QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#244773#7759. Permutation Counting 2Dualqwq100 ✓1745ms8924kbC++232.2kb2023-11-09 15:39:272023-11-09 15:39:33

Judging History

你现在查看的是最新测评结果

  • [2023-11-09 15:39:33]
  • 评测
  • 测评结果:100
  • 用时:1745ms
  • 内存:8924kb
  • [2023-11-09 15:39:27]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
const int N = 5e2 + 5;
int n,P;
inline void Plus(int &x,const int &y) { x += y;if(x >= P) x -= P;}
int fac[N * N],ifac[N * N];
inline void init(int n) {
	fac[0] = 1;
	for(int i = 1;i <= n;i++) fac[i] = 1ll * fac[i - 1] * i % P;
	ifac[1] = 1;
	for(int i = 2;i <= n;i++) ifac[i] = 1ll * ifac[P % i] * (P - P / i) % P;
	ifac[0] = 1;
	for(int i = 1;i <= n;i++) ifac[i] = 1ll * ifac[i - 1] * ifac[i] % P;
}
inline int C(int n,int m) { if(n < 0 || m < 0 || n < m) return 0; return 1ll * fac[n] * ifac[m] % P * ifac[n - m] % P;}
inline int E(int n,int m) { return C(n + m - 1,m - 1);}
int Binom[N][N];
int A[N][N],B[N][N];
int main() {
	// freopen("tmp.in","r",stdin);
	// freopen("tmp.out","w",stdout);
	cin >> n >> P;
	init(N * N - 1);
	Binom[0][0] = 1;
	for(int i = 1;i <= n;i++) {
		Binom[i][0] = Binom[i][i] = 1;
		for(int j = 1;j < i;j++)
			Binom[i][j] = (Binom[i - 1][j] + Binom[i - 1][j - 1]) % P;
	}
	for(int i = 1;i <= n;i++)
		for(int j = 1;j <= n;j++)
			A[i][j] = E(n,i * j); // 两维分别有 i,j 个上升段
	for(int i = 1;i <= n;i++)
		for(int j = n;j >= 1;j--)
			for(int k = 1;k < j;k++)
				if((j - k) & 1)
				Plus(A[i][j],P - 1ll * A[i][k] * Binom[j][k] % P);
				else Plus(A[i][j],1ll * A[i][k] * Binom[j][k] % P);
	for(int j = 1;j <= n;j++)
		for(int i = n;i >= 1;i--)
			for(int k = 1;k < i;k++)
				if((i - k) & 1)
				Plus(A[i][j],P - 1ll * A[k][j] * Binom[i][k] % P);
				else Plus(A[i][j],1ll * A[k][j] * Binom[i][k] % P);
	for(int i = 1;i <= n;i++)
		for(int j = 1;j <= n;j++)
			B[n - i][n - j] = A[i][j];
	for(int i = 0;i < n;i++)
		for(int j = 0;j < n;j++)
			for(int k = j + 1;k < n;k++)
				if((k - j) & 1) Plus(B[i][j],P - 1ll * B[i][k] * Binom[k][j] % P);
				else Plus(B[i][j],1ll * B[i][k] * Binom[k][j] % P);
	for(int j = 0;j < n;j++)
		for(int i = 0;i < n;i++)
			for(int k = i + 1;k < n;k++)
				if((k - i) & 1) Plus(B[i][j],P - 1ll * B[k][j] * Binom[k][i] % P);
				else Plus(B[i][j],1ll * B[k][j] * Binom[k][i] % P);
	for(int i = 0;i < n;i++,cout << endl)
		for(int j = 0;j < n;j++)
			cout << B[i][j] << ' ';
	cerr << 1.0 * clock() / CLOCKS_PER_SEC << endl;
	return 0;
}			

Details

Tip: Click on the bar to expand more detailed information

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 0ms
memory: 7808kb

input:

7 1001458121

output:

1 0 0 0 0 0 0 
0 56 56 8 0 0 0 
0 56 659 440 36 0 0 
0 8 440 1520 440 8 0 
0 0 36 440 659 56 0 
0 0 0 8 56 56 0 
0 0 0 0 0 0 1 

result:

ok 49 tokens

Test #2:

score: 0
Accepted
time: 6ms
memory: 7468kb

input:

8 1008735209

output:

1 0 0 0 0 0 0 0 
0 84 126 36 1 0 0 0 
0 126 1773 1980 405 9 0 0 
0 36 1980 8436 4761 405 1 0 
0 1 405 4761 8436 1980 36 0 
0 0 9 405 1980 1773 126 0 
0 0 0 1 36 126 84 0 
0 0 0 0 0 0 0 1 

result:

ok 64 tokens

Subtask #2:

score: 15
Accepted

Test #3:

score: 15
Accepted
time: 6ms
memory: 8900kb

input:

14 1000253273

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 455 3003 6435 5005 1365 105 1 0 0 0 0 0 0 
0 3003 112905 730665 1629435 1456560 529956 71940 2835 15 0 0 0 0 
0 6435 730665 10865585 46433475 75169560 50184540 13633740 1349931 36735 120 0 0 0 
0 5005 1629435 46433475 336576825 860578230 885230850 375891370 62035485 33...

