test/verify/aoj-2405.test.cpp

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• Last update: 2026-08-10 15:36:17+00:00
• 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)
• Montgomery Mod Int (math/combinatorics/montgomery-mod-int.hpp)

Code

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

#include <algorithm>
#include <functional>
#include <iostream>
#include <set>
#include <utility>
#include <vector>

#include "../../graph/others/tree-decomposition-width-2.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"

using namespace std;

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);
    function<void(int)> rec = [&](int idx) {
      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);
    };
    rec(0);
    auto& dp = dps[0];
    cout << dp.back() << endl;
  }
}

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

#include <algorithm>
#include <functional>
#include <iostream>
#include <set>
#include <utility>
#include <vector>

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

#line 4 "graph/others/tree-decomposition-width-2.hpp"
#include <iterator>
#include <queue>
#line 7 "graph/others/tree-decomposition-width-2.hpp"
#include <stack>
#line 10 "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 {
  std::vector<int> bag, child;

  DecompNode() = default;
};

struct TreeDecompositionWidth2 {
  std::vector<std::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);
  }

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

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

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

    std::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) std::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(std::vector<DecompNode>& g, int root = 0) {
  for (auto& p : g) {
    std::sort(p.bag.begin(), p.bag.end());
  }

  std::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];

      std::vector<int> latte, malta;
      std::set_difference(g[idx].bag.begin(), g[idx].bag.end(),
                          g[ch].bag.begin(), g[ch].bag.end(),
                          std::back_inserter(latte));
      std::set_difference(g[ch].bag.begin(), g[ch].bag.end(),
                          g[idx].bag.begin(), g[idx].bag.end(),
                          std::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(std::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 2 "math/combinatorics/montgomery-mod-int.hpp"

#include <cstdint>
#line 5 "math/combinatorics/montgomery-mod-int.hpp"

template <std::uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = std::int32_t;
  using i64 = std::int64_t;
  using u32 = std::uint32_t;
  using u64 = std::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 std::ostream& operator<<(std::ostream& os, const mint& p) {
    return os << p.val();
  }

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

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

template <std::uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 14 "test/verify/aoj-2405.test.cpp"

using namespace std;

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);
    function<void(int)> rec = [&](int idx) {
      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);
    };
    rec(0);
    auto& dp = dps[0];
    cout << dp.back() << endl;
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	testcase_00	AC	754 ms	62 MB
g++	testcase_01	AC	750 ms	62 MB
g++	testcase_02	AC	775 ms	62 MB
g++	testcase_03	AC	764 ms	62 MB
clang++	testcase_00	AC	778 ms	60 MB
clang++	testcase_01	AC	751 ms	60 MB
clang++	testcase_02	AC	768 ms	59 MB
clang++	testcase_03	AC	749 ms	59 MB

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