#991122 (C++17) No.2801 Unique Maximum

提出ソース

結果

問題	No.2801 Unique Maximum
ユーザー	shobonvip
提出日時	2024-06-28 20:30:01
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	8,249 bytes
コンパイル時間	5,255 ms
コンパイル使用メモリ	281,952 KB
実行使用メモリ	55,468 KB
最終ジャッジ日時	2024-06-28 20:30:24
合計ジャッジ時間	16,813 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

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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	6 ms 12,032 KB
testcase_01	AC	81 ms 12,280 KB
testcase_02	TLE	-
testcase_03	--	-
testcase_04	--	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-

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ソースコード

raw source code

#include<bits/stdc++.h>
using namespace std;

//* ATCODER
#include<atcoder/all>
using namespace atcoder;
typedef modint998244353 mint;
//*/

/* BOOST MULTIPRECISION
#include<boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
//*/

typedef long long ll;

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)

template <typename T> bool chmin(T &a, const T &b) {
	if (a <= b) return false;
	a = b;
	return true;
}

template <typename T> bool chmax(T &a, const T &b) {
	if (a >= b) return false;
	a = b;
	return true;
}

template <typename T> T max(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]);
	return ret;
}

template <typename T> T min(vector<T> &a){
	assert(!a.empty());
	T ret = a[0];
	for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]);
	return ret;
}

template <typename T> T sum(vector<T> &a){
	T ret = 0;
	for (int i=0; i<(int)a.size(); i++) ret += a[i];
	return ret;
}

// importbisect
template <typename T>
int bisect_left(vector<T> &X, T v){
	return lower_bound(X.begin(), X.end(), v) - X.begin();
}

template <typename T>
int bisect_right(vector<T> &X, T v){
	return upper_bound(X.begin(), X.end(), v) - X.begin();
}
// ----

// defcomp
template <typename T>
vector<T> compress(vector<T> &X) {
	vector<T> vals = X;
	sort(vals.begin(), vals.end());
	vals.erase(unique(vals.begin(), vals.end()), vals.end());
	return vals;
}
// -----

//defmodfact
const int COMinitMAX = 1100000;
mint fact[COMinitMAX+1], factinv[COMinitMAX+1];

void modfact(){
	fact[0] = 1;
	for (int i=1; i<=COMinitMAX; i++){
		fact[i] = fact[i-1] * i;
	}
	factinv[COMinitMAX] = fact[COMinitMAX].inv();
	for (int i=COMinitMAX-1; i>=0; i--){
		factinv[i] = factinv[i+1] * (i+1);
	}
}

mint cmb(int a, int b){
	if (a<b || b<0) return mint(0);
	return fact[a]*factinv[b]*factinv[a-b];
}
//--------

// makediv
vector<ll> makediv(ll n){
	vector<ll> ld, ud;
	for (ll i=1; i*i<=n; i++){
		if (n%i == 0){
			ld.push_back(i);
			if (i != n/i){
				ud.push_back(n/i);
			}
		}
	}
	reverse(ud.begin(), ud.end());
	ld.insert(ld.end(), ud.begin(), ud.end());
	return ld;
}
// -----

// Fast Factorization
// https://judge.yosupo.jp/submission/38126
// !!! CHANGED THE PRIMARY TEST !!!
typedef unsigned int uint;

struct Mint {
	uint64_t n;
	static uint64_t mod, inv, r2;
	Mint() : n(0) { }
	Mint(const uint64_t &x) : n(init(x)) { }
	static uint64_t init(const uint64_t &w) { return reduce(__uint128_t(w) * r2); }
	static void set_mod(const uint64_t &m) {
		mod = inv = m;
		for(int i = 0; i < 5; i++)	inv *= 2 - inv * m;
		r2 = -__uint128_t(m) % m;
	}
	static uint64_t reduce(const __uint128_t &x) {
		uint64_t y = uint64_t(x >> 64) - uint64_t((__uint128_t(uint64_t(x) * inv) * mod) >> 64);
		return int64_t(y) < 0 ? y + mod : y;
	}
	Mint& operator+= (const Mint &x) { n += x.n - mod; if(int64_t(n) < 0) n += mod; return *this; }
	Mint& operator+ (const Mint &x) const { return Mint(*this) += x; }
	Mint& operator*= (const Mint &x) { n = reduce(__uint128_t(n) * x.n); return *this; }
	Mint& operator* (const Mint &x) const { return Mint(*this) *= x; }
	uint64_t val() const { return reduce(n); }
};

