#945965 (C++23) No.2613 Sum of Combination

提出ソース

結果

問題	No.2613 Sum of Combination
ユーザー	Misuki
提出日時	2024-01-23 17:41:40
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	213 ms / 4,500 ms
コード長	9,975 bytes
コンパイル時間	3,730 ms
コンパイル使用メモリ	232,076 KB
実行使用メモリ	14,940 KB
最終ジャッジ日時	2024-09-28 06:49:58
合計ジャッジ時間	9,231 ms
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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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	6 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	1 ms 5,376 KB
testcase_10	AC	1 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	8 ms 5,376 KB
testcase_14	AC	8 ms 5,376 KB
testcase_15	AC	5 ms 5,376 KB
testcase_16	AC	8 ms 5,376 KB
testcase_17	AC	8 ms 5,376 KB
testcase_18	AC	8 ms 5,376 KB
testcase_19	AC	9 ms 5,376 KB
testcase_20	AC	3 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	15 ms 5,376 KB
testcase_23	AC	199 ms 14,088 KB
testcase_24	AC	199 ms 14,068 KB
testcase_25	AC	191 ms 13,012 KB
testcase_26	AC	205 ms 14,856 KB
testcase_27	AC	102 ms 9,388 KB
testcase_28	AC	198 ms 14,784 KB
testcase_29	AC	197 ms 14,320 KB
testcase_30	AC	199 ms 14,868 KB
testcase_31	AC	206 ms 14,508 KB
testcase_32	AC	200 ms 14,256 KB
testcase_33	AC	201 ms 14,916 KB
testcase_34	AC	198 ms 14,916 KB
testcase_35	AC	201 ms 14,920 KB
testcase_36	AC	202 ms 14,940 KB
testcase_37	AC	198 ms 14,916 KB
testcase_38	AC	191 ms 14,832 KB
testcase_39	AC	197 ms 14,760 KB
testcase_40	AC	194 ms 14,888 KB
testcase_41	AC	197 ms 14,700 KB
testcase_42	AC	213 ms 14,688 KB
testcase_43	AC	196 ms 14,756 KB
testcase_44	AC	196 ms 14,912 KB
testcase_45	AC	2 ms 5,376 KB
testcase_46	AC	2 ms 5,376 KB
testcase_47	AC	2 ms 5,376 KB
testcase_48	AC	2 ms 5,376 KB
testcase_49	AC	2 ms 5,376 KB
testcase_50	AC	198 ms 14,912 KB
testcase_51	AC	197 ms 14,892 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

#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)

#define clock chrono::steady_clock::now().time_since_epoch().count()

#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;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
//#define double ldb

template<class T>
ostream& operator<<(ostream& os, const pair<T, T> pr) {
  return os << pr.first << ' ' << pr.second;
}
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: 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;
  }
};

//source: KACTL(https://github.com/kth-competitive-programming/kactl)

ull modmul(ull a, ull b, ull M) {
	ll ret = a * b - M * ull(1.L / M * a * b);
	return ret + M * (ret < 0) - M * (ret >= (ll)M);
}

ull modpow(ull b, ull e, ull mod) {
	ull ans = 1;
	for (; e; b = modmul(b, b, mod), e /= 2)
		if (e & 1) ans = modmul(ans, b, mod);
	return ans;
}

bool isPrime(ull n) {
	if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
	ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
	    s = __builtin_ctzll(n-1), d = n >> s;
	for (ull a : A) {   // ^ count trailing zeroes
		ull p = modpow(a%n, d, n), i = s;
		while (p != 1 && p != n - 1 && a % n && i--)
			p = modmul(p, p, n);
		if (p != n-1 && i != s) return 0;
	}
	return 1;
}

ull pollard(ull n) {
  static mt19937_64 rng(clock);
  uniform_int_distribution<ull> unif(0, n - 1);
  ull c = 1;
	auto f = [n, &c](ull x) { return modmul(x, x, n) + c % n; };
	ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
	while (t++ % 40 || __gcd(prd, n) == 1) {
		if (x == y) c = unif(rng), x = ++i, y = f(x);
		if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
		x = f(x), y = f(f(y));
	}
	return __gcd(prd, n);
}

vector<ull> factor(ull n) {
	if (n == 1) return {};
	if (isPrime(n)) return {n};
	ull x = pollard(n);
	auto l = factor(x), r = factor(n / x);
	l.insert(l.end(), r.begin(), r.end());
	return l;
}

//#include "fastFactorize.cpp"

ull primitiveRoot(ull p) {
  auto fac = factor(p - 1);
  R::sort(fac);
  fac.resize(unique(fac.begin(), fac.end()) - fac.begin());
  auto test = [p, fac](ull x) {
    for(ull d : fac)
      if (modpow(x, (p - 1) / d, p) == 1)
        return false;
    return true;
  };
  static mt19937_64 rng(clock);
  uniform_int_distribution<ull> unif(1, p - 1);
  ull root;
  while(!test(root = unif(rng)));
  return root;
}

struct mulConvolution {
  const int P, root;
  vector<int> powR, logR;

  mulConvolution(int _P) : P(_P), root(primitiveRoot(_P)), powR(P - 1), logR(P) {
    for(int i = 0, tmp = 1; i < P - 1; i++, tmp = (ll)tmp * root % P)
      powR[i] = tmp, logR[tmp] = i;
  }

  template<class Mint>
  vector<Mint> transform(vector<Mint> &f) {
    assert(ssize(f) == P);
    vector<Mint> g(P - 1);
    for(int i = 1; i < P; i++)
      g[logR[i]] = f[i];
    return g;
  }

  template<class Mint>
  vector<Mint> invTransform(vector<Mint> &f) {
    assert(ssize(f) == P - 1);
    vector<Mint> g(P);
    for(int i = 0; i < P - 1; i++)
      g[powR[i]] = f[i];
    return g;
  }
};

int p;
int fac[200000], facInv[200000];
int C(int a, int b) {
  if (b > a or b < 0) return 0;
  else return (ll)fac[a] * facInv[b] % p * facInv[a - b] % p;
}

NTT ntt;

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

  ll n; cin >> n >> p;

  fac[0] = 1;
  for(int i = 1; i < p; i++)
    fac[i] = (ll)fac[i - 1] * i % p;
  facInv[p - 1] = modpow(fac[p - 1], p - 2, p);
  for(int i = p - 2; i >= 0; i--)
    facInv[i] = (ll)facInv[i + 1] * (i + 1) % p;

  mulConvolution mu(p);

  vector<mint> f(p - 1);
  f[0] = 1;
  while(n) {
    int nd = n % p; n /= p;
    vector<mint> g(p);
    for(int i = 0; i < p; i++)
      g[C(nd, i)] += 1;
    g = mu.transform(g);
    f = ntt.conv(f, g);
    for(int i = p - 1; i < 2 * p - 3; i++)
      f[i - (p - 1)] += f[i];
    f.resize(p - 1);
  }

  f = mu.invTransform(f);

  mint ans = 0;
  for(int i = 1; i < p; i++)
    ans += f[i] * i;

  cout << ans << '\n';

  return 0;
}

yukicoder

結果

テストケース

ソースコード