#726522 (C++14) No.1796 木上のクーロン

提出ソース

結果

問題	No.1796 木上のクーロン
ユーザー	👑 hos.lyric
提出日時	2021-12-25 22:19:23
言語	C++14 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	1,980 ms / 10,000 ms
コード長	13,623 bytes
コンパイル時間	2,057 ms
コンパイル使用メモリ	132,168 KB
実行使用メモリ	46,608 KB
最終ジャッジ日時	2023-10-22 02:35:25
合計ジャッジ時間	21,816 ms
ジャッジサーバーID （参考情報）	judge9 / judge10

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	8 ms 8,520 KB
testcase_01	AC	8 ms 8,520 KB
testcase_02	AC	8 ms 8,520 KB
testcase_03	AC	8 ms 8,520 KB
testcase_04	AC	8 ms 8,520 KB
testcase_05	AC	8 ms 8,520 KB
testcase_06	AC	8 ms 8,520 KB
testcase_07	AC	8 ms 8,520 KB
testcase_08	AC	9 ms 8,548 KB
testcase_09	AC	9 ms 8,556 KB
testcase_10	AC	9 ms 8,560 KB
testcase_11	AC	9 ms 8,552 KB
testcase_12	AC	9 ms 8,564 KB
testcase_13	AC	8 ms 8,544 KB
testcase_14	AC	8 ms 8,556 KB
testcase_15	AC	9 ms 8,600 KB
testcase_16	AC	10 ms 8,604 KB
testcase_17	AC	9 ms 8,588 KB
testcase_18	AC	8 ms 8,584 KB
testcase_19	AC	9 ms 8,568 KB
testcase_20	AC	125 ms 12,972 KB
testcase_21	AC	127 ms 13,032 KB
testcase_22	AC	295 ms 17,736 KB
testcase_23	AC	286 ms 17,576 KB
testcase_24	AC	481 ms 22,260 KB
testcase_25	AC	486 ms 22,416 KB
testcase_26	AC	677 ms 27,384 KB
testcase_27	AC	683 ms 27,416 KB
testcase_28	AC	1,980 ms 46,420 KB
testcase_29	AC	1,933 ms 46,608 KB
testcase_30	AC	323 ms 36,864 KB
testcase_31	AC	366 ms 35,728 KB
testcase_32	AC	800 ms 26,828 KB
testcase_33	AC	1,084 ms 44,452 KB
testcase_34	AC	1,016 ms 42,292 KB
testcase_35	AC	1,301 ms 33,284 KB
testcase_36	AC	1,278 ms 33,908 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#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 <map>
#include <numeric>
#include <queue>
#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> 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; }


////////////////////////////////////////////////////////////////////////////////
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;
}
////////////////////////////////////////////////////////////////////////////////


constexpr int LIM = 400'010;
Mint inv[LIM], fac[LIM], invFac[LIM];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


/*
  [0, n] * [0, n - m + 1]
  
  [ a[0]                     ]
  [ ...    a[0]              ]
  [ a[m-1] ...               ]
  [        a[m-1]            ]
  [               ...        ]
  [                   a[0]   ]
  [                   ...    ]
  [                   a[m-1] ]
  
  [x^j] (rev(a) b)  m - 1 <= j <= n - 1
*/
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;
}


