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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#417096#8721. 括号序列zhoukangyang#AC ✓1230ms33856kbC++148.8kb2024-05-22 14:17:512024-05-22 14:17:52

Judging History

你现在查看的是最新测评结果

  • [2024-05-22 14:17:52]
  • 评测
  • 测评结果:AC
  • 用时:1230ms
  • 内存:33856kb
  • [2024-05-22 14:17:51]
  • 提交

answer

#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); ++i)
#define R(i, j, k) for(int i = (j); i >= (k); --i)
#define ll long long
#define sz(a) ((int) (a).size())
#define vi vector < int >
#define me(a, x) memset(a, x, sizeof(a))
#define ull unsigned long long
#define ld __float128
#define pb emplace_back
using namespace std;
const int mod = 998244353, _G = 3, N = (1 << 21), inv2 = (mod + 1) / 2;
#define add(a, b) (a + b >= mod ? a + b - mod : a + b)
#define dec(a, b) (a < b ? a - b + mod : a - b)
int qpow(int x, int y = mod - 2) {
	int res = 1;
	for(; y; x = (ll) x * x % mod, y >>= 1) if(y & 1) res = (ll) res * x % mod;
	return res;
}
int fac[N + 1], ifac[N + 1], inv[N + 1];
void init(int x) {
	fac[0] = ifac[0] = inv[1] = 1;
	L(i, 2, x) inv[i] = (ll) inv[mod % i] * (mod - mod / i) % mod;
	L(i, 1, x) fac[i] = (ll) fac[i - 1] * i % mod, ifac[i] = (ll) ifac[i - 1] * inv[i] % mod;
}
int C(int x, int y) {
	return y < 0 || x < y ? 0 : (ll) fac[x] * ifac[y] % mod * ifac[x - y] % mod;
}
inline int sgn(int x) {
	return (x & 1) ? mod - 1 : 1;
}
int rt[N], Lim;
void Pinit(int x) {
	for(Lim = 1; Lim <= x; Lim <<= 1) ;
	for(int i = 1; i < Lim; i <<= 1) {
		int sG = qpow (_G, (mod - 1) / (i << 1));
		rt[i] = 1;
		L(j, i + 1, i * 2 - 1) rt[j] = (ll) rt[j - 1] * sG % mod;
	}
}
struct poly {
	vector<int> a;
	int size() { return sz(a); }
	int & operator [] (int x) { return a[x]; }
	int v(int x) { return x < 0 || x >= sz(a) ? 0 : a[x]; }
	void clear() { vector<int> ().swap(a); }
	void rs(int x = 0) { a.resize(x); }
	poly (int n = 0) { rs(n); }
	poly (vector<int> o) { a = o; }
	poly (const poly &o) { a = o.a; }
	poly Rs(int x = 0) { vi res = a; res.resize(x); return res; }
	inline void dif() {
		int n = sz(a);
		for (int l = n >> 1; l >= 1; l >>= 1) 
			for(int j = 0; j < n; j += l << 1) 
				for(int k = 0, *w = rt + l; k < l; k++, w++) {
					int x = a[j + k], y = a[j + k + l];
					a[j + k] = add(x, y);
					a[j + k + l] = (ll) * w * dec(x, y) % mod;
				}
	}
	void dit () {
		int n = sz(a);
		for(int i = 2; i <= n; i <<= 1) 
			for(int j = 0, l = (i >> 1); j < n; j += i) 
				for(int k = 0, *w = rt + l; k < l; k++, w++) {
					int pa = a[j + k], pb = (ll) a[j + k + l] * *w % mod;
					a[j + k] = add(pa, pb), a[j + k + l] = dec(pa, pb);
				}
		reverse(a.begin() + 1, a.end());
