#687960 (C++17) No.1561 connect x connect

提出ソース

結果

問題	No.1561 connect x connect
ユーザー	👑 emthrm
提出日時	2021-08-11 03:22:33
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	10,893 bytes
コンパイル時間	3,436 ms
コンパイル使用メモリ	256,664 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-09-24 10:01:54
合計ジャッジ時間	27,225 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	3 ms 6,940 KB
testcase_02	AC	34 ms 6,944 KB
testcase_03	AC	2 ms 6,948 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	WA	-
testcase_10	WA	-
testcase_11	WA	-
testcase_12	WA	-
testcase_13	AC	34 ms 6,940 KB
testcase_14	AC	246 ms 6,944 KB
testcase_15	AC	248 ms 6,944 KB
testcase_16	WA	-
testcase_17	WA	-
testcase_18	WA	-
testcase_19	WA	-
testcase_20	WA	-
testcase_21	WA	-
testcase_22	WA	-
testcase_23	WA	-
testcase_24	WA	-
testcase_25	WA	-
testcase_26	TLE	-
testcase_27	TLE	-
testcase_28	TLE	-
testcase_29	TLE	-
testcase_30	TLE	-
testcase_31	WA	-
testcase_32	AC	33 ms 6,944 KB
testcase_33	AC	247 ms 6,940 KB
testcase_34	WA	-
testcase_35	TLE	-
testcase_36	TLE	-
testcase_37	TLE	-

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ソースコード

raw source code

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int M>
struct MInt {
  unsigned int val;
  MInt(): val(0) {}
  MInt(long long x) : val(x >= 0 ? x % M : x % M + M) {}
  static constexpr int get_mod() { return M; }
  static void set_mod(int divisor) { assert(divisor == M); }
  static void init(int x = 10000000) { inv(x, true); fact(x); fact_inv(x); }
  static MInt inv(int x, bool init = false) {
    // assert(0 <= x && x < M && std::__gcd(x, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    int prev = inverse.size();
    if (init && x >= prev) {
      // "x!" and "M" must be disjoint.
      inverse.resize(x + 1);
      for (int i = prev; i <= x; ++i) inverse[i] = -inverse[M % i] * (M / i);
    }
    if (x < inverse.size()) return inverse[x];
    unsigned int a = x, b = M; int u = 1, v = 0;
    while (b) {
      unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }
  static MInt fact(int x) {
    static std::vector<MInt> f{1};
    int prev = f.size();
    if (x >= prev) {
      f.resize(x + 1);
      for (int i = prev; i <= x; ++i) f[i] = f[i - 1] * i;
    }
    return f[x];
  }
  static MInt fact_inv(int x) {
    static std::vector<MInt> finv{1};
    int prev = finv.size();
    if (x >= prev) {
      finv.resize(x + 1);
      finv[x] = inv(fact(x).val);
      for (int i = x; i > prev; --i) finv[i - 1] = finv[i] * i;
    }
    return finv[x];
  }
  static MInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    if (n - k > k) k = n - k;
    return fact(n) * fact_inv(k) * fact_inv(n - k);
  }
  static MInt nPk(int n, int k) { return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k); }
  static MInt nHk(int n, int k) { return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k)); }
  static MInt large_nCk(long long n, int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv(k, true);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) res *= inv(i) * n--;
    return res;
  }
  MInt pow(long long exponent) const {
    MInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  MInt &operator+=(const MInt &x) { if((val += x.val) >= M) val -= M; return *this; }
  MInt &operator-=(const MInt &x) { if((val += M - x.val) >= M) val -= M; return *this; }
  MInt &operator*=(const MInt &x) { val = static_cast<unsigned long long>(val) * x.val % M; return *this; }
  MInt &operator/=(const MInt &x) { return *this *= inv(x.val); }
  bool operator==(const MInt &x) const { return val == x.val; }
  bool operator!=(const MInt &x) const { return val != x.val; }
  bool operator<(const MInt &x) const { return val < x.val; }
  bool operator<=(const MInt &x) const { return val <= x.val; }
  bool operator>(const MInt &x) const { return val > x.val; }
  bool operator>=(const MInt &x) const { return val >= x.val; }
  MInt &operator++() { if (++val == M) val = 0; return *this; }
  MInt operator++(int) { MInt res = *this; ++*this; return res; }
  MInt &operator--() { val = (val == 0 ? M : val) - 1; return *this; }
  MInt operator--(int) { MInt res = *this; --*this; return res; }
  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(val ? M - val : 0); }
  MInt operator+(const MInt &x) const { return MInt(*this) += x; }
  MInt operator-(const MInt &x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt &x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt &x) const { return MInt(*this) /= x; }
  friend std::ostream &operator<<(std::ostream &os, const MInt &x) { return os << x.val; }
  friend std::istream &operator>>(std::istream &is, MInt &x) { long long val; is >> val; x = MInt(val); return is; }
};
namespace std { template <int M> MInt<M> abs(const MInt<M> &x) { return x; } }
using ModInt = MInt<MOD>;

