test/verify/aoj-2405.test.cpp

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2405

Depends on

• Tree Decomposition Width 2(木幅2の木分解) (graph/others/tree-decomposition-width-2.hpp)
• math/combinatorics/montgomery-mod-int.hpp
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2405

#include "../../template/template.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"

#include "../../graph/others/tree-decomposition-width-2.hpp"

constexpr int MOD = 1000003;
using Mint = modint< MOD >;

int main() {
  int N, M;
  while(cin >> N >> M, N) {
    TreeDecompositionWidth2 td(N);
    set< pair< int, int > > edges;
    for(int i = 0; i < N; i++) {
      td.add_edge(i, (i + 1) % N);
      edges.emplace(minmax(i, (i + 1) % N));
    }
    for(int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      --a, --b;
      td.add_edge(a, b);
      edges.emplace(minmax(a, b));
    }

    if(N % 2) {
      cout << 0 << endl;
      continue;
    }

    auto t = td.build();
    to_nice(t);
    vector< vector< Mint > > dps(t.size());
    vector< int > buff(N), buff2(N, -1);
    MFP([&](auto rec, int idx) -> void {

      auto &ch = t[idx].child;
      auto &bag = t[idx].bag;

      for(auto &to : ch) rec(to);
      vector< Mint > dp(1 << bag.size());

      if(ch.empty()) { // leaf
        dp[0] = 1;
      } else if(ch.size() == 2) { // join
        for(int i = 0; i < dp.size(); i++) {
          for(int j = 0; j < dp.size(); j++) {
            if((i & j) == 0) dp[i | j] += dps[ch[0]][i] * dps[ch[1]][j];
          }
        }
      } else {
        auto &ch_bag = t[ch[0]].bag;
        auto &ch_dp = dps[ch[0]];

        for(int i = 0; i < bag.size(); i++) {
          buff[bag[i]] = 1 << i;
          buff2[bag[i]] = idx;
        }

        if(ch_bag.size() + 1 == bag.size()) { // introduce
          for(int i = 0; i < ch_dp.size(); i++) {
            int bit = 0;
            for(int j = 0; j < ch_bag.size(); j++) {
              if((i >> j) & 1) bit |= buff[ch_bag[j]];
            }
            dp[bit] = ch_dp[i];
          }
        } else { // forget
          int v = -1;
          for(int i = 0; i < ch_bag.size(); i++) {
            if(buff2[ch_bag[i]] != idx) v = ch_bag[i];
          }
          vector< int > ok_match(bag.size());
          for(int i = 0; i < bag.size(); i++) {
            ok_match[i] = edges.count(minmax(bag[i], v));
          }

          for(int i = 0; i < ch_dp.size(); i++) {
            int bit = 0;
            bool v_use = false;
            for(int j = 0; j < ch_bag.size(); j++) {
              if((i >> j) & 1) {
                if(v != ch_bag[j]) bit |= buff[ch_bag[j]];
              } else {
                if(v == ch_bag[j]) v_use = true;
              }
            }
            if(v_use) {
              for(int j = 0; j < bag.size(); j++) {
                if((bit >> j) & 1) continue;
                if(ok_match[j]) dp[bit | (1 << j)] += ch_dp[i];
              }
            } else {
              dp[bit] += ch_dp[i];
            }
          }
        }
      }
      dps[idx].swap(dp);
    })(0);
    auto &dp = dps[0];
    cout << dp.back() << endl;
  }
}

#line 1 "test/verify/aoj-2405.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2405

#line 1 "template/template.hpp"
#include<bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};
 
template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}
#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template< uint32_t mod_, bool fast = false >
struct MontgomeryModInt {
private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

public:
  MontgomeryModInt(): x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const {
    return pow(mod() - 2);
  }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template< uint32_t mod >
using modint = MontgomeryModInt< mod >;
using modint998244353 = modint< 998244353 >;
using modint1000000007 = modint< 1000000007 >;
#line 5 "test/verify/aoj-2405.test.cpp"

#line 2 "graph/others/tree-decomposition-width-2.hpp"

