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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#72091#622. 多项式多点求值Qingyu0 1306ms41108kbC++233.9kb2023-01-14 00:19:162023-01-14 00:19:20

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-01-14 00:19:20]
  • 评测
  • 测评结果:0
  • 用时:1306ms
  • 内存:41108kb
  • [2023-01-14 00:19:16]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
constexpr int mod = 998244353, G = 3;
using poly = vector<int>;
constexpr int maxn = 1 << 18, N = (1 << 18) + 10;
int w[N], inv[N], lg[N], rev[N];
inline int add(int a, int b) {return (a += b - mod), a += a >> 31 & mod;}
inline int sub(int a, int b) {return (a -= b), a += a >> 31 & mod;}
inline int fpw(int a, int b) {
	int ans = 1;
	for(; b; b >>= 1, a = 1ll * a * a % mod) if(b & 1) ans = 1ll * ans * a % mod;
	return ans;
}
void init() {
	inv[1] = 1;
	for(int i = 2; i < N; i ++) lg[i] = lg[i + 1 >> 1] + 1;
	for(int i = 2; i < N; i ++) inv[i] = 1ll * inv[mod % i] * (mod - mod / i) % mod;
	int wn = fpw(G, (mod - 1) / maxn); w[0] = 1;
	for(int i = 1; i < N; i ++) w[i] = 1ll * wn * w[i - 1] % mod;
}
void dft(poly &a, int len) {
	for(int i = len >> 1; i >= 1; i >>= 1) {
		int s = maxn / (i << 1);
		for(int j = 0; j < len; j += i << 1) {
			for(int k = 0, *p = w; k < i; k ++, p += s) {
				int x = a[j + k], y = a[i + j + k];
				a[j + k] = add(x, y);
				a[i + j + k] = 1ll * *p * sub(x, y) % mod;
			}
		}
	}
}
void idft(poly &a, int len) {
	for(int i = 1; i < len; i <<= 1) {
		int s = maxn / (i << 1);
		for(int j = 0; j < len; j += i << 1) {
			for(int k = 0, *p = w; k < i; k ++, p += s) {
				int x = a[j + k], y = 1ll * *p * a[i + j + k] % mod;
				a[j + k] = add(x, y);
				a[i + j + k] = sub(x, y);
			}
		}
	}
	reverse(a.begin() + 1, a.end());
	for(int &x : a) x = 1ll * x * inv[len] % mod;
}
poly polymul(poly a, poly b, int len) {
	if(a.size() > len) a.resize(len);
	if(b.size() > len) b.resize(len);
	if(len <= 40) {
		poly c(len);
		for(int i = 0; i < a.size(); i ++) {
			for(int j = 0; j < min(len - i, int(b.size())); j ++) {
				c[i + j] = add(c[i + j], 1ll * a[i] * b[j] % mod);
			}
		}
		return c;
	}
	int mxlen = 1 << lg[a.size() + b.size() - 1];
	a.resize(mxlen), b.resize(mxlen);
	dft(a, mxlen), dft(b, mxlen);
	for(int i = 0; i < mxlen; i ++) a[i] = 1ll * a[i] * b[i] % mod;
	idft(a, mxlen), a.resize(len);
	return a;
}
poly polyinv(poly a, int len) {
	if(len == 1) return poly{fpw(a[0], mod - 2)};
	int mid = len + 1 >> 1, mxlen = 1 << lg[len * 3];
	poly f = polyinv(a, mid);
	f.resize(mxlen), a.resize(mxlen);
	dft(f, mxlen), dft(a, mxlen);
	for(int i = 0; i < mxlen; i ++) f[i] = sub(2ll * f[i] % mod, 1ll * f[i] * f[i] % mod * a[i] % mod);
	idft(f, mxlen); f.resize(len);
	return f;
}
void qiudao(poly &a, int len) {
	for(int i = 0; i < len - 1; i ++) a[i] = 1ll * a[i + 1] * (i + 1) % mod;
}
void jifen(poly &a, int len) {
	for(int i = len - 1; i >= 1; i --) a[i] = 1ll * a[i - 1] * inv[i] % mod;
	a[0] = 0;
}
poly polydiv(poly a, poly b) {
	int n = a.size(), m = b.size();
	reverse(a.begin(), a.end()), reverse(b.begin(), b.end());
	b.resize(n - m + 1);
	poly p = polymul(a, polyinv(b, n - m + 1), n - m + 1);
	reverse(p.begin(), p.end());
	return p;
}
poly polymod(poly a, poly b) {
	int n = a.size(), m = b.size();
	if(n < m) return a;
	poly p = polydiv(a, b);
	poly q = polymul(b, p, m - 1);
	for(int i = 0; i < m - 1; i ++) q[i] = sub(a[i], q[i]);
	return q;
}
poly sum[N << 1];
int x[N], y[N];
#define ls u << 1 
#define rs u << 1 | 1
void dfs1(int u, int l, int r) {
	if(l == r) {
		sum[u] = {mod - x[l], 1};
	} else {
		int mid = l + r >> 1;
		dfs1(ls, l, mid), dfs1(rs, mid + 1, r);
		sum[u] = polymul(sum[ls], sum[rs], r - l + 2);
	}
}
void dfs2(int u, int l, int r, poly f) {
	f = polymod(f, sum[u]);
	if(l == r) {
		y[l] = f[0];
	} else {
		int mid = l + r >> 1;
		dfs2(ls, l, mid, f), dfs2(rs, mid + 1, r, f);
	}
}
#undef ls
#undef rs
int main() {
	// freopen("in.txt", "r", stdin);
	ios::sync_with_stdio(false), cin.tie(0);
	init();
	int n, m;
	cin >> n >> m;
	poly f(n), a(m);
	for(int &x : f) cin >> x;
	for(int i = 0; i < m; i ++) cin >> x[i]; 
	dfs1(1, 0, m - 1);
	dfs2(1, 0, m - 1, f);
	for(int i = 0; i < m; i ++) cout << y[i] << '\n';
	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 0
Wrong Answer
time: 3ms
memory: 20284kb

