結果

問題 No.2605 Pickup Parentheses
ユーザー MisukiMisuki
提出日時 2024-01-12 22:35:19
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 318 ms / 2,000 ms
コード長 13,438 bytes
コンパイル時間 2,425 ms
コンパイル使用メモリ 213,936 KB
実行使用メモリ 15,504 KB
最終ジャッジ日時 2024-09-30 06:27:23
合計ジャッジ時間 8,062 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 5 ms
6,820 KB
testcase_01 AC 5 ms
6,820 KB
testcase_02 AC 4 ms
6,820 KB
testcase_03 AC 5 ms
6,816 KB
testcase_04 AC 6 ms
6,820 KB
testcase_05 AC 6 ms
6,816 KB
testcase_06 AC 7 ms
6,820 KB
testcase_07 AC 6 ms
6,820 KB
testcase_08 AC 7 ms
6,816 KB
testcase_09 AC 5 ms
6,820 KB
testcase_10 AC 6 ms
6,816 KB
testcase_11 AC 6 ms
6,816 KB
testcase_12 AC 5 ms
6,820 KB
testcase_13 AC 5 ms
6,816 KB
testcase_14 AC 4 ms
6,816 KB
testcase_15 AC 5 ms
6,820 KB
testcase_16 AC 5 ms
6,820 KB
testcase_17 AC 5 ms
6,816 KB
testcase_18 AC 151 ms
10,028 KB
testcase_19 AC 79 ms
8,176 KB
testcase_20 AC 18 ms
6,816 KB
testcase_21 AC 13 ms
6,820 KB
testcase_22 AC 7 ms
6,820 KB
testcase_23 AC 162 ms
10,212 KB
testcase_24 AC 18 ms
6,820 KB
testcase_25 AC 179 ms
10,716 KB
testcase_26 AC 194 ms
11,372 KB
testcase_27 AC 153 ms
10,824 KB
testcase_28 AC 9 ms
6,816 KB
testcase_29 AC 21 ms
6,816 KB
testcase_30 AC 48 ms
7,188 KB
testcase_31 AC 6 ms
6,816 KB
testcase_32 AC 5 ms
6,820 KB
testcase_33 AC 98 ms
8,724 KB
testcase_34 AC 8 ms
6,816 KB
testcase_35 AC 5 ms
6,816 KB
testcase_36 AC 8 ms
6,816 KB
testcase_37 AC 81 ms
8,060 KB
testcase_38 AC 35 ms
8,004 KB
testcase_39 AC 13 ms
6,820 KB
testcase_40 AC 86 ms
9,936 KB
testcase_41 AC 79 ms
10,708 KB
testcase_42 AC 112 ms
10,328 KB
testcase_43 AC 24 ms
6,992 KB
testcase_44 AC 21 ms
7,024 KB
testcase_45 AC 5 ms
6,816 KB
testcase_46 AC 11 ms
6,820 KB
testcase_47 AC 4 ms
6,820 KB
testcase_48 AC 6 ms
6,820 KB
testcase_49 AC 62 ms
8,160 KB
testcase_50 AC 27 ms
6,828 KB
testcase_51 AC 5 ms
6,816 KB
testcase_52 AC 41 ms
7,900 KB
testcase_53 AC 60 ms
8,224 KB
testcase_54 AC 28 ms
7,056 KB
testcase_55 AC 46 ms
8,028 KB
testcase_56 AC 12 ms
6,816 KB
testcase_57 AC 5 ms
6,816 KB
testcase_58 AC 265 ms
15,504 KB
testcase_59 AC 159 ms
11,332 KB
testcase_60 AC 207 ms
11,896 KB
testcase_61 AC 196 ms
11,824 KB
testcase_62 AC 215 ms
11,352 KB
testcase_63 AC 210 ms
11,296 KB
testcase_64 AC 244 ms
11,904 KB
testcase_65 AC 168 ms
11,440 KB
testcase_66 AC 318 ms
14,172 KB
testcase_67 AC 194 ms
11,844 KB
testcase_68 AC 5 ms
6,816 KB
testcase_69 AC 6 ms
6,820 KB
testcase_70 AC 5 ms
6,820 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

diff # 

#pragma GCC optimize("O2")
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <compare>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numbers>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>

//#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#ifdef DEBUG
#define dbg(x) cout << (#x) << " = " << x << '\n'
#else
#define dbg(x)
#endif

namespace R = std::ranges;
namespace V = std::views;

using namespace std;

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
//#define double ldb

template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(const T &X : arr)
    os << X << ' ';
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(const T &X : vec)
    os << X << ' ';
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(const T &x : s)
    os << x << ' ';
  return os;
}