int N;
vector<Mint> Q;
vector<int> A, B;
vector<vector<int>> G;
vector<int> sz, del;
void dfsSz(int u, int p) {
  sz[u] = 1;
  for (const int i : G[u]) {
    const int v = A[i] ^ B[i] ^ u;
    if (v != p) {
      dfsSz(v, u);
      sz[u] += sz[v];
    }
  }
}
string dfsDebug(int u, int p) {
  ostringstream oss;
  oss << "[" << u;
  for (const int i : G[u]) {
    const int v = A[i] ^ B[i] ^ u;
    if (!del[v] && v != p) {
      oss << " " << dfsDebug(v, u);
    }
  }
  oss << "]";
  return oss.str();
}
vector<Mint> ans, tot, sub;
vector<vector<pair<int, int>>> duss;
int dfsSub(int j, int u, int p, int d) {
  duss[j].emplace_back(d, u);
  tot[d] += Q[u];
  sub[d] += Q[u];
  int ret = d;
  for (const int i : G[u]) {
    const int v = A[i] ^ B[i] ^ u;
    if (!del[v] && v != p) {
      chmax(ret, dfsSub(j, v, u, d + 1));
    }
  }
  return ret;
}
void solveSubtree(int r) {
#ifdef LOCAL
  cerr << "solveSubtree " << dfsDebug(r, -1) << endl;
#endif
  vector<int> is;
  for (const int i : G[r]) {
    const int v = A[i] ^ B[i] ^ r;
    if (!del[v]) {
      is.push_back(i);
    }
  }
  const int len = is.size();
  tot.assign(sz[r], 0);
  tot[0] += Q[r];
  duss.assign(len + 1, {});
  duss[len].emplace_back(0, r);
  int dMax = 0;
  for (int j = 0; j < len; ++j) {
    const int i = is[j];
    const int v = A[i] ^ B[i] ^ r;
    sub.assign(sz[v] + 1, 0);
    const int d = dfsSub(j, v, r, 1);
    chmax(dMax, d);
    sub.resize(d + 1);
    vector<Mint> coef(2 * d + 1);
    for (int k = 0; k <= 2 * d; ++k) {
      coef[k] = inv[k + 1] * inv[k + 1];
    }
    const auto res = middle(sub, coef);
    for (const auto &du : duss[j]) {
      ans[du.second] -= res[du.first];
    }
  }
  tot.resize(dMax + 1);
  {
    vector<Mint> coef(2 * dMax + 1);
    for (int k = 0; k <= 2 * dMax; ++k) {
      coef[k] = inv[k + 1] * inv[k + 1];
    }
    const auto res = middle(tot, coef);
    for (int j = 0; j <= len; ++j) for (const auto &du : duss[j]) {
      ans[du.second] += res[du.first];
    }
  }
}
void solveRec(int u) {
  for (; ; ) {
    int vm = -1;
    for (const int i : G[u]) {
      const int v = A[i] ^ B[i] ^ u;
      if (!del[v]) {
        if (vm == -1 || sz[vm] < sz[v]) {
          vm = v;
        }
      }
    }
    if (vm == -1 || sz[u] >= 2 * sz[vm]) {
      solveSubtree(u);
      del[u] = true;
      for (const int i : G[u]) {
        const int v = A[i] ^ B[i] ^ u;
        if (!del[v]) {
          solveRec(v);
        }
      }
      break;
    } else {
      sz[u] -= sz[vm];
      sz[vm] += sz[u];
      u = vm;
    }
  }
}
void solveCentroidDecomp() {
  sz.assign(N, 0);
  del.assign(N, 0);
  dfsSz(0, -1);
  ans.assign(N, 0);
  solveRec(0);
}

int main() {
  prepare();
  
  for (; ~scanf("%d", &N); ) {
    Q.resize(N);
    for (int u = 0; u < N; ++u) {
      scanf("%u", &Q[u].x);
    }
    A.resize(N - 1);
    B.resize(N - 1);
    for (int i = 0; i < N - 1; ++i) {
      scanf("%d%d", &A[i], &B[i]);
      --A[i];
      --B[i];
    }
    
    G.assign(N, {});
    for (int i = 0; i < N - 1; ++i) {
      G[A[i]].push_back(i);
      G[B[i]].push_back(i);
    }
    solveCentroidDecomp();
    
    for (int u = 0; u < N; ++u) {
      ans[u] *= fac[N] * fac[N];
    }
    
    for (int u = 0; u < N; ++u) {
      printf("%u\n", ans[u].x);
    }
  }
  return 0;
}

yukicoder

結果

テストケース

ソースコード