input:

100 94
575336069 33153864 90977269 80162592 25195235 334936051 108161572 14050526 356949084 797375084 805865808 286113858 995555121 938794582 458465004 379862532 563357556 293989886 273730531 13531923 113366106 126368162 405344025 443053020 475686818 734878619 338356543 661401660 834651229 527993675...

output:

871209652
937929160
460324803
490352555
246855408
362694921
772418007
83116982
319523354
695415352
198532508
714040570
648830843
644676914
596261365
947763107
611023228
465578001
975784011
588331850
24829908
823777203
926956610
69530883
820495006
19956095
994146054
379398409
446811175
80555777
23364...

result:

wrong answer 1st numbers differ - expected: '940122667', found: '871209652'

Test #2:

score: 0
Wrong Answer
time: 34ms
memory: 20952kb

input:

5000 4999
410683245 925831211 726803342 144364185 955318244 291646122 334752751 893945905 484134283 203760731 533867267 813509277 491860093 413174124 584582617 594704162 976489328 978500071 196938934 628117769 169796671 858963950 562124570 582491326 647830593 238623335 20782490 674939336 656529076 2...

output:

977663369
765337142
67689056
755350135
415800819
167559386
847044786
670489889
386448974
478734782
167377300
855437005
692965546
689870618
712895126
922541615
513448234
321981893
397359972
817354833
236782410
317549553
379699194
149957493
439886891
919574385
791885212
276454746
64447490
537933893
61...

result:

wrong answer 1st numbers differ - expected: '683038054', found: '977663369'

Test #3:

score: 0
Wrong Answer
time: 277ms
memory: 25164kb

input:

30000 29995
536696866 881441742 356233606 594487396 991820796 695996817 7219464 149265950 843761437 329761701 260625152 80366362 598729314 133794090 12808683 67477659 320740422 878134577 879383179 940923483 660160621 18082378 886078389 524050341 35092018 137623841 988429688 258507355 138475726 75726...

output:

33062490
855798352
783002238
35969522
544889772
141350827
600293617
396056708
139015593
637303002
784650413
26338904
639917123
275268193
98147736
153034789
8355610
594517547
386515881
731499589
88448444
210118340
850067516
285670441
72556672
61684973
696606306
329500674
754398740
676122627
450163133...

result:

wrong answer 1st numbers differ - expected: '319541931', found: '33062490'

Test #4:

score: 0
Wrong Answer
time: 1306ms
memory: 41108kb

input:

100000 99989
703908936 826436271 431732352 607460686 960390248 897906950 506352459 662618885 172508812 713410533 704313866 156459539 879660919 98030681 46358006 400134234 121190289 498201666 616888945 210891377 39623412 687350951 269444705 980768130 381802923 553892268 644461704 287608268 554761733 ...

output:

862421151
902434305
957470441
716273818
740278009
787094739
852922471
35358211
903496234
507003897
805218028
3449007
238355153
882887531
662754044
699506376
234890205
128517077
451052646
257661475
169178192
105293139
155459823
540060567
578065714
357774660
442692970
968020082
630474973
827259670
697...

result:

wrong answer 1st numbers differ - expected: '135579851', found: '862421151'

Test #5:

score: 0
Runtime Error

input:

1000000 999998
326289172 459965021 432610030 381274775 890620650 133203219 755508578 820410129 100497878 978894337 34545975 484258543 341383383 556328539 705716773 985485996 201697555 806763870 456757110 445252781 501965590 655584951 516373423 475444481 554722275 106826011 433893131 385018453 687541...

output:


result: