#431463 (C++17) No.287 場合の数

• 問題: No.287 場合の数
• ユーザー: emthrm
• 提出日時: 2020-02-18 19:50:59
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 10 ms / 5,000 ms
• コード長: 9,104 bytes
• コンパイル時間: 2,178 ms
• コンパイル使用メモリ: 199,064 KB
• 最終ジャッジ日時: 2025-01-09 01:03:24
• ジャッジサーバーID （参考情報）: judge1 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 22

ソースコード

#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;
template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const 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; }
template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

template <typename T>
function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) {
  int n = a.size(), m = b.size();
  vector<T> res(n + m - 1, T(0));
  REP(i, n) REP(j, m) res[i + j] += a[i] * b[j];
  return res;
};

template <typename T>
function<bool(const T&, T&)> sqr = [](const T &a, T &res) {
  return false;
};

template <typename T>
struct FPS {
  vector<T> co;

  FPS(int deg = 0) : co(deg + 1, T(0)) {}
  FPS(const vector<T> &co) : co(co) {}
  FPS(initializer_list<T> init) : co(init.begin(), init.end()) {}
  template <typename InputIter> FPS(InputIter first, InputIter last) : co(first, last) {}

  inline const T &operator[](int term) const { return co[term]; }
  inline T &operator[](int term) { return co[term]; }

  void resize(int deg) {
    int prev = co.size();
    co.resize(deg + 1);
    if (prev < deg + 1) fill(co.begin() + prev, co.end(), T(0));
  }

  void shrink() { while (co.size() > 1 && co.back() == T(0)) co.pop_back(); }

  int degree() const { return static_cast<int>(co.size()) - 1; }

  FPS &operator=(const vector<T> &new_co) {
    co.resize(new_co.size());
    copy(ALL(new_co), co.begin());
    return *this;
  }

  FPS &operator=(const FPS &x) {
    co.resize(x.co.size());
    copy(ALL(x.co), co.begin());
    return *this;
  }

  FPS &operator+=(const FPS &x) {
    int n = x.co.size();
    if (n > co.size()) resize(n - 1);
    REP(i, n) co[i] += x.co[i];
    return *this;
  }

  FPS &operator-=(const FPS &x) {
    int n = x.co.size();
    if (n > co.size()) resize(n - 1);
    REP(i, n) co[i] -= x.co[i];
    return *this;
  }

  FPS &operator*=(T x) {
    for (T &e : co) e *= x;
    return *this;
  }

  FPS &operator*=(const FPS &x) { return *this = mul<T>(co, x.co); }

  FPS &operator/=(T x) {
    assert(x != T(0));
    T inv_x = T(1) / x;
    for (T &e : co) e *= inv_x;
    return *this;
  }

  FPS &operator/=(const FPS &x) {
    if (x.co.size() > co.size()) return *this = FPS();
    int n = co.size() - x.co.size() + 1;
    FPS a(co.rbegin(), co.rbegin() + n), b(x.co.rbegin(), x.co.rbegin() + min(static_cast<int>(x.co.size()), n));
    b = b.inv(n - 1);
    a *= b;
    return *this = FPS(a.co.rend() - n, a.co.rend());
  }

  FPS &operator%=(const FPS &x) {
    *this -= *this / x * x;
    co.resize(static_cast<int>(x.co.size()) - 1);
    if (co.empty()) co = {T(0)};
    return *this;
  }

  FPS &operator<<=(int n) {
    co.insert(co.begin(), n, T(0));
    return *this;
  }

  FPS &operator>>=(int n) {
    if (co.size() < n) return *this = FPS();
    co.erase(co.begin(), co.begin() + n);
    return *this;
  }

  bool operator==(const FPS &x) const {
    FPS a(*this), b(x);
    a.shrink(); b.shrink();
    int n = a.co.size();
    if (n != b.co.size()) return false;
    REP(i, n) if (a.co[i] != b.co[i]) return false;
    return true;
  }

  bool operator!=(const FPS &x) const { return !(*this == x); }

  FPS operator+() const { return *this; }

  FPS operator-() const {
    FPS res(*this);
    for (T &e : res.co) e = T(-e);
    return res;
  }

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

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

  FPS operator*(T x) const { return FPS(*this) *= x; }

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

  FPS operator/(T x) const { return FPS(*this) /= x; }

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

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

  FPS operator<<(int n) const { return FPS(*this) <<= n; }

  FPS operator>>(int n) const { return FPS(*this) >>= n; }

  T horner(T val) const {
    T res = T(0);
    for (int i = static_cast<int>(co.size()) - 1; i >= 0; --i) (res *= val) += co[i];
    return res;
  }

  FPS differential() const {
    int n = co.size();
    assert(n >= 1);
    FPS res(n - 1);
    FOR(i, 1, n) res.co[i - 1] = co[i] * T(i);
    return res;
  }

  FPS integral() const {
    int n = co.size();
    FPS res(n + 1);
    REP(i, n) res[i + 1] = co[i] / T(i + 1);
    return res;
  }

