library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub maspypy/library

:heavy_check_mark: test/mytest/matching_line_graph.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "random/random_graph.hpp"
#include "graph/maximum_matching_size.hpp"
#include "graph/maximum_matching_of_line_graph.hpp"

void test() {
  FOR(100) {
    FOR(n, 10) {
      Graph<int, 0> G(n);
      for (auto& [a, b]: random_graph<false>(n, true)) G.add(a, b);
      G.build();
      int m = G.M;
      Graph<int, 0> LG(m);
      FOR(i, m) FOR(j, i) if (i != j) {
        auto ei = G.edges[i];
        auto ej = G.edges[j];
        bool ok = 0;
        if (ei.frm == ej.frm) ok = 1;
        if (ei.frm == ej.to) ok = 1;
        if (ei.to == ej.frm) ok = 1;
        if (ei.to == ej.to) ok = 1;
        if (ok) LG.add(i, j);
      }
      LG.build();
      vc<pair<int, int>> res = maximum_matching_of_line_graph(G);
      assert(len(res) == maximum_matching_size(LG));
      vc<int> done(m);
      for (auto&& [a, b]: res) {
        assert(!done[a]);
        assert(!done[b]);
        done[a] = done[b] = 1;
        auto ei = G.edges[a];
        auto ej = G.edges[b];
        bool ok = 0;
        if (ei.frm == ej.frm) ok = 1;
        if (ei.frm == ej.to) ok = 1;
        if (ei.to == ej.frm) ok = 1;
        if (ei.to == ej.to) ok = 1;
        assert(ok);
      }
    }
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();
  return 0;
}
#line 1 "test/mytest/matching_line_graph.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 2 "graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (len(used_e) <= e.id) used_e.resize(e.id + 1);
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 2 "random/base.hpp"

u64 RNG_64() {
  static uint64_t x_
      = uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                     chrono::high_resolution_clock::now().time_since_epoch())
                     .count())
        * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "random/shuffle.hpp"

template <typename T>
void shuffle(vc<T>& A) {
  FOR(i, len(A)) swap(A[i], A[RNG(0, i + 1)]);
}
#line 2 "ds/unionfind/unionfind.hpp"

struct UnionFind {
  int n, n_comp;
  vc<int> dat; // par or (-size)
  UnionFind(int n = 0) { build(n); }

  void build(int m) {
    n = m, n_comp = m;
    dat.assign(n, -1);
  }

  void reset() { build(n); }

  int operator[](int x) {
    while (dat[x] >= 0) {
      int pp = dat[dat[x]];
      if (pp < 0) { return dat[x]; }
      x = dat[x] = pp;
    }
    return x;
  }

  ll size(int x) {
    x = (*this)[x];
    return -dat[x];
  }

  bool merge(int x, int y) {
    x = (*this)[x], y = (*this)[y];
    if (x == y) return false;
    if (-dat[x] < -dat[y]) swap(x, y);
    dat[x] += dat[y], dat[y] = x, n_comp--;
    return true;
  }

  vc<int> get_all() {
    vc<int> A(n);
    FOR(i, n) A[i] = (*this)[i];
    return A;
  }
};
#line 5 "random/random_graph.hpp"

void random_relabel(int N, vc<pair<int, int>>& G) {
  shuffle(G);
  vc<int> A(N);
  FOR(i, N) A[i] = i;
  shuffle(A);
  for (auto& [a, b]: G) a = A[a], b = A[b];
}

template <int DIRECTED>
vc<pair<int, int>> random_graph(int n, bool simple) {
  vc<pair<int, int>> G, cand;
  FOR(a, n) FOR(b, n) {
    if (simple && a == b) continue;
    if (!DIRECTED && a > b) continue;
    cand.eb(a, b);
  }
  int m = RNG(0, len(cand) + 1);
  set<int> ss;
  FOR(m) {
    while (1) {
      int i = RNG(0, len(cand));
      if (simple && ss.count(i)) continue;
      ss.insert(i);
      auto [a, b] = cand[i];
      G.eb(a, b);
      break;
    }
  }
  random_relabel(n, G);
  return G;
}

vc<pair<int, int>> random_tree(int n) {
  vc<pair<int, int>> G;
  FOR(i, 1, n) { G.eb(RNG(0, i), i); }
  random_relabel(n, G);
  return G;
}