/**
 * @brief Tree Decomposition Width 2(木幅2の木分解)
 * @see https://ei1333.hateblo.jp/entry/2020/02/12/150319
 * 
 */
struct DecompNode {
  vector< int > bag, child;

  DecompNode() = default;
};

struct TreeDecompositionWidth2 {

  vector< vector< int > > g;

  explicit TreeDecompositionWidth2(int V) : g(V) {}

  void add_edge(int a, int b) {
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }

  vector< DecompNode > build() {
    const int N = (int) g.size();

    vector< int > used(N, -1), deg(N);
    queue< int > que;
    for(int i = 0; i < N; i++) {
      deg[i] = (int) g[i].size();
      if(deg[i] <= 2) que.emplace(i);
    }

    vector< set< int > > exists(N);
    for(int i = 0; i < N; i++) {
      for(auto &j : g[i]) {
        if(i < j) exists[i].emplace(j);
      }
    }

    vector< DecompNode > ret;
    ret.emplace_back();
    while(!que.empty()) {
      int idx = que.front();
      que.pop();
      if(deg[idx] > 2 || used[idx] != -1) continue;

      DecompNode r;
      r.bag.emplace_back(idx);
      int u = -1, v = -1;
      for(auto &to : g[idx]) {
        if(used[to] == -1) {
          (u == -1 ? u : v) = to;
          r.bag.emplace_back(to);
        } else if(used[to] >= 0) {
          r.child.emplace_back(used[to]);
          used[to] = -2;
        }
      }

      if(u == -1) {

      } else if(v == -1) {
        --deg[u];
      } else {
        if(u > v) swap(u, v);
        if(!exists[u].count(v)) {
          g[u].emplace_back(v);
          g[v].emplace_back(u);
          exists[u].emplace(v);
        } else {
          --deg[u];
          --deg[v];
        }
      }

      for(auto &to : g[idx]) {
        if(deg[to] <= 2) que.emplace(to);
      }

      used[idx] = (int) ret.size();
      deg[idx] = 0;
      ret.emplace_back(r);
    }
    for(int i = 0; i < N; i++) {
      if(deg[i] > 0) return {};
    }
    ret.front() = ret.back();
    ret.pop_back();
    return ret;
  }
};


void to_nice(vector< DecompNode > &g, int root = 0) {

  for(auto &p : g) {
    sort(p.bag.begin(), p.bag.end());
  }

  stack< int > st;
  st.emplace(root);

  while(!st.empty()) {
    int idx = st.top();
    st.pop();

    // join
    while(g[idx].child.size() > 2) {
      DecompNode r;
      r.child.resize(2);
      r.child[0] = g[idx].child.back();
      g[idx].child.pop_back();
      r.child[1] = g[idx].child.back();
      g[idx].child.pop_back();
      r.bag = g[idx].bag;
      g[idx].child.emplace_back((int) g.size());
      g.emplace_back(r);
    }

    if(g[idx].child.size() == 2) {
      for(auto &ch : g[idx].child) {
        if(g[ch].bag != g[idx].bag) {
          DecompNode r;
          r.child = {ch};
          r.bag = g[idx].bag;
          ch = (int) g.size();
          g.emplace_back(r);
        }
      }
    }

    // introduce / forget
    if(g[idx].child.size() == 1) {
      int &ch = g[idx].child[0];

      vector< int > latte, malta;
      set_difference(g[idx].bag.begin(), g[idx].bag.end(),
                     g[ch].bag.begin(), g[ch].bag.end(),
                     back_inserter(latte));
      set_difference(g[ch].bag.begin(), g[ch].bag.end(),
                     g[idx].bag.begin(), g[idx].bag.end(),
                     back_inserter(malta));
      if(latte.size() + malta.size() > 1) {
        DecompNode r;
        r.child = {ch};
        r.bag = g[idx].bag;
        if(!latte.empty()) {
          r.bag.erase(find(r.bag.begin(), r.bag.end(), latte.back()));
        } else {
          r.bag.emplace_back(malta.back());
        }
        ch = (int) g.size();
        g.emplace_back(r);
      }
    }

