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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
#233199#7632. Balanced ArrayszhoukangyangAC ✓166ms59816kbC++117.0kb2023-10-31 15:03:302023-10-31 15:03:32

Judging History

你现在查看的是最新测评结果

  • [2023-10-31 15:03:32]
  • 评测
  • 测评结果:AC
  • 用时:166ms
  • 内存:59816kb
  • [2023-10-31 15:03:30]
  • 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 vi vector <int>
#define sz(a) ((int) (a).size())
#define me(f, x) memset(f, x, sizeof(f))
#define uint unsigned int
#define ull unsigned long long 
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());
	}
} ;


int n, m;
int main () {
//	freopen("ex_water1.in", "r", stdin);
//	freopen("ex_water1.ans", "w", stdout);
	ios :: sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	cin >> n >> m;
	init(1 << 21);
	Pinit(1 << 20);
	int ans = 1;
	poly f(max(n, m) + 1);
	poly g(max(n, m) + 1);
	poly h(max(n, m) + 1);
	L(s, 1, m) {
		f[s] = (ll) fac[s] * fac[s - 1] % mod * ifac[s * 2] % mod;
	} 
	L(k, 1, (n + 1) / 2) {
		g[k] = (ll) ifac[k - 1] * ifac[k - 1] % mod * inv[k] % mod * ifac[n - k * 2 + 1] % mod;
	}
	L(d, 0, m) {
		h[d] = (ll) ifac[d] * ifac[d + 1] % mod * fac[d * 2 + n + 1] % mod;
	}
	h *= g;
	L(i, 1, m) {
		(ans += (ll) h[i] * f[i] % mod) %= mod;
	}
//	L(s, 1, m) {
//		L(k, 1, min((n + 1) / 2, s)) {
//			(ans += (ll) fac[s] * ifac[k - 1] % mod * fac[s - 1] % mod * ifac[k - 1] % mod
//				* ifac[s - k + 1] % mod * ifac[s - k] % mod * 
//				fac[s * 2 + n + 1 - k * 2] % mod * ifac[s * 2] % mod * ifac[n - k * 2 + 1] % mod
//				* inv[k] % mod) %= mod;
//		}	
//	}
	cout << ans << '\n';
	return 0;
}

这程序好像有点Bug,我给组数据试试?

详细

Test #1:

score: 100
Accepted
time: 32ms
memory: 36280kb

input:

2 2

output:

9

result:

ok 1 number(s): "9"

Test #2:

score: 0
Accepted
time: 158ms
memory: 59748kb

input:

500000 500000

output:

984531374

result:

ok 1 number(s): "984531374"

Test #3:

score: 0
Accepted
time: 121ms
memory: 59748kb

input:

500000 1

output:

219705876

result:

ok 1 number(s): "219705876"

Test #4:

score: 0
Accepted
time: 121ms
memory: 59656kb

input:

1 500000

output:

500001

result:

ok 1 number(s): "500001"

Test #5:

score: 0
Accepted
time: 158ms
memory: 59816kb

input:

500000 353535

output:

33730077

result:

ok 1 number(s): "33730077"

Test #6:

score: 0
Accepted
time: 156ms
memory: 59800kb

input:

353535 500000

output:

182445298

result:

ok 1 number(s): "182445298"

Test #7:

score: 0
Accepted
time: 149ms
memory: 59796kb

input:

499999 499999

output:

933220940

result:

ok 1 number(s): "933220940"

Test #8:

score: 0
Accepted
time: 164ms
memory: 59756kb

input:

499999 499998

output:

899786345

result:

ok 1 number(s): "899786345"

Test #9:

score: 0
Accepted
time: 160ms
memory: 56360kb

input:

377773 400009

output:

206748715

result:

ok 1 number(s): "206748715"

Test #10:

score: 0
Accepted
time: 147ms
memory: 59748kb

input:

499999 100001

output:

482775773

result:

ok 1 number(s): "482775773"

Test #11:

score: 0
Accepted
time: 152ms
memory: 59316kb

input:

444445 488884

output:

70939759

result:

ok 1 number(s): "70939759"

Test #12:

score: 0
Accepted
time: 150ms
memory: 59372kb

input:

488885 444449

output:

591315327

result:

ok 1 number(s): "591315327"

Test #13:

score: 0
Accepted
time: 133ms
memory: 59796kb

input:

500000 111

output:

313439156

result:

ok 1 number(s): "313439156"

Test #14:

score: 0
Accepted
time: 166ms
memory: 57896kb

input:

333333 444444

output:

403492103

result:

ok 1 number(s): "403492103"

Test #15:

score: 0
Accepted
time: 154ms
memory: 59728kb

input:

499994 343433

output:

334451699

result:

ok 1 number(s): "334451699"

Test #16:

score: 0
Accepted
time: 155ms
memory: 58936kb

input:

477774 411113

output:

63883341

result:

ok 1 number(s): "63883341"

Test #17:

score: 0
Accepted
time: 155ms
memory: 57640kb

input:

123456 432109

output:

238795570

result:

ok 1 number(s): "238795570"

Test #18:

score: 0
Accepted
time: 160ms
memory: 58708kb

input:

131331 467777

output:

834790039

result:

ok 1 number(s): "834790039"

Test #19:

score: 0
Accepted
time: 119ms
memory: 59760kb

input:

500000 2

output:

304727284

result:

ok 1 number(s): "304727284"

Test #20:

score: 0
Accepted
time: 23ms
memory: 36244kb

input:

1111 111

output:

98321603

result:

ok 1 number(s): "98321603"

Test #21:

score: 0
Accepted
time: 153ms
memory: 59324kb

input:

416084 493105

output:

916827025

result:

ok 1 number(s): "916827025"

Test #22:

score: 0
Accepted
time: 83ms
memory: 44308kb

input:

53888 138663

output:

57263952

result:

ok 1 number(s): "57263952"

Test #23:

score: 0
Accepted
time: 155ms
memory: 55932kb

input:

219161 382743

output:

304889787

result:

ok 1 number(s): "304889787"

Test #24:

score: 0
Accepted
time: 154ms
memory: 53936kb

input:

181392 318090

output:

12528742

result:

ok 1 number(s): "12528742"

Test #25:

score: 0
Accepted
time: 147ms
memory: 57284kb

input:

135930 422947

output:

554153000

result:

ok 1 number(s): "554153000"

Test #26:

score: 0
Accepted
time: 164ms
memory: 52716kb

input:

280507 210276

output:

812816587

result:

ok 1 number(s): "812816587"

Test #27:

score: 0
Accepted
time: 164ms
memory: 57148kb

input:

253119 420465

output:

124024302

result:

ok 1 number(s): "124024302"

Test #28:

score: 0
Accepted
time: 149ms
memory: 57916kb

input:

446636 97448

output:

150388382

result:

ok 1 number(s): "150388382"

Test #29:

score: 0
Accepted
time: 156ms
memory: 52784kb

input:

284890 126665

output:

786559507

result:

ok 1 number(s): "786559507"

Test #30:

score: 0
Accepted
time: 84ms
memory: 45876kb

input:

186708 28279

output:

607509026

result:

ok 1 number(s): "607509026"

Extra Test:

score: 0
Extra Test Passed