struct UnionFind {
  UnionFind(int n) : data(n, -1) {}

  int root(int ver) { return data[ver] < 0 ? ver : data[ver] = root(data[ver]); }

  bool unite(int u, int v) {
    u = root(u);
    v = root(v);
    if (u == v) return false;
    if (data[u] > data[v]) std::swap(u, v);
    data[u] += data[v];
    data[v] = u;
    return true;
  }

  bool same(int u, int v) { return root(u) == root(v); }

  int size(int ver) { return -data[root(ver)]; }

private:
  std::vector<int> data;
};

template <typename T>
struct Matrix {
  Matrix(int m, int n, T val = 0) : dat(m, std::vector<T>(n, val)) {}

  int height() const { return dat.size(); }

  int width() const { return dat.front().size(); }

  Matrix pow(long long exponent) const {
    int n = height();
    Matrix<T> tmp = *this, res(n, n, 0);
    for (int i = 0; i < n; ++i) res[i][i] = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }

  inline const std::vector<T> &operator[](const int idx) const { return dat[idx]; }
  inline std::vector<T> &operator[](const int idx) { return dat[idx]; }

  Matrix &operator=(const Matrix &x) {
    int m = x.height(), n = x.width();
    dat.resize(m, std::vector<T>(n));
    for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] = x[i][j];
    return *this;
  }

  Matrix &operator+=(const Matrix &x) {
    int m = height(), n = width();
    for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] += x[i][j];
    return *this;
  }

  Matrix &operator-=(const Matrix &x) {
    int m = height(), n = width();
    for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] -= x[i][j];
    return *this;
  }

  Matrix &operator*=(const Matrix &x) {
    int m = height(), n = x.width(), l = width();
    std::vector<std::vector<T>> res(m, std::vector<T>(n, 0));
    for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) {
      for (int k = 0; k < l; ++k) res[i][j] += dat[i][k] * x[k][j];
    }
    std::swap(dat, res);
    return *this;
  }

  Matrix operator+(const Matrix &x) const { return Matrix(*this) += x; }

  Matrix operator-(const Matrix &x) const { return Matrix(*this) -= x; }

  Matrix operator*(const Matrix &x) const { return Matrix(*this) *= x; }

private:
  std::vector<std::vector<T>> dat;
};

template <typename T>
T kita_masa(const std::vector<T> &c, const std::vector<T> &a, long long n) {
  if (n == 0) return a[0];
  int k = c.size();
  std::vector<T> coefficient[3];
  for (int i = 0; i < 3; ++i) coefficient[i].assign(k, 0);
  if (k == 1) {
    coefficient[0][0] = c[0] * a[0];
  } else {
    coefficient[0][1] = 1;
  }
  auto succ = [&c, k, &coefficient]() -> void {
    for (int i = 0; i < k - 1; ++i) coefficient[0][i] += coefficient[0].back() * c[i + 1];
    coefficient[0].back() *= c[0];
    std::rotate(coefficient[0].begin(), coefficient[0].begin() + k - 1, coefficient[0].end());
  };
  for (int bit = 62 - __builtin_clzll(n); bit >= 0; --bit) {
    for (int i = 1; i < 3; ++i) std::copy(coefficient[0].begin(), coefficient[0].end(), coefficient[i].begin());
    for (T &e : coefficient[1]) e *= coefficient[2][0];
    for (int i = 1; i < k; ++i) {
      succ();
      for (int j = 0; j < k; ++j) coefficient[1][j] += coefficient[2][i] * coefficient[0][j];
    }
    coefficient[0].swap(coefficient[1]);
    if (n >> bit & 1) succ();
  }
  T res = 0;
  for (int i = 0; i < k; ++i) res += coefficient[0][i] * a[i];
  return res;
}