    // leaf
    if(g[idx].child.empty()) {
      if(g[idx].bag.size() > 1) {
        DecompNode r;
        r.bag = g[idx].bag;
        r.bag.pop_back();
        g[idx].child.emplace_back((int) g.size());
        g.emplace_back(r);
      }
    }

    for(auto &ch : g[idx].child) {
      st.emplace(ch);
    }
  }
}
#line 7 "test/verify/aoj-2405.test.cpp"

constexpr int MOD = 1000003;
using Mint = modint< MOD >;

int main() {
  int N, M;
  while(cin >> N >> M, N) {
    TreeDecompositionWidth2 td(N);
    set< pair< int, int > > edges;
    for(int i = 0; i < N; i++) {
      td.add_edge(i, (i + 1) % N);
      edges.emplace(minmax(i, (i + 1) % N));
    }
    for(int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      --a, --b;
      td.add_edge(a, b);
      edges.emplace(minmax(a, b));
    }

    if(N % 2) {
      cout << 0 << endl;
      continue;
    }

    auto t = td.build();
    to_nice(t);
    vector< vector< Mint > > dps(t.size());
    vector< int > buff(N), buff2(N, -1);
    MFP([&](auto rec, int idx) -> void {

      auto &ch = t[idx].child;
      auto &bag = t[idx].bag;

      for(auto &to : ch) rec(to);
      vector< Mint > dp(1 << bag.size());

      if(ch.empty()) { // leaf
        dp[0] = 1;
      } else if(ch.size() == 2) { // join
        for(int i = 0; i < dp.size(); i++) {
          for(int j = 0; j < dp.size(); j++) {
            if((i & j) == 0) dp[i | j] += dps[ch[0]][i] * dps[ch[1]][j];
          }
        }
      } else {
        auto &ch_bag = t[ch[0]].bag;
        auto &ch_dp = dps[ch[0]];

        for(int i = 0; i < bag.size(); i++) {
          buff[bag[i]] = 1 << i;
          buff2[bag[i]] = idx;
        }

        if(ch_bag.size() + 1 == bag.size()) { // introduce
          for(int i = 0; i < ch_dp.size(); i++) {
            int bit = 0;
            for(int j = 0; j < ch_bag.size(); j++) {
              if((i >> j) & 1) bit |= buff[ch_bag[j]];
            }
            dp[bit] = ch_dp[i];
          }
        } else { // forget
          int v = -1;
          for(int i = 0; i < ch_bag.size(); i++) {
            if(buff2[ch_bag[i]] != idx) v = ch_bag[i];
          }
          vector< int > ok_match(bag.size());
          for(int i = 0; i < bag.size(); i++) {
            ok_match[i] = edges.count(minmax(bag[i], v));
          }

          for(int i = 0; i < ch_dp.size(); i++) {
            int bit = 0;
            bool v_use = false;
            for(int j = 0; j < ch_bag.size(); j++) {
              if((i >> j) & 1) {
                if(v != ch_bag[j]) bit |= buff[ch_bag[j]];
              } else {
                if(v == ch_bag[j]) v_use = true;
              }
            }
            if(v_use) {
              for(int j = 0; j < bag.size(); j++) {
                if((bit >> j) & 1) continue;
                if(ok_match[j]) dp[bit | (1 << j)] += ch_dp[i];
              }
            } else {
              dp[bit] += ch_dp[i];
            }
          }
        }
      }
      dps[idx].swap(dp);
    })(0);
    auto &dp = dps[0];
    cout << dp.back() << endl;
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	testcase_00	AC	627 ms	63 MB
g++	testcase_01	AC	633 ms	63 MB
g++	testcase_02	AC	621 ms	63 MB
g++	testcase_03	AC	634 ms	64 MB
clang++	testcase_00	AC	624 ms	66 MB
clang++	testcase_01	AC	612 ms	66 MB
clang++	testcase_02	AC	610 ms	64 MB
clang++	testcase_03	AC	617 ms	65 MB

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