result:

ok 196 tokens

Test #4:

score: 0
Accepted
time: 6ms
memory: 7020kb

input:

15 1009800301

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 560 4368 11440 11440 4368 560 16 0 0 0 0 0 0 0 
0 4368 188682 1482416 4160120 4899264 2511376 536384 41328 800 1 0 0 0 0 
0 11440 1482416 26232784 139089120 291102560 265085216 106311200 17712368 1048560 15232 16 0 0 0 
0 11440 4160120 139089120 216926039 947184153 3...

result:

ok 225 tokens

Test #5:

score: 0
Accepted
time: 6ms
memory: 7964kb

input:

16 1006729121

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 680 6188 19448 24310 12376 2380 136 1 0 0 0 0 0 0 0 
0 6188 305150 2867696 9916066 14924539 10288876 3196000 410329 17748 153 0 0 0 0 0 
0 19448 2867696 59852036 387206263 15304436 216863763 683915984 173666645 18275272 650641 4828 1 0 0 0 
0 24310 9916066 38720626...

result:

ok 256 tokens

Subtask #3:

score: 25
Accepted

Test #6:

score: 25
Accepted
time: 7ms
memory: 7656kb

input:

36 1003299797

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 7770 435897 10295472 124403620 854992152 552567909 334501587 855871755 616535351 836177106 87288018 849183199 348330136 38608020 2324784 66045 666 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 435897 133844910 939232742 752696285 94...

result:

ok 1296 tokens

Test #7:

score: 0
Accepted
time: 3ms
memory: 8224kb

input:

37 1009736899

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 8436 501942 12620256 163011640 193585389 366265801 325233075 508510208 4472335 508510208 325233075 366265801 193585389 163011640 12620256 501942 8436 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 501942 164674938 380061172 7953...

result:

ok 1369 tokens

Test #8:

score: 0
Accepted
time: 7ms
memory: 8780kb

input:

38 1002064493

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 9139 575757 15380937 211915132 673991551 105909500 89228335 917893160 782878886 231145424 634874749 53537001 904603957 635745396 61523748 3262623 82251 741 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 575757 201514950 2661126...

result:

ok 1444 tokens

Test #9:

score: 0
Accepted
time: 7ms
memory: 7664kb

input:

39 1000696681

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 9880 658008 18643560 273438880 310408078 24862708 197477816 671070872 191143189 191143189 671070872 197477816 24862708 310408078 273438880 18643560 658008 9880 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 658008 24533645...

result:

ok 1521 tokens

Test #10:

score: 0
Accepted
time: 3ms
memory: 8864kb

input:

40 1002813283

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 10660 749398 22481940 350343565 151022119 572250549 255038067 159674717 979042431 374977376 547170717 790491840 141687815 878961939 118286125 95548245 4496388 101270 820 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 7493...

result:

ok 1600 tokens

Subtask #4:

score: 25
Accepted

Test #11:

score: 25
Accepted
time: 19ms
memory: 8360kb

input:

96 1005401729

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 147440 64446024 781420036 468430311 27733626 62151757 454795566 711626792 885805006 401110492 711423106 3...

result:

ok 9216 tokens

Test #12:

score: 0
Accepted
time: 15ms
memory: 8792kb

input:

97 1003022927

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 152096 67910864 795115101 924546504 230011659 577127906 564913191 11843263 171607987 697964156 4314087 ...

result:

ok 9409 tokens

Test #13:

score: 0
Accepted
time: 19ms
memory: 8220kb

input:

98 1000259233

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 156849 71523144 883402282 582472554 858367843 730708960 476781508 806308877 286962083 221796390 32768...

result:

ok 9604 tokens

Test #14:

score: 0
Accepted
time: 13ms
memory: 8000kb

input:

99 1000444889

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 161700 75287520 442576 386074411 823487426 504618380 971268883 734797176 388493421 848753352 857480...

result:

ok 9801 tokens

Test #15:

score: 0
Accepted
time: 21ms
memory: 8172kb

input:

100 1008746839

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 166650 79208745 50916937 213745970 953400361 882774939 595265332 362179793 339853992 820776686 20...

result:

ok 10000 tokens

Subtask #5:

score: 25
Accepted

Test #16:

score: 25
Accepted
time: 1699ms
memory: 8892kb

input:

496 1005266363

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 246016 tokens

Test #17:

score: 0
Accepted
time: 1714ms
memory: 8908kb

input:

497 1000331767

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 247009 tokens

Test #18:

score: 0
Accepted
time: 1718ms
memory: 8924kb

input:

498 1000148759

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 248004 tokens

Test #19:

score: 0
Accepted
time: 1731ms
memory: 8700kb

input:

499 1000176851

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 249001 tokens

Test #20:

score: 0
Accepted
time: 1745ms
memory: 8892kb

input:

500 1002873259

output:

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...

result:

ok 250000 tokens