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IDSubmission IDProblemHackerOwnerResultSubmit timeJudge time
#576#355837#1097. 多项式复合Crysflyhos_lyricFailed.2024-03-17 11:03:182024-03-17 15:21:56

Details

Extra Test:

Invalid Input

input:

5
1 2 3 4 5
1 2 3 4 5

output:


result:

FAIL Condition failed: "g[0] == 0"

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#355837#1097. 多项式复合hos_lyric100 ✓425ms41068kbC++1413.6kb2024-03-17 10:33:522024-03-17 15:20:41

answer

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};

// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = n;
  if (m >>= 1) {
    for (int i = 0; i < m; ++i) {
      const unsigned x = as[i + m].x;  // < MO
      as[i + m].x = as[i].x + MO - x;  // < 2 MO
      as[i].x += x;  // < 2 MO
    }
  }
  if (m >>= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned x = (prod * as[i + m]).x;  // < MO
        as[i + m].x = as[i].x + MO - x;  // < 3 MO
        as[i].x += x;  // < 3 MO
      }
      prod *= FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  for (; m; ) {
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i + m].x = as[i].x + MO - x;  // < 4 MO
          as[i].x += x;  // < 4 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
          as[i + m].x = as[i].x + MO - x;  // < 3 MO
          as[i].x += x;  // < 3 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
    as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x;  // < MO
  }
}

// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = 1;
  if (m < n >> 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
    m <<= 1;
  }
  for (; m < n >> 1; m <<= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + (m >> 1); ++i) {
        const unsigned long long y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
        as[i].x += as[i + m].x;  // < 4 MO
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  if (m < n) {
    for (int i = 0; i < m; ++i) {
      const unsigned y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
      as[i].x += as[i + m].x;  // < 4 MO
      as[i + m].x = y;  // < 4 MO
    }
  }
  const Mint invN = Mint(n).inv();
  for (int i = 0; i < n; ++i) {
    as[i] *= invN;
  }
}

void fft(vector<Mint> &as) {
  fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
  invFft(as.data(), as.size());
}

vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
  if (as.empty() || bs.empty()) return {};
  const int len = as.size() + bs.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  bs.resize(n); fft(bs);
  for (int i = 0; i < n; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(len);
  return as;
}
vector<Mint> square(vector<Mint> as) {
  if (as.empty()) return {};
  const int len = as.size() + as.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  for (int i = 0; i < n; ++i) as[i] *= as[i];
  invFft(as);
  as.resize(len);
  return as;
}
////////////////////////////////////////////////////////////////////////////////

/*
  [0, n-1] * [0, n-m]
  
  [ a[0]                     ]
  [ ...    a[0]              ]
  [ a[m-1] ...               ]
  [        a[m-1]            ]
  [               ...        ]
  [                   a[0]   ]
  [                   ...    ]
  [                   a[m-1] ]
  
  computes (multiply by a)^T
  |as| = m, |bs| = n
  cs[k] = \sum[j-i=k] as[i] bs[j]  (0 <= k <= n-m)
*/
vector<Mint> middle(vector<Mint> as, vector<Mint> bs) {
  const int m = as.size();
  const int n = bs.size();
  assert(m <= n);
  int nn = 1;
  for (; nn < n; nn <<= 1) {}
  reverse(as.begin(), as.end());
  as.resize(nn, 0);
  fft(as);
  bs.resize(nn, 0);
  fft(bs);
  for (int i = 0; i < nn; ++i) bs[i] *= as[i];
  invFft(bs);
  bs.resize(n);
  bs.erase(bs.begin(), bs.begin() + (m - 1));
  return bs;
}


vector<vector<Mint>> mul(const vector<vector<Mint>> &ass, const vector<vector<Mint>> &bss) {
  const int m = ass.size();
  const int n = ass[0].size();
  assert((int)bss.size() == m);
  for (int i = 0; i < m; ++i) assert((int)ass[i].size() == n);
  for (int i = 0; i < m; ++i) assert((int)bss[i].size() == n);
  vector<Mint> as(m * (2*n-1), 0), bs(m * (2*n-1), 0);
  for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) as[i * (2*n-1) + j] = ass[i][j];
  for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) bs[i * (2*n-1) + j] = bss[i][j];
  const auto cs = convolve(as, bs);
  vector<vector<Mint>> css(2*m-1, vector<Mint>(2*n-1));
  for (int i = 0; i < 2*m-1; ++i) for (int j = 0; j < 2*n-1; ++j) css[i][j] = cs[i * (2*n-1) + j];
  return css;
}