  FPS exp(int deg = -1) const {
    assert(co[0] == T(0));
    if (deg == -1) deg = static_cast<int>(co.size()) - 1;
    FPS one({T(1)}), res = one;
    for (int i = 1; i <= deg; i <<= 1) {
      res *= FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) - res.log((i << 1) - 1) + one;
      res.co.resize(i << 1);
    }
    res.co.resize(deg + 1);
    return res;
  }

  FPS inv(int deg = -1) const {
    assert(co[0] != T(0));
    if (deg == -1) deg = static_cast<int>(co.size()) - 1;
    FPS res({T(1) / co[0]});
    for (int i = 1; i <= deg; i <<= 1) {
      res = res + res - res * res * FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1));
      res.co.resize(i << 1);
    }
    res.co.resize(deg + 1);
    return res;
  }

  FPS log(int deg = -1) const {
    assert(co[0] == T(1));
    if (deg == -1) deg = static_cast<int>(co.size()) - 1;
    FPS integrand = differential() * inv(deg - 1);
    integrand.co.resize(deg);
    return integrand.integral();
  }

  FPS pow(ll exponent, int deg = -1) const {
    int n = co.size();
    if (deg == -1) deg = n - 1;
    REP(i, n) {
      if (co[i] != T(0)) {
        ll shift = exponent * i;
        if (shift > deg) break;
        T tmp = 1, base = co[i];
        ll e = exponent;
        while (e > 0) {
          if (e & 1) tmp *= base;
          base *= base;
          e >>= 1;
        }
        return ((((*this >> i) * (T(1) / co[i])).log(deg - shift) * T(exponent)).exp(deg - shift) * tmp) << shift;
      }
    }
    return FPS(deg);
  }

  FPS mod_pow(ll exponent, const FPS &md) const {
    FPS inv_rev_md = FPS(md.co.rbegin(), md.co.rend()).inv();
    int deg_of_md = md.co.size();
    function<void(FPS&, const FPS&)> mod_mul = [&](FPS &multiplicand, const FPS &multiplier) {
      multiplicand *= multiplier;
      if (deg_of_md <= multiplicand.co.size()) {
        int n = multiplicand.co.size() - deg_of_md + 1;
        FPS quotient = FPS(multiplicand.co.rbegin(), multiplicand.co.rbegin() + n) * FPS(inv_rev_md.co.begin(), inv_rev_md.co.begin() + min(static_cast<int>(inv_rev_md.co.size()), n));
        multiplicand -= FPS(quotient.co.rend() - n, quotient.co.rend()) * md;
      }
      multiplicand.co.resize(deg_of_md - 1);
      if (multiplicand.co.empty()) multiplicand.co = {T(0)};
    };
    FPS res({T(1)}), base = *this;
    mod_mul(base, res);
    while (exponent > 0) {
      if (exponent & 1) mod_mul(res, base);
      mod_mul(base, base);
      exponent >>= 1;
    }
    return res;
  }

  FPS sqrt(int deg = -1) const {
    int n = co.size();
    if (deg == -1) deg = n - 1;
    if (co[0] == T(0)) {
      FOR(i, 1, n) {
        if (co[i] == T(0)) continue;
        if (i & 1) return FPS(-1);
        int shift = i >> 1;
        if (deg < shift) break;
        FPS res = (*this >> i).sqrt(deg - shift);
        if (res.co.empty()) return FPS(-1);
        res <<= shift;
        res.resize(deg);
        return res;
      }
      return FPS(deg);
    }
    T s;
    if (!sqr<T>(co[0], s)) return FPS(-1);
    FPS res({s});
    T half = T(1) / T(2);
    for (int i = 1; i <= deg; i <<= 1) {
      (res += FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) * res.inv((i << 1) - 1)) *= half;
    }
    res.resize(deg);
    return res;
  }

  FPS translate(T c) const {
    int n = co.size();
    vector<T> fact(n, T(1)), inv_fact(n, T(1));
    FOR(i, 1, n) fact[i] = fact[i - 1] * T(i);
    inv_fact[n - 1] = T(1) / fact[n - 1];
    for (int i = n - 1; i > 0; --i) inv_fact[i - 1] = inv_fact[i] * T(i);
    vector<T> g(n), ex(n);
    REP(i, n) g[n - 1 - i] = co[i] * fact[i];
    T pow_c = T(1);
    REP(i, n) {
      ex[i] = pow_c * inv_fact[i];
      pow_c *= c;
    }
    vector<T> conv = mul<T>(g, ex);
    FPS res(n - 1);
    REP(i, n) res[i] = conv[n - 1 - i] * inv_fact[i];
    return res;
  }
};

int main() {
  int n; cin >> n;
  FPS<ll> fps(6 * n);
  REP(i, n + 1) fps[i] = 1;
  FPS<ll> ans = fps;
  FOR(_, 1, 8) ans *= fps;
  cout << ans[6 * n] << '\n';
  return 0;
}