/**
 * template name: MontgomeryModInt
 * author: Misuki
 * reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
 * last update: 2023/11/30
 * note: mod should be a prime less than 2^30.
 */

template<uint32_t mod>
struct MontgomeryModInt {
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 res = 1, base = mod;
    for(i32 i = 0; i < 31; i++)
      res *= base, base *= base;
    return -res;
  }

  static constexpr u32 get_mod() {
    return mod;
  }

  static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
  static constexpr u32 r = get_r(); //-P^{-1} % 2^32

  u32 a;

  static u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * r) * mod) >> 32;
  }

  static u32 transform(const u64 &b) {
    return reduce(u64(b) * n2);
  }

  MontgomeryModInt() : a(0) {}
  MontgomeryModInt(const int64_t &b) 
    : a(transform(b % mod + mod)) {}

  mint pow(u64 k) const {
    mint res(1), base(*this);
    while(k) {
      if (k & 1) 
        res *= base;
      base *= base, k >>= 1;
    }
    return res;
  }

  mint inverse() const { return (*this).pow(mod - 2); }

  u32 get() const {
    u32 res = reduce(a);
    return res >= mod ? res - mod : res;
  }

  mint& operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  mint& operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  mint& operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  mint& operator/=(const mint &b) {
    a = reduce(u64(a) * b.inverse().a);
    return *this;
  }

  mint operator-() { return mint() - mint(*this); }
  bool operator==(mint b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(mint b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }

  friend mint operator+(mint a, mint b) { return a += b; }
  friend mint operator-(mint a, mint b) { return a -= b; }
  friend mint operator*(mint a, mint b) { return a *= b; }
  friend mint operator/(mint a, mint b) { return a /= b; }

  friend ostream& operator<<(ostream& os, const mint& b) {
    return os << b.get();
  }
  friend istream& operator>>(istream& is, mint& b) {
    int64_t val;
    is >> val;
    b = mint(val);
    return is;
  }
};

using mint = MontgomeryModInt<998244353>;

/**
 * template name: comb
 * author: Misuki
 * last update: 2023/01/22
 * note: remember to call init() before using it.
 */

const int MAX = 200002;
mint fac[MAX], facInv[MAX], pow2[MAX];
void init() {
  fac[0] = 1;
  for(int i = 1; i < MAX; i++)
    fac[i] = fac[i - 1] * i;
  facInv[MAX - 1] = 1 / fac[MAX - 1];
  for(int i = MAX - 2; i >= 0; i--)
    facInv[i] = facInv[i + 1] * (i + 1);
  pow2[0] = 1;
  for(int i = 1; i < MAX; i++)
    pow2[i] = pow2[i - 1] * 2;
}

mint binom(int a, int b) {
  if (b < 0 or a < b)
    return 0;
  else
    return fac[a] * facInv[b] * facInv[a - b];
}

mint C(int k) {
  return fac[k] * facInv[k + 1] * binom(2 * k, k);
}

/**
 * template name: NTTmint
 * reference: https://judge.yosupo.jp/submission/69896
 * last update: 2024/01/07
 * include: mint
 * remark: MOD = 2^K * C + 1, R is a primitive root modulo MOD
 * remark: a.size() <= 2^K must be satisfied
 * some common modulo: 998244353  = 2^23 * 119 + 1, R = 3
 *                     469762049  = 2^26 * 7   + 1, R = 3
 *                     1224736769 = 2^24 * 73  + 1, R = 3
 * verify: Library Checker - Convolution
 */

template<int32_t k = 23, int32_t c = 119, int32_t r = 3, class Mint = MontgomeryModInt<998244353>>
struct NTT {

  using u32 = uint32_t;
  static constexpr u32 mod = (1 << k) * c + 1;
  static constexpr u32 get_mod() { return mod; }

  static void ntt(vector<Mint> &a, bool inverse) {
    static array<Mint, 30> w, w_inv;
    if (w[0] == 0) {
      Mint root = 2;
      while(root.pow((mod - 1) / 2) == 1) root += 1;
      for(int i = 0; i < 30; i++)
        w[i] = -(root.pow((mod - 1) >> (i + 2))), w_inv[i] = 1 / w[i];
    }
    int n = ssize(a);
    if (not inverse) {
      for(int m = n; m >>= 1; ) {
        Mint ww = 1;
        for(int s = 0, l = 0; s < n; s += 2 * m) {
          for(int i = s, j = s + m; i < s + m; i++, j++) {
            Mint x = a[i], y = a[j] * ww;
            a[i] = x + y, a[j] = x - y;
          }
          ww *= w[__builtin_ctz(++l)];
        }
      }
    } else {
      for(int m = 1; m < n; m *= 2) {
        Mint ww = 1;
        for(int s = 0, l = 0; s < n; s += 2 * m) {
          for(int i = s, j = s + m; i < s + m; i++, j++) {
            Mint x = a[i], y = a[j];
            a[i] = x + y, a[j] = (x - y) * ww;
          }
          ww *= w_inv[__builtin_ctz(++l)];
        }
      }
      Mint inv = 1 / Mint(n);
      for(Mint &x : a) x *= inv;
    }
  }