// EDGE = true: 各辺が唯一のサイクル（関節点でサイクルまたは辺）
// EDGE = false： 各頂点が唯一のサイクル（橋でサイクルまたは辺）
vc<pair<int, int>> random_cactus(int N, bool EDGE) {
  if (!EDGE) {
    // n 頂点を 1 または 3 以上に分割
    vvc<int> A;
    int n = RNG(1, N + 1);
    vc<int> S(n, 1);
    int rest = N - n;
    while (rest > 0) {
      int k = RNG(0, n);
      if (S[k] == 1) {
        if (rest == 1) {
          S.eb(1), rest = 0;
        } else {
          S[k] += 2, rest -= 2;
        }
      } else {
        S[k]++, rest--;
      }
    }
    n = len(S);
    int p = 0;
    FOR(i, n) {
      vc<int> C;
      FOR(v, p, p + S[i]) C.eb(v);
      A.eb(C);
      p += S[i];
    }
    int m = len(A);
    auto H = random_tree(m);
    vc<pair<int, int>> G;
    FOR(i, m) {
      vc<int>& V = A[i];
      if (len(V) == 1) continue;
      FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
    }
    for (auto& [c1, c2]: H) {
      int a = A[c1][RNG(0, len(A[c1]))];
      int b = A[c2][RNG(0, len(A[c2]))];
      G.eb(a, b);
    }
    random_relabel(N, G);
    return G;
  }
  assert(EDGE);
  if (N == 1) return {};
  int n = RNG(1, N);
  vc<int> S(n, 2);
  int rest = N - 1 - n;
  while (rest > 0) {
    int k = RNG(0, n);
    S[k]++, --rest;
  }
  vvc<int> A;
  int p = 0;
  FOR(i, n) {
    vc<int> C;
    FOR(v, p, p + S[i]) C.eb(v);
    A.eb(C);
    p += S[i];
  }
  assert(p == N + n - 1);
  UnionFind uf(p);
  auto H = random_tree(n);
  for (auto& [c1, c2]: H) {
    int a = A[c1][RNG(0, len(A[c1]))];
    int b = A[c2][RNG(0, len(A[c2]))];
    uf.merge(a, b);
  }
  vc<int> new_idx(p);
  int x = 0;
  FOR(i, p) if (uf[i] == i) new_idx[i] = x++;
  assert(x == N);
  FOR(i, p) new_idx[i] = new_idx[uf[i]];
  vc<pair<int, int>> G;
  FOR(i, n) {
    vc<int>& V = A[i];
    for (auto& v: V) v = new_idx[v];
    if (len(V) == 2) {
      G.eb(V[0], V[1]);
    } else {
      FOR(k, len(V)) { G.eb(V[k], V[(1 + k) % len(V)]); }
    }
  }
  random_relabel(N, G);
  return G;
}
#line 2 "mod/modint61.hpp"

struct modint61 {
  static constexpr u64 mod = (1ULL << 61) - 1;
  u64 val;
  constexpr modint61() : val(0ULL) {}
  constexpr modint61(u32 x) : val(x) {}
  constexpr modint61(u64 x) : val(x % mod) {}
  constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {}
  constexpr modint61(ll x)
      : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod))
                                              : x) {}
  static constexpr u64 get_mod() { return mod; }
  modint61 &operator+=(const modint61 &a) {
    val = ((val += a.val) >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 &operator-=(const modint61 &a) {
    val = ((val -= a.val) >= mod) ? (val + mod) : val;
    return *this;
  }
  modint61 &operator*=(const modint61 &a) {
    const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val;
    val = (y >> 61) + (y & mod);
    val = (val >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 operator-() const { return modint61(val ? mod - val : u64(0)); }
  modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); }
  modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
  modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
  modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
  modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
  bool operator==(const modint61 &p) const { return val == p.val; }
  bool operator!=(const modint61 &p) const { return val != p.val; }
  modint61 inverse() const {
    ll a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint61(u);
  }
  modint61 pow(ll n) const {
    assert(n >= 0);
    modint61 ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul, n >>= 1;
    }
    return ret;
  }
};

