#1089450 (C++14) No.3123 Inversion

• 問題: No.3123 Inversion
• ユーザー: 👑 hos.lyric
• 提出日時: 2025-05-31 12:16:40
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 542 ms / 10,000 ms
• コード長: 6,709 bytes
• コンパイル時間: 1,472 ms
• コンパイル使用メモリ: 117,960 KB
• 実行使用メモリ: 75,684 KB
• 最終ジャッジ日時: 2025-05-31 12:17:03
• 合計ジャッジ時間: 22,912 ms
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 1
other	AC * 21

コンパイルメッセージ

main.cpp: In function ‘int main()’:
main.cpp:147:12: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  147 |       scanf("%d", &Ns[t]);
      |       ~~~~~^~~~~~~~~~~~~~

ソースコード

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#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")

////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  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) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= 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; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////

using Mint = ModInt;

/*
  r: rotate 90deg
  s: transpose
  
              D_8
     <s, r^2> <r> <sr, r^2>
    /   |   \  |  / |  \
  <s> <sr^2> <r^2> <sr> <s^3r>
               1
  
  count perm. fixed by a subgroup
  N >= 2 ==> sr, sr^3 must change
  
  
    2 2          +6 -2
  4 4 4  ~~>  -4 -4 -4
      8             +8
*/

void exper() {
  for (int N = 0; N <= 10; ++N) {
    vector<int> ps(N);
    for (int x = 0; x < N; ++x) ps[x] = x;
    int cnt = 0;
    do {
      bool ok = true;
      for (int x = 0; x < N; ++x) {
        const int y = ps[x];
        ok = ok && (ps[y] == x && ps[N - 1 - x] == N - 1 - y);
        // ok = ok && (ps[N - 1 - y] == x);
      }
      if (ok) ++cnt;
    } while (next_permutation(ps.begin(), ps.end()));
    cerr << N << ": " << cnt << endl;
  }
}

vector<Mint> fac, two, match, invol, invol2;

Mint calc_s_r2(int N) { return invol2[N/2]; }
Mint calc_r(int N) { return (N/2 % 2 != 0) ? 0 : (match[N/2 / 2] * two[N/2 / 2]); }
Mint calc_s(int N) { return invol[N]; }
Mint calc_sr2(int N) { return invol[N]; }
Mint calc_r2(int N) { return fac[N/2] * two[N/2]; }
Mint calc_1(int N) { return fac[N]; }

int T, M;
vector<int> Ns;

int main() {
  // exper();
  
  for (; ~scanf("%d%d", &T, &M); ) {
    Mint::setM(M);
    Ns.resize(T);
    for (int t = 0; t < T; ++t) {
      scanf("%d", &Ns[t]);
    }
    
    {
      const int N = *max_element(Ns.begin(), Ns.end());
      fac.resize(N + 1);
      fac[0] = 1;
      for (int i = 1; i <= N; ++i) fac[i] = fac[i - 1] * i;
      two.resize(N/2 + 1);
      two[0] = 1;
      for (int i = 1; i <= N/2; ++i) two[i] = two[i - 1] * 2;
      match.resize(N/2 + 1);
      match[0] = 1;
      for (int i = 1; i <= N/2; ++i) match[i] = match[i - 1] * (2*i - 1);
      invol.resize(N + 1);
      invol[0] = invol[1] = 1;
      for (int i = 2; i <= N; ++i) invol[i] = invol[i - 1] + (i - 1) * invol[i - 2];
      invol2.resize(max(N/2, 1) + 1);
      invol2[0] = 1;
      invol2[1] = 2;
      for (int i = 2; i <= N/2; ++i) invol2[i] = 2 * (invol2[i - 1] + (i - 1) * invol2[i - 2]);
// cerr<<"invol = "<<invol<<endl;
// cerr<<"invol2 = "<<invol2<<endl;
    }
// cerr<<"<s, r^2>: ";for(int N=0;N<=20;++N)cerr<<calc_s_r2(N)<<" ";cerr<<endl;
// cerr<<"<r>: "     ;for(int N=0;N<=20;++N)cerr<<calc_r   (N)<<" ";cerr<<endl;
    
    for (int t = 0; t < T; ++t) {
      const int N = Ns[t];
      Mint ans;
      if (N == 1) {
        ans = 1;
      } else {
        ans = 0;
        ans += 6 * calc_s_r2(N);
        ans -= 2 * calc_r(N);
        ans -= 4 * (calc_s(N) + calc_sr2(N) + calc_r2(N));
        ans += 8 * calc_1(N);
      }
      printf("%u\n", ans.x);
    }
  }
  return 0;
}