  static vector<Mint> conv(vector<Mint> a, vector<Mint> b) {
    int sz = ssize(a) + ssize(b) - 1;
    int n = bit_ceil((u32)sz);

    a.resize(n, 0);
    ntt(a, false);
    b.resize(n, 0);
    ntt(b, false);

    for(int i = 0; i < n; i++)
      a[i] *= b[i];

    ntt(a, true);

    a.resize(sz);

    return a;
  }
};

/**
 * template name: FPS
 * author: Misuki
 * last update: 2024/01/10
 * include: NTT/mint
 * verify: Library Checker - Inv of Formal Power Series
 *         Library Checker - Exp of Formal Power Series
 *         Library Checker - Log of Formal Power Series
 *         Library Checker - Pow of Formal Power Series
 *         Library Checker - Convolution
 *         Library Checker - Division of Polynomials
 *         Library Checker - Multipoint Evaluation
 *         Library Checker - Polynomial Interpolation
 */

template<class Mint>
struct FPS : vector<Mint> {

  static function<vector<Mint>(vector<Mint>, vector<Mint>)> conv;

  FPS(vector<Mint> v) { *this = v; }

  using vector<Mint>::vector;
  FPS& operator+=(FPS b) {
    if (ssize(*this) < ssize(b)) this -> resize(ssize(b), 0);
    for(int i = 0; i < ssize(b); i++)
      (*this)[i] += b[i];
    return *this;
  }

  FPS& operator-=(FPS b) {
    if (ssize(*this) < ssize(b)) this -> resize(ssize(b), 0);
    for(int i = 0; i < ssize(b); i++)
      (*this)[i] -= b[i];
    return *this;
  }

  FPS& operator*=(FPS b) {
    auto c = conv(*this, b);
    this -> resize(ssize(*this) + ssize(b) - 1);
    copy(c.begin(), c.end(), this -> begin());
    return *this;
  }

  FPS& operator*=(Mint b) {
    for(int i = 0; i < ssize(*this); i++)
      (*this)[i] *= b;
    return *this;
  }

  FPS& operator/=(Mint b) {
    b = Mint(1) / b;
    for(int i = 0; i < ssize(*this); i++)
      (*this)[i] *= b;
    return *this;
  }

  FPS shrink() {
    FPS F = *this;
    while(ssize(F) > 1 and F.back() == 0)
      F.pop_back();
    return F;
  }

  FPS integral() {
    vector<Mint> Inv(ssize(*this) + 1);
    Inv[1] = 1;
    for(int i = 2; i < ssize(Inv); i++)
      Inv[i] = (Mint::get_mod() - Mint::get_mod() / i) * Inv[Mint::get_mod() % i];
    FPS Q(ssize(*this) + 1, 0);
    for(int i = 0; i < ssize(*this); i++)
      Q[i + 1] = (*this)[i] * Inv[i + 1];
    return Q;
  }

  FPS derivative() {
    assert(!this -> empty());
    FPS Q(ssize(*this) - 1);
    for(int i = 1; i < ssize(*this); i++)
      Q[i - 1] = (*this)[i] * i;
    return Q;
  }

  Mint eval(Mint x) {
    Mint base = 1, res = 0;
    for(int i = 0; i < ssize(*this); i++, base *= x)
      res += (*this)[i] * base;
    return res;
  }

  FPS inv(int k) { // 1 / FPS (mod x^k)
    assert(!this -> empty() and (*this)[0] != 0);
    FPS Q(1, 1 / (*this)[0]);
    for(int i = 1; (1 << (i - 1)) < k; i++) {
      FPS P = (*this);
      P.resize(1 << i, 0);
      Q = Q * (FPS(1, 2) - P * Q);
      Q.resize(1 << i, 0);
    }
    Q.resize(k);
    return Q;
  }

  array<FPS, 2> div(FPS G) {
    FPS F = this -> shrink();
    G = G.shrink();
    assert(!G.empty());
    if (ssize(G) > ssize(F))
      return {{{}, F}};
    int n = ssize(F) - ssize(G) + 1;
    auto FR = F, GR = G;
    R::reverse(FR);
    R::reverse(GR);
    FPS Q = FR * GR.inv(n);
    Q.resize(n);
    R::reverse(Q);
    return {Q, (F - G * Q).shrink()};
  }