// https://github.com/beet-aizu/library/blob/bca52958e61426377b8f56817d63f912070b3487/polynomial/berlekampmassey.cpp
template<typename T>
vector<T> berlekamp_massey(vector<T> &as){
  using Poly = vector<T>;
  int n=as.size();
  Poly bs({-T(1)}),cs({-T(1)});
  T y(1);
  for(int ed=1;ed<=n;ed++){
    int l=cs.size(),m=bs.size();
    T x(0);
    for(int i=0;i<l;i++) x+=cs[i]*as[ed-l+i];
    bs.emplace_back(0);
    m++;
    if(x==T(0)) continue;
    T freq=x/y;
    if(m<=l){
      for(int i=0;i<m;i++)
        cs[l-1-i]-=freq*bs[m-1-i];
      continue;
    }
    auto ts=cs;
    cs.insert(cs.begin(),m-l,T(0));
    for(int i=0;i<m;i++) cs[m-1-i]-=freq*bs[m-1-i];
    bs=ts;
    y=x;
  }
  for(auto &c:cs) c/=cs.back();
  return cs;
}

int main() {
  int n; ll m; cin >> n >> m;
  int size = 2;
  map<vector<int>, int> mp;
  mp[vector<int>(n, -1)] = 0;
  vector<vector<int>> reach(size);
  vector<bool> finish{false, true};
  queue<vector<int>> que({vector<int>(n, -1)});
  while (!que.empty()) {
    vector<int> prev = que.front(); que.pop();
    int id = mp[prev];
    if (id > 0) {
      bool is_con = true;
      int only = *max_element(ALL(prev));
      REP(i, n) is_con &= prev[i] == -1 || prev[i] == only;
      if (is_con) reach[id].emplace_back(1);
    }
    FOR(b, 1, 1 << n) {
      UnionFind uf(n * 2);
      REP(i, n) {
        if (prev[i] == -1) continue;
        FOR(j, i + 1, n) {
          if (prev[j] == prev[i]) uf.unite(i, j);
        }
      }
      FOR(i, 1, n) {
        if ((b >> (i - 1) & 1) && (b >> i & 1)) uf.unite(n + i - 1, n + i);
      }
      REP(i, n) {
        if (prev[i] != -1 && (b >> i & 1)) uf.unite(i, n + i);
      }
      vector<int> nx(n, -1);
      map<int, int> root;
      REP(i, n) {
        if (b >> i & 1) {
          int rt = uf.root(n + i);
          if (root.count(rt) == 0) {
            int tmp = root.size();
            root[rt] = tmp;
          }
          nx[i] = root[rt];
        }
      }
      bool is_con = true;
      REP(i, n) is_con &= prev[i] == -1 || root.count(uf.root(i)) == 1;
      if (is_con) {
        if (mp.count(nx) == 0) {
          mp[nx] = size++;
          que.emplace(nx);
          reach.emplace_back();
          finish.emplace_back(root.size() == 1);
        }
        reach[id].emplace_back(mp[nx]);
      }
    }
  }
  vector<ModInt> dp(size, 0), a;
  dp[0] = 1;
  while (a.size() < size) {
    vector<ModInt> nx(size, 0);
    nx[0] += dp[0];
    nx[1] += dp[1];
    REP(i, size) for (int j : reach[i]) nx[j] += dp[i];
    dp.swap(nx);
    a.emplace_back(0);
    REP(i, size) {
      if (finish[i]) a.back() += dp[i];
    }
  }
  cout << kita_masa(berlekamp_massey(a), a, m - 1) << '\n';
  return 0;
}

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結果

テストケース

ソースコード