  int u, v;
  cin >> u >> v, --u, --v;
  int x= uf.leader(u), y= uf.leader(v);
  b[x]= b[y]= b[x] & b[y];
  if (!uf.unite(u, v, 1)) b[x]= b[y]= 0;
 }
 long long one= 0, bin= 0, oth= 0;
 vector<int> used(N, 0);
 for (int i= 0; i < N; ++i) {
  int v= uf.leader(i);
  if (used[v]) continue;
  used[v]= 1;
  if (uf.size(v) == 1) ++one;
  else if (b[v]) ++bin;
  else ++oth;
 }
 cout << one * N * 2 - one * one + bin * bin * 2 + bin * oth * 2 + oth * oth << '\n';
 return 0;
}

#line 1 "test/atcoder/agc011_c.UFPU.test.cpp"
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/agc011/tasks/agc011_c
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
// ポテンシャルUF (2部グラフ判定+連結成分)
#include <iostream>
#line 2 "src/DataStructure/UnionFind_Potentialized_Undoable.hpp"
#include <vector>
#include <algorithm>
#include <cassert>
template <class weight_t> class UnionFind_Potentialized_Undoable {
 std::vector<int> par;
 std::vector<weight_t> val;
 std::vector<std::tuple<int, int, weight_t, int>> his;
 int cur;
public:
 UnionFind_Potentialized_Undoable(int n): par(n, -1), val(n), his{{-1, -1, weight_t(), 1}}, cur(0) { his.reserve(n + 1); }
 int leader(int u) const { return par[u] < 0 ? u : leader(par[u]); }
 //  -p(v) + p(u) = w
 bool unite(int u, int v, weight_t w) {
  if constexpr (std::is_same_v<weight_t, bool>) w^= potential(v) ^ potential(u);
  else w= potential(v) + w - potential(u);
  if (++cur; (u= leader(u)) == (v= leader(v))) return ++std::get<3>(his.back()), w == weight_t();
  if (par[v] > par[u]) std::swap(u, v), w= -w;
  return his.emplace_back(u, par[u], val[u], 1), par[v]+= par[u], par[u]= v, val[u]= w, true;
 }
 bool connected(int u, int v) { return leader(u) == leader(v); }
 int size(int u) { return -par[leader(u)]; }
 weight_t potential(int u) {
  if (par[u] < 0) return val[u];
  if constexpr (std::is_same_v<weight_t, bool>) return potential(par[u]) ^ val[u];
  else return potential(par[u]) + val[u];
 }
 //  -p(v) + p(u)
 weight_t diff(int u, int v) {
  if constexpr (std::is_same_v<weight_t, bool>) return potential(u) ^ potential(v);
  else return -potential(v) + potential(u);
 }
 int time() const { return cur; }
 void undo() {
  if (assert(cur > 0), --cur; --std::get<3>(his.back()) == 0) {
   auto [u, p, v, _]= his.back();
   par[par[u]]-= p, par[u]= p, val[u]= v, his.pop_back();
  }
 }
 void rollback(int t) {
  assert(0 <= t), assert(t <= cur);
  if (t == cur) return;
  for (;;) {
   auto &[u, p, v, i]= his.back();
   if (cur-= i; cur < t) {
    i= t - cur, cur= t;
    break;
   }
   par[par[u]]-= p, par[u]= p, val[u]= v, his.pop_back();
  }
 }
};
#line 8 "test/atcoder/agc011_c.UFPU.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 UnionFind_Potentialized_Undoable<bool> uf(N);
 vector<int> b(N, 1);
 for (int i= 0; i < M; ++i) {
  int u, v;
  cin >> u >> v, --u, --v;
  int x= uf.leader(u), y= uf.leader(v);
  b[x]= b[y]= b[x] & b[y];
  if (!uf.unite(u, v, 1)) b[x]= b[y]= 0;
 }
 long long one= 0, bin= 0, oth= 0;
 vector<int> used(N, 0);
 for (int i= 0; i < N; ++i) {
  int v= uf.leader(i);
  if (used[v]) continue;
  used[v]= 1;
  if (uf.size(v) == 1) ++one;
  else if (b[v]) ++bin;
  else ++oth;
 }
 cout << one * N * 2 - one * one + bin * bin * 2 + bin * oth * 2 + oth * oth << '\n';
 return 0;
}

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