  FPS log(int k) {
    assert(!this -> empty() and (*this)[0] == 1);
    FPS Q = *this;
    Q = (Q.derivative() * Q.inv(k));
    Q.resize(k - 1);
    return Q.integral();
  }

  FPS exp(int k) {
    assert(!this -> empty() and (*this)[0] == 0);
    FPS Q(1, 1);
    for(int i = 1; (1 << (i - 1)) < k; i++) {
      FPS P = (*this);
      P.resize(1 << i, 0);
      Q = Q * (FPS(1, 1) + P - Q.log(1 << i));
      Q.resize(1 << i, 0);
    }
    Q.resize(k);
    return Q;
  }

  FPS pow(ll idx, int k) {
    if (idx == 0) {
      FPS res(k, 0);
      res[0] = 1;
      return res;
    }
    for(int i = 0; i < ssize(*this) and i * idx < k; i++) {
      if ((*this)[i] != 0) {
        Mint Inv = 1 / (*this)[i];
        FPS Q(ssize(*this) - i);
        for(int j = i; j < ssize(*this); j++)
          Q[j - i] = (*this)[j] * Inv;
        Q = (Q.log(k) * idx).exp(k);
        FPS Q2(k, 0);
        Mint Pow = (*this)[i].pow(idx);
        for(int j = 0; j + i * idx < k; j++)
          Q2[j + i * idx] = Q[j] * Pow;
        return Q2;
      }
    } 
    return FPS(k, 0);
  }

  vector<Mint> multieval(vector<Mint> xs) {
    int n = ssize(xs);
    vector<FPS> data(2 * n);
    for(int i = 0; i < n; i++)
      data[n + i] = {-xs[i], 1};
    for(int i = n - 1; i > 0; i--)
      data[i] = data[i << 1] * data[i << 1 | 1];
    data[1] = (this -> div(data[1]))[1];
    for(int i = 1; i < n; i++) {
      data[i << 1] = data[i].div(data[i << 1])[1];
      data[i << 1 | 1] = data[i].div(data[i << 1 | 1])[1];
    }
    vector<Mint> res(n);
    for(int i = 0; i < n; i++)
      res[i] = data[n + i][0];
    return res;
  }

  static vector<Mint> interpolate(vector<Mint> xs, vector<Mint> ys) {
    assert(ssize(xs) == ssize(ys));
    int n = ssize(xs);
    vector<FPS> data(2 * n), res(2 * n);
    for(int i = 0; i < n; i++)
      data[n + i] = {-xs[i], 1};
    for(int i = n - 1; i > 0; i--)
      data[i] = data[i << 1] * data[i << 1 | 1];
    res[1] = data[1].derivative().div(data[1])[1];
    for(int i = 1; i < n; i++) {
      res[i << 1] = res[i].div(data[i << 1])[1];
      res[i << 1 | 1] = res[i].div(data[i << 1 | 1])[1];
    }
    for(int i = 0; i < n; i++)
      res[n + i][0] = ys[i] / res[n + i][0];
    for(int i = n - 1; i > 0; i--)
      res[i] = res[i << 1] * data[i << 1 | 1] + res[i << 1 | 1] * data[i << 1];
    return res[1];
  }

  friend FPS operator+(FPS a, FPS b) { return a += b; }
  friend FPS operator-(FPS a, FPS b) { return a -= b; }
  friend FPS operator*(FPS a, FPS b) { return a *= b; }
  friend FPS operator*(FPS a, Mint b) { return a *= b; }
  friend FPS operator/(FPS a, Mint b) { return a /= b; }
};

NTT ntt;
using fps = FPS<mint>;
template<>
function<vector<mint>(vector<mint>, vector<mint>)> fps::conv = ntt.conv;

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  init();

  int n, m; cin >> n >> m;
  vector<fps> poly;
  poly.push_back(fps(1, 1));
  while(m--) {
    int l, r; cin >> l >> r;
    if ((r - l + 1) % 2 == 0) {
      poly.push_back(fps(r - l + 2, 0));
      poly.back()[0] = 1, poly.back().back() = -C((r - l + 1) / 2);
    }
  }

  if (n & 1) {
    cout << 0 << '\n';
    return 0;
  }

  auto calc = [&](int l, int r, auto self) -> fps {
    if (l + 1 == r)
      return poly[l];
    else
      return self(l, (l + r) / 2, self) * self((l + r) / 2, r, self);
  };

  auto f = calc(0, ssize(poly), calc);
  mint ans = 0;
  for(int i = 0; i < ssize(f); i += 2)
    ans += f[i] * C((n - i) / 2);

  cout << ans << '\n';

  return 0;
}
0