		for(int i = 0, iv = qpow(n); i < n; i++) a[i] = (ll) a[i] * iv % mod;
	} 
	friend poly operator * (poly aa, poly bb) {
		if(!sz(aa) || !sz(bb)) return {};
		int lim, all = sz(aa) + sz(bb) - 1;
		for(lim = 1; lim < all; lim <<= 1);
		aa.rs(lim), bb.rs(lim), aa.dif(), bb.dif();
		L(i, 0, lim - 1) aa[i] = (ll) aa[i] * bb[i] % mod;
		aa.dit(), aa.a.resize(all);
		return aa;
	}
	poly Inv() {
		poly res, f, g;
		res.rs(1), res[0] = qpow(a[0]);
		for(int m = 1, pn; m < sz(a); m <<= 1) {
			pn = m << 1, f = res, g.rs(pn), f.rs(pn);
			for(int i = 0; i < pn; i++) g[i] = (*this).v(i);
			f.dif(), g.dif();
			for(int i = 0; i < pn; i++) g[i] = (ll) f[i] * g[i] % mod;
			g.dit();
			for(int i = 0; i < m; i++) g[i] = 0;
			g.dif();
			for(int i = 0; i < pn; i++) g[i] = (ll) f[i] * g[i] % mod;
			g.dit(), res.rs(pn);
			for(int i = m; i < min(pn, sz(a)); i++) res[i] = (mod - g[i]) % mod;
		} 
		return res.rs(sz(a)), res;
	}
	poly Shift (int x) {
		poly zm (sz(a) + x);
		L(i, max(-x, 0), sz(a) - 1) zm[i + x] = a[i];
		return zm; 
	}
	friend poly operator * (poly aa, int bb) {
		poly res(sz(aa));
		L(i, 0, sz(aa) - 1) res[i] = (ll) aa[i] * bb % mod;
		return res;
	}
	friend poly operator + (poly aa, poly bb) {
		vector<int> res(max(sz(aa), sz(bb)));
		L(i, 0, sz(res) - 1) res[i] = add(aa.v(i), bb.v(i));
		return poly(res);
	}
	friend poly operator - (poly aa, poly bb) {
		vector<int> res(max(sz(aa), sz(bb)));
		L(i, 0, sz(res) - 1) res[i] = dec(aa.v(i), bb.v(i));
		return poly(res);
	}
	poly & operator += (poly o) {
		rs(max(sz(a), sz(o)));
		L(i, 0, sz(a) - 1) (a[i] += o.v(i)) %= mod;
		return (*this);
	}
	poly & operator -= (poly o) {
		rs(max(sz(a), sz(o)));
		L(i, 0, sz(a) - 1) (a[i] += mod - o.v(i)) %= mod;
		return (*this);
	}
	poly & operator *= (poly o) {
		return (*this) = (*this) * o;
	}
	poly Integ() {
		if(!sz(a)) return poly();
		poly res(sz(a) + 1);
		L(i, 1, sz(a)) res[i] = (ll) a[i - 1] * inv[i] % mod;
		return res;
	}
	poly Deriv() {
		if(!sz(a)) return poly();
		poly res(sz(a) - 1); 
		L(i, 1, sz(a) - 1) res[i - 1] = (ll) a[i] * i % mod;
		return res;
	}
	poly Ln() {
		poly g = ((*this).Inv() * (*this).Deriv()).Integ();
		return g.rs(sz(a)), g;
	}
	poly Exp() {
		poly res(1), f; 
		res[0] = 1;
		for(int m = 1, pn; m < sz(a); m <<= 1) {
			pn = min(m << 1, sz(a)), f.rs(pn), res.rs(pn);
			for(int i = 0; i < pn; i++) f[i] = (*this).v(i);
			f -= res.Ln(), (f[0] += 1) %= mod, res *= f, res.rs(pn); 
		}
		return res.rs(sz(a)), res;
	}
	poly pow(int x, int rx = -1) { // x : the power % mod; rx : the power % (mod - 1)
		if(rx == -1) rx = x;
		int cnt = 0;
		while (a[cnt] == 0 && cnt < sz(a)) cnt += 1;
		