uint64_t Mint::mod, Mint::inv, Mint::r2;

bool suspect(const uint64_t &a, const uint64_t &s, uint64_t d, const uint64_t &n) {
	if(Mint::mod != n)	Mint::set_mod(n);
	Mint x(1), xx(a), o(x), m(n - 1);
	while(d > 0) {
		if(d & 1)	x *= xx;
		xx *= xx;
		d >>= 1;
	}
	if(x.n == o.n)	return true;
	for(uint r = 0; r < s; r++) {
		if(x.n == m.n)	return true;
		x *= x;
	}
	return false;
}

bool is_prime(const uint64_t &n) {
	if(n <= 1 || (n > 2 && (~n & 1)))	return false;
	uint64_t d = n - 1, s = 0;
	while(~d & 1)	s++, d >>= 1;
	static const uint64_t a_big[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
	static const uint64_t a_smo[] = {2, 7, 61};
	if(n < 4759123141LL) {
		for(auto &&p : a_smo) {
			if(p >= n)	break;
			if(!suspect(p, s, d, n))	return false;
		}
	} else {
		for(auto &&p : a_big) {
			if(p >= n)	break;
			if(!suspect(p, s, d, n))	return false;
		}
	}
	return true;
}

uint64_t rho_pollard(const uint64_t &n) {
	if(~n & 1)	return 2u;
	static random_device rng;
	uniform_int_distribution<uint64_t> rr(1, n - 1);
	if(Mint::mod != n)	Mint::set_mod(n);
	for(;;) {
		uint64_t c_ = rr(rng), g = 1, r = 1, m = 500;
		Mint y(rr(rng)), xx(0), c(c_), ys(0), q(1);
		while(g == 1) {
			xx.n = y.n;
			for(uint i = 1; i <= r; i++)	y *= y, y += c;
			uint64_t k = 0; g = 1;
			while(k < r && g == 1) {
				for(uint i = 1; i <= (m > (r - k) ? (r - k) : m); i++) {
					ys.n = y.n;
					y *= y; y += c;
					uint64_t xxx = xx.val(), yyy = y.val();
					q *= Mint(xxx > yyy ? xxx - yyy : yyy - xxx);
				}
				g = __gcd<uint64_t>(q.val(), n);
				k += m;
			}
			r *= 2;
		}
		if(g == n)	g = 1;
		while(g == 1) {
			ys *= ys; ys += c;
			uint64_t xxx = xx.val(), yyy = ys.val();
			g = __gcd<uint64_t>(xxx > yyy ? xxx - yyy : yyy - xxx, n);
		}
		if(g != n && is_prime(g))	return g;
	}
	assert(69 == 420);
}

template <typename T>
vector<T> inter_factor(const T &n) {
	if(n < 2)	return { };
	if(is_prime(n))	return {n};
	T d = rho_pollard(static_cast<uint64_t>(n));
	vector<T> l = inter_factor(d), r = inter_factor(n / d);
	l.insert(l.end(), r.begin(), r.end());
	return l;
}

template <typename T>
vector<T> factor(T n) {
	vector<T> f1;
	for(uint i = 2; i < 100; i += (i & 1) + 1)
		while(n % i == 0)	f1.push_back(i), n /= i;
	vector<T> f2 = inter_factor(n);
	f1.insert(f1.end(), f2.begin(), f2.end());
	sort(f1.begin(), f1.end());
	return f1;
}