/*
  a: deg n in x
  b: deg 2n in x (but zeros trimmed)
  css[i''][j''] = \sum[i'-i=i'', j'-j=j''] ass[i][j] bss[i'][j']
*/
vector<vector<Mint>> middle(int n, const vector<vector<Mint>> &ass, const vector<vector<Mint>> &bss) {
  const int ma = ass.size();
  const int mb = bss.size();
  assert(ma <= mb);
  for (int i = 0; i < ma; ++i) assert((int)ass[i].size() == n + 1);
  for (int i = 0; i < mb; ++i) assert((int)bss[i].size() == n + 1);
  vector<Mint> as(ma * (2*n+1) - n, 0), bs(mb * (2*n+1), 0);
  for (int i = 0; i < ma; ++i) for (int j = 0; j <= n; ++j) as[i * (2*n+1) + j] = ass[i][j];
  for (int i = 0; i < mb; ++i) for (int j = 0; j <= n; ++j) bs[i * (2*n+1) + j] = bss[i][j];
  const auto cs = middle(as, bs);
  vector<vector<Mint>> css(mb - ma + 1, vector<Mint>(n + 1));
  for (int i = 0; i <= mb - ma; ++i) for (int j = 0; j <= n; ++j) css[i][j] = cs[i * (2*n+1) + j];
  return css;
}

/*
  m: deg in t (numerator: m-1)
  n: deg in x
  (m + 1) * (n + 1) -> m * (n + 1)
*/
vector<vector<Mint>> comRec(int m, int n, const vector<Mint> &as, const vector<vector<Mint>> &qss) {
  assert((int)qss.size() == m + 1);
  for (int i = 0; i <= m; ++i) assert((int)qss[i].size() == n + 1);
  if (!n) {
    vector<vector<Mint>> ret(m, vector<Mint>(1));
    for (int i = 0; i < (int)as.size(); ++i) ret[i][0] = as[i];
    return ret;
  }
  auto negQss = qss;
  for (int i = 0; i <= m; ++i) for (int j = 1; j <= n; j += 2) negQss[i][j] = -negQss[i][j];
  auto qqss = mul(qss, negQss);
  for (int i = 0; i <= m << 1; ++i) {
    for (int j = 0; j <= n >> 1; ++j) qqss[i][j] = qqss[i][j << 1];
    qqss[i].resize((n >> 1) + 1);
  }
  const auto res = comRec(m << 1, n >> 1, as, qqss);
  vector<vector<Mint>> pss(m << 1, vector<Mint>(n + 1, 0));
  for (int i = 0; i < m << 1; ++i) for (int j = 0; j <= n >> 1; ++j) pss[i][j << 1 | (n & 1)] = res[i][j];
  const auto ret = middle(n, negQss, pss);
  assert((int)ret.size() == m);
  for (int i = 0; i < m; ++i) assert((int)ret[i].size() == n + 1);
  return ret;
}

/*
  a(b(x))
  transpose and rev: p(x) -> [x^(N-1)] p(x) b(x)^i for each i
  [x^(N-1)] p(x) / (1 - t b(x))
*/
vector<Mint> com(int n, const vector<Mint> &as, const vector<Mint> &bs) {
  assert((int)as.size() == n);
  assert((int)bs.size() == n);
  assert(!bs[0]);
  vector<vector<Mint>> qss(2, vector<Mint>(n, 0));
  qss[0][0] = 1;
  for (int j = 0; j < n; ++j) qss[1][j] = -bs[j];
  auto cs = comRec(1, n - 1, as, qss)[0];
  reverse(cs.begin(), cs.end());
  return cs;
}

int main() {
  int N;
  for (; ~scanf("%d", &N); ) {
    vector<Mint> A(N), B(N);
    for (int i = 0; i < N; ++i) scanf("%u", &A[i].x);
    for (int i = 0; i < N; ++i) scanf("%u", &B[i].x);
    const auto C = com(N, A, B);
    for (int i = 0; i < N; ++i) {
      if (i) printf(" ");
      printf("%u", C[i].x);
    }
    puts("");
  }
  return 0;
}