		poly res = (*this);
		L(i, cnt, sz(a) - 1) res[i - cnt] = res[i];
		L(i, sz(a) - cnt, sz(a) - 1) res[i] = 0;
		int c = res[0], w = qpow (res[0]);
		L(i, 0, sz(res) - 1) res[i] = (ll) res[i] * w % mod;
		res = res.Ln();
		L(i, 0, sz(res) - 1) res[i] = (ll) res[i] * x % mod;
		res = res.Exp();
		c = qpow (c, rx);
		L(i, 0, sz(res) - 1) res[i] = (ll) res[i] * c % mod;
		
		if((ll) cnt * x > sz(a)) L(i, 0, sz(a) - 1) res[i] = 0;
		else if(cnt) {
			R(i, sz(a) - cnt * x - 1, 0) res[i + cnt * x] = res[i];
			L(i, 0, cnt * x - 1) res[i] = 0; 
		}
		return res;
	}
	poly sqrt(int rt = 1) {
		poly res(1), f; 
		res[0] = rt;
		for(int m = 1, pn; m < sz(a); m <<= 1) {
			pn = min(m << 1, sz(a)), f.rs(pn);
			for(int i = 0; i < pn; i++) f[i] = (*this).v(i);
			f += res * res, f.rs(pn), res.rs(pn), res = f * res.Inv(), res.rs(pn);
			for(int i = 0; i < pn; i++) res[i] = (ll) res[i] * inv2 % mod;
		} 
		return res;
	}
	void Rev() {
		reverse(a.begin(), a.end());
	}
	friend pair < poly, poly > div (poly f, poly g) { /* f / g = first, f % g = second */
		f.rs(max(sz(f), sz(g))), f.Rev(), g.Rev();
		int n = sz(f), m = sz(g);
		poly A = g.Rs(n - m + 1).Inv(), t;
		A *= f.Rs(n - m + 1), A.rs(n - m + 1), A.Rev(), g.Rev(), f.Rev(), t = f - A * g, t.rs(m - 1);
		return make_pair(A, t);
	} 
} ;

int n;
int a[N], b[N], c[N];
poly Mult(poly aa, poly bb, int len) {
	int lim, all = len;
	for(lim = 1; lim < all; lim <<= 1);
	aa.rs(lim), bb.rs(lim), aa.dif(), bb.dif();
	L(i, 0, lim - 1) aa[i] = (ll) aa[i] * bb[i] % mod;
	aa.dit(), aa.a.resize(all);
	return aa;
} 

void dc(int l, int r) {
	if(l == r) {
		if(l == 0) return ;
		int i = l;
		(a[i] += (ll) c[i] * 2 % mod) %= mod;
		// L(j, 1, i - 1) {
		// 	(a[i] += (ll) c[j] * a[i - j] % mod) %= mod;
		// }
		// (a[i] += c[i]) %= mod;
		a[i] = (ll)a[i] * inv[i] % mod;
		return;
	}
	int mid = (l + r) >> 1;
	dc(l, mid);
	{
		poly A(r - l + 1), B(mid - l + 1);
		L(i, 0, r - l) if(i <= mid) 
			A[i] = (ll) a[i] * ((l == 0 ? 1 : 2)) % mod;
		L(i, 0, mid - l)
			B[i] = a[i + l];
		A = Mult(A, B, r - l + 2);
		L(j, 0, r - l - 1) if(mid + 1 <= l + j + 1 && l + j + 1 <= r) {
			(c[l + j + 1] += A[j]) %= mod;
		}
	}
	{
		poly A(r - l + 1), B(mid - l + 1);
		L(i, 1, r - l) if(i <= mid) 
			A[i] = c[i];
		L(i, 0, mid - l)
			B[i] = a[i + l];
		A = Mult(A, B, r - l + 2);
		L(j, 0, r - l) if(mid + 1 <= l + j && l + j <= r) {
			(a[l + j] += A[j]) %= mod;
		}
	}
	if(l) {
		poly A(r - l + 1), B(mid - l + 1);
		L(i, 1, r - l) if(i <= mid) 
			A[i] = a[i];
		L(i, 0, mid - l)
			B[i] = c[i + l];
		A = Mult(A, B, r - l + 2);
		L(j, 0, r - l) if(mid + 1 <= l + j && l + j <= r) {
			(a[l + j] += A[j]) %= mod;
		}
	}
	dc(mid + 1, r);
}
void dc2(int l, int r) {
	if(l == r) {
		if(l == 0) return ;
		int i = l;
		(b[i] += c[i]) %= mod;
		b[i] = (ll)b[i] * inv[i] % mod;
		return;
	}
	int mid = (l + r) >> 1;
	dc2(l, mid);
	{
		poly A(r - l + 1), B(mid - l + 1);
		L(i, 0, r - l) if(i <= mid) 
			A[i] = (ll) b[i] * ((l == 0 ? 1 : 2)) % mod;
		L(i, 0, mid - l)
			B[i] = b[i + l];
		A = Mult(A, B, r - l + 2);

