結果

問題 No.2513 Power Eraser
ユーザー SSRSSSRS
提出日時 2023-10-20 22:11:38
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 5,707 ms / 6,000 ms
コード長 3,774 bytes
コンパイル時間 15,690 ms
コンパイル使用メモリ 305,916 KB
最終ジャッジ日時 2025-02-17 09:41:01
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 34 TLE * 1 -- * 4
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

diff # 

#include <bits/stdc++.h>
#include <atcoder/convolution>
using namespace std;
const long long MOD = 998244353;
long long modpow(long long a, long long b){
  long long ans = 1;
  while (b > 0){
    if (b % 2 == 1){
      ans *= a;
      ans %= MOD;
    }
    a *= a;
    a %= MOD;
    b /= 2;
  }
  return ans;
}
long long modinv(long long a){
  return modpow(a, MOD - 2);
}
vector<long long> diff(vector<long long> A){
  int N = A.size();
  vector<long long> B(N - 1);
  for (int i = 1; i < N; i++){
    B[i - 1] = A[i] * i % MOD;
  }
  return B;
}
vector<long long> polynomial_inverse(vector<long long> f){
  int N = f.size();
  vector<long long> ans(1);
  ans[0] = modinv(f[0]);
  for (int i = 1; i < N * 2; i *= 2){
    vector<long long> ans2 = ans;
    ans2.resize(i * 4);
    int N2 = min(N, i * 2);
    vector<long long> f2(i * 4, 0);
    for (int j = 0; j < N2; j++){
      f2[j] = f[j];
    }
    ans2 = atcoder::convolution(ans2, ans2);
    ans2.resize(i * 2);
    ans2 = atcoder::convolution(ans2, f2);
    ans2.resize(i * 2);
    for (int j = 0; j < i; j++){
      ans2[j] = MOD - ans2[j] + ans[j] * 2;
      ans2[j] %= MOD;
    }
    swap(ans, ans2);
  }
  ans.resize(N);
  return ans;
}
vector<long long> polynomial_quotient(vector<long long> f, vector<long long> g){
  int N = f.size(), M = g.size();
  if (N < M){
    return {0};
  }
  reverse(g.begin(), g.end());
  g.resize(N - M + 1);
  vector<long long> t = polynomial_inverse(g);
  reverse(f.begin(), f.end());
  vector<long long> q = atcoder::convolution(f, t);
  q.resize(N - M + 1);
  reverse(q.begin(), q.end());
  return q;
}
vector<long long> polynomial_remainder(vector<long long> f, vector<long long> g){
  int N = f.size();
  int M = g.size();
  if (M <= 100){
    for (int i = N - M; i >= 0; i--){
      long long q = f[i + M - 1] * modinv(g[M - 1]) % MOD;
      for (int j = 0; j < M; j++){
        f[i + j] += MOD - q * g[j] % MOD;
        f[i + j] %= MOD;
      }
      f.pop_back();
    }
    return f;
  } else {
    vector<long long> q = polynomial_quotient(f, g);
    vector<long long> b = atcoder::convolution(g, q);
    for (int i = 0; i < N; i++){
      f[i] += MOD - b[i];
      f[i] %= MOD;
    }
    f.resize(M - 1);
    return f;
  }
}
vector<long long> multipoint_evaluation(vector<long long> &f, vector<long long> x){
  int M = x.size();
  int M2 = 1;
  while (M2 < M){
    M2 *= 2;
  }
  vector<vector<long long>> g(M2 * 2 - 1, {1});
  for (int i = 0; i < M; i++){
    g[M2 - 1 + i] = vector<long long>{MOD - x[i], 1};
  }
  for (int i = M2 - 2; i >= 0; i--){
    g[i] = atcoder::convolution(g[i * 2 + 1], g[i * 2 + 2]);
  }
  g[0] = polynomial_remainder(f, g[0]);
  for (int i = 1; i < M2 * 2 - 1; i++){
    g[i] = polynomial_remainder(g[(i - 1) / 2], g[i]);
  }
  vector<long long> ans(M);
  for (int i = 0; i < M; i++){
    ans[i] = g[M2 - 1 + i][0];
  }
  return ans;
}
int main(){
  int N;
  cin >> N;
  vector<int> A(N);
  for (int i = 0; i < N; i++){
    cin >> A[i];
  }
  long long ans = 1;
  auto dfs = [&](auto dfs, int L, int R){
    if (R - L == 1){
      return;
    }
    int m = (L + R) / 2;
    vector<vector<long long>> P(m - L);
    for (int i = 0; i < m - L; i++){
      P[i] = {MOD - A[L + i], 1};
    }
    for (int i = m - L - 1; i >= 1; i--){
      P[i / 2] = atcoder::convolution(P[i / 2], P[i]);
      P.pop_back();
    }
    vector<long long> f = P[0];
    vector<long long> x(R - m);
    for (int i = 0; i < R - m; i++){
      x[i] = A[m + i];
    }
    vector<long long> y = multipoint_evaluation(f, x);
    for (int i = 0; i < R - m; i++){
      ans *= y[i];
      ans %= MOD;
    }
    dfs(dfs, L, m);
    dfs(dfs, m, R);
  };
  dfs(dfs, 0, N);
  if ((long long) N * (N - 1) / 2 % 2 == 1){
    ans = (MOD - ans) % MOD;
  }
  cout << ans << endl;
}
0