#ifdef FASTIO
void rd(modint61 &x) {
  fastio::rd(x.val);
  assert(0 <= x.val && x.val < modint61::mod);
}

void wt(modint61 x) { fastio::wt(x.val); }
#endif
#line 1 "linalg/matrix_rank.hpp"
template <typename T>
int matrix_rank(vc<vc<T>> a, int n = -1, int m = -1) {
  if (n == 0) return 0;
  if (n == -1) { n = len(a), m = len(a[0]); }
  assert(n == len(a) && m == len(a[0]));
  int rk = 0;
  FOR(j, m) {
    if (rk == n) break;
    if (a[rk][j] == 0) {
      FOR(i, rk + 1, n) if (a[i][j] != T(0)) {
        swap(a[rk], a[i]);
        break;
      }
    }
    if (a[rk][j] == 0) continue;
    T c = T(1) / a[rk][j];
    FOR(k, j, m) a[rk][k] *= c;
    FOR(i, rk + 1, n) {
      T c = a[i][j];
      FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
    }
    ++rk;
  }
  return rk;
}
#line 4 "graph/maximum_matching_size.hpp"

template <typename GT>
int maximum_matching_size(GT& G) {
  static_assert(!GT::is_directed);
  using mint = modint61;
  int N = G.N;
  vv(mint, tutte, N, N);
  for (auto&& e: G.edges) {
    mint x = RNG(mint::get_mod());
    int i = e.frm, j = e.to;
    tutte[i][j] += x;
    tutte[j][i] -= x;
  }
  return matrix_rank(tutte, N, N) / 2;
}
#line 2 "graph/maximum_matching_of_line_graph.hpp"

// 同じ頂点に接続する 2 辺をマッチできる
template <typename GT>
vc<pair<int, int>> maximum_matching_of_line_graph(GT& G) {
  assert(!GT::is_directed);
  assert(G.is_prepared());
  const int N = G.N, M = G.M;
  vc<pair<int, int>> ANS;
  vc<int> V;
  vc<int> par(N, -1); // eid
  {
    vc<int> done(N);
    FOR(v, N) {
      if (done[v]) continue;
      int cnt = 0;
      auto dfs = [&](auto& dfs, int v, int p) -> void {
        V.eb(v);
        par[v] = p;
        done[v] = 1;
        for (auto&& e: G[v]) {
          ++cnt;
          if (done[e.to]) continue;
          dfs(dfs, e.to, v);
        }
      };
      dfs(dfs, v, -1);
    }
  }
  vc<int> ord(N);
  FOR(i, N) ord[V[i]] = i;
  vc<int> done(M);
  FOR_R(i, N) {
    int v = V[i];
    vc<int> down;
    int up = -1;
    for (auto&& e: G[v]) {
      if (done[e.id]) continue;
      if (up == -1 && e.to == par[v]) up = e.id;
      if (ord[e.to] > ord[v]) down.eb(e.id);
    }
    while (len(down) >= 2) {
      auto i = POP(down);
      auto j = POP(down);
      ANS.eb(i, j);
      done[i] = done[j] = 1;
    }
    if (len(down) == 0) continue;
    if (up != -1) {
      int x = up;
      int y = down[0];
      done[x] = done[y] = 1;
      ANS.eb(x, y);
    }
  }
  return ANS;
}
#line 6 "test/mytest/matching_line_graph.test.cpp"

void test() {
  FOR(100) {
    FOR(n, 10) {
      Graph<int, 0> G(n);
      for (auto& [a, b]: random_graph<false>(n, true)) G.add(a, b);
      G.build();
      int m = G.M;
      Graph<int, 0> LG(m);
      FOR(i, m) FOR(j, i) if (i != j) {
        auto ei = G.edges[i];
        auto ej = G.edges[j];
        bool ok = 0;
        if (ei.frm == ej.frm) ok = 1;
        if (ei.frm == ej.to) ok = 1;
        if (ei.to == ej.frm) ok = 1;
        if (ei.to == ej.to) ok = 1;
        if (ok) LG.add(i, j);
      }
      LG.build();
      vc<pair<int, int>> res = maximum_matching_of_line_graph(G);
      assert(len(res) == maximum_matching_size(LG));
      vc<int> done(m);
      for (auto&& [a, b]: res) {
        assert(!done[a]);
        assert(!done[b]);
        done[a] = done[b] = 1;
        auto ei = G.edges[a];
        auto ej = G.edges[b];
        bool ok = 0;
        if (ei.frm == ej.frm) ok = 1;
        if (ei.frm == ej.to) ok = 1;
        if (ei.to == ej.frm) ok = 1;
        if (ei.to == ej.to) ok = 1;
        assert(ok);
      }
    }
  }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();
  return 0;
}
Back to top page