		L(j, 0, r - l - 1) if(mid + 1 <= l + j + 1 && l + j + 1 <= r) {
			(c[l + j + 1] += A[j]) %= mod;
		}
	}
	{
		poly A(r - l + 1), B(mid - l + 1);
		L(i, 1, r - l)  
			A[i] = a[i];
		L(i, 0, mid - l)
			B[i] = c[i + l];
		A = Mult(A, B, r - l + 2);
		L(j, 0, r - l) if(mid + 1 <= l + j && l + j <= r) {
			(b[l + j] += A[j]) %= mod;
		}
	}
	dc2(mid + 1, r);
}
int main() {
	ios :: sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	//n=2.5e5;
	// n=100;
	 cin >> n;
	init(1 << 19);
	Pinit(1 << 19);
	a[0] = 1;
	dc(0, n);
	b[0] = 1;
	L(i, 0, n) c[i] = 0;
	dc2(0, n);
	cout << (ll) b[n] * fac[n] % mod << '\n';
	return 0;
} 
/*
100
423669705
*/

这程序好像有点Bug,我给组数据试试?

詳細信息

Test #1:

score: 100
Accepted
time: 9ms
memory: 26332kb

input:

3

output:

28

result:

ok 1 number(s): "28"

Test #2:

score: 0
Accepted
time: 8ms
memory: 26104kb

input:

1

output:

1

result:

ok 1 number(s): "1"

Test #3:

score: 0
Accepted
time: 6ms
memory: 26108kb

input:

2

output:

4

result:

ok 1 number(s): "4"

Test #4:

score: 0
Accepted
time: 6ms
memory: 26112kb

input:

4

output:

282

result:

ok 1 number(s): "282"

Test #5:

score: 0
Accepted
time: 4ms
memory: 26404kb

input:

5

output:

3718

result:

ok 1 number(s): "3718"

Test #6:

score: 0
Accepted
time: 8ms
memory: 26172kb

input:

6

output:

60694

result:

ok 1 number(s): "60694"

Test #7:

score: 0
Accepted
time: 13ms
memory: 26116kb

input:

7

output:

1182522

result:

ok 1 number(s): "1182522"

Test #8:

score: 0
Accepted
time: 12ms
memory: 26176kb

input:

8

output:

26791738

result:

ok 1 number(s): "26791738"

Test #9:

score: 0
Accepted
time: 5ms
memory: 26376kb

input:

9

output:

692310518

result:

ok 1 number(s): "692310518"

Test #10:

score: 0
Accepted
time: 6ms
memory: 26176kb

input:

10

output:

135061370

result:

ok 1 number(s): "135061370"

Test #11:

score: 0
Accepted
time: 6ms
memory: 26408kb

input:

100

output:

423669705

result:

ok 1 number(s): "423669705"

Test #12:

score: 0
Accepted
time: 10ms
memory: 26216kb

input:

1234

output:

878522960

result:

ok 1 number(s): "878522960"

Test #13:

score: 0
Accepted
time: 246ms
memory: 27260kb

input:

54321

output:

827950477

result:

ok 1 number(s): "827950477"

Test #14:

score: 0
Accepted
time: 450ms
memory: 28004kb

input:

65536

output:

380835743

result:

ok 1 number(s): "380835743"

Test #15:

score: 0
Accepted
time: 960ms
memory: 30592kb

input:

131072

output:

842796122

result:

ok 1 number(s): "842796122"

Test #16:

score: 0
Accepted
time: 970ms
memory: 30380kb

input:

131071

output:

981021531

result:

ok 1 number(s): "981021531"

Test #17:

score: 0
Accepted
time: 887ms
memory: 29316kb

input:

131070

output:

480197639

result:

ok 1 number(s): "480197639"

Test #18:

score: 0
Accepted
time: 993ms
memory: 30436kb

input:

131074

output:

383000585

result:

ok 1 number(s): "383000585"

Test #19:

score: 0
Accepted
time: 982ms
memory: 30544kb

input:

131073

output:

316664839

result:

ok 1 number(s): "316664839"

Test #20:

score: 0
Accepted
time: 1226ms
memory: 33856kb

input:

250000

output:

119658643

result:

ok 1 number(s): "119658643"

Test #21:

score: 0
Accepted
time: 1230ms
memory: 33436kb

input:

249999

output:

78110138

result:

ok 1 number(s): "78110138"

Test #22:

score: 0
Accepted
time: 1225ms
memory: 32732kb

input:

249998

output:

297253469

result:

ok 1 number(s): "297253469"

Extra Test:

score: 0
Extra Test Passed