// COMPOSITION
// https://qoj.ac/submission/356957
// hos_lyricさんの提出を改変
/*
  q: rev([0, m]) * [0, n], [t^0] q(t, x) = 1 omitted
  ret: [0, m-1] * [0, n]
*/

vector<mint> comRec(int m, int n, const vector<mint> &as, const vector<mint> &qss) {
  if (!n) { auto ret = as; ret.resize(m, 0); return ret; }
  // reuse DFT(q(t, -x)); (2n+2) instead of (2n+1)
  int len;
  for (len = 2; len < (2*m) * (2*n+2); len <<= 1) {}
  vector<mint> qs(len, 0);
  for (int i = 0; i < m; ++i) for (int j = 0; j <= n; ++j) qs[i * (2*n+2) + j] = qss[i * (n+1) + j];
  internal::butterfly(qs);
  vector<mint> work(len >> 1, 0);
  for (int k = 0; k < len >> 1; ++k) { work[k] = qs[k << 1] * qs[k << 1 | 1]; swap(qs[k << 1], qs[k << 1 | 1]); }
  internal::butterfly_inv(work);
  {
	mint tmp = mint((int)work.size()).inv();
	for (int k = 0; k < len >> 1; ++k) work[k] *= tmp;
  }
  vector<mint> qqss((2*m) * (n/2+1), 0);
  for (int i = 0; i < 2*m-1; ++i) for (int j = 0; j <= n/2; ++j) qqss[i * (n/2+1) + j] = work[i * (n+1) + j];
  for (int i = 0; i < m; ++i) for (int j = 0; j <= n/2; ++j) qqss[(m+i) * (n/2+1) + j] += qss[i * (n+1) + 2*j] + qss[i * (n+1) + 2*j];
  const auto res = comRec(2*m, n/2, as, qqss);
  vector<mint> ps(len, 0);
  for (int i = 0; i < 2*m; ++i) for (int j = 0; j <= n/2; ++j) ps[i * (2*n+2) + (2*n+1) - (2*j+(n&1))] = res[i * (n/2+1) + j];
  internal::butterfly(ps);
  for (int k = 0; k < len; ++k) ps[k] *= qs[k];
  internal::butterfly_inv(ps);
  {
	mint tmp = mint((int)ps.size()).inv();
    for (int k = 0; k < len; ++k) ps[k] *= tmp;
  }
  vector<mint> ret(m * (n+1));
  for (int i = 0; i < m; ++i) for (int j = 0; j <= n; ++j) ret[i * (n+1) + j] = ps[(m+i) * (2*n+2) + (2*n+1) - j];
  for (int i = 0; i < m; ++i) for (int j = 0; j <= n/2; ++j) ret[i * (n+1) + (2*j+(n&1))] += res[i * (n/2+1) + j];
  return ret;
}

/*
  a(b(x))
  transpose and rev: p(x) -> [x^(N-1)] p(x) b(x)^i for each i
  [x^(N-1)] p(x) / (1 - t b(x))
*/
vector<mint> com(int n, const vector<mint> &as, const vector<mint> &bs) {
  assert((int)as.size() <= n);
  assert((int)bs.size() <= n);
  vector<mint> qss(n, 0);
  for (int j = 0; j < (int)bs.size(); ++j) qss[j] = -bs[j];
  auto cs = comRec(1, n - 1, as, qss);
  reverse(cs.begin(), cs.end());
  return cs;
}




int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	int n, m; cin >> n >> m;
	n++;

	vector g(30, vector<mint>(n+1));
	g[0][1] = 1;
	g[0][2] = 1;

	rep(i,0,29){
		g[i+1] = com(n+1, g[i], g[i]);
		g[i+1].resize(n+1);
	}

	vector<mint> f(n+1);
	f[1] = 1;
	rep(i,0,30){
		if (m>>i&1){
			vector<mint> nf = com(n+1, f, g[i]);
			f = nf;
			f.resize(n+1);
		}	
	}

	cout << f[n].val() << '\n';
}

yukicoder

結果

テストケース

ソースコード