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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#337370#7759. Permutation Counting 2Harry27182100 ✓743ms9648kbC++141.9kb2024-02-25 11:14:152024-02-25 11:14:16

Judging History

你现在查看的是最新测评结果

  • [2024-02-25 11:14:16]
  • 评测
  • 测评结果:100
  • 用时:743ms
  • 内存:9648kb
  • [2024-02-25 11:14:15]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
int n,mod,fac[250505],inv[250505],dp[505][505],f[505][505],g[505][505],c[505][505];
int qpow(int x,int y)
{
	int res=1;
	while(y)
	{
		if(y&1)res=1ll*res*x%mod;
		x=1ll*x*x%mod;y/=2;
	}
	return res;
}
void Add(int &x,int y){x=(x+y>=mod?x+y-mod:x+y);}
int C(int x,int y){return (x<y?0:1ll*fac[x]*inv[y]%mod*inv[x-y]%mod);}
int main()
{
    cin.tie(0)->sync_with_stdio(0);
    cin>>n>>mod;fac[0]=inv[0]=c[0][0]=1;
    for(int i=1;i<=n;i++)
    {
    	c[i][0]=1;
    	for(int j=1;j<=i;j++)c[i][j]=(c[i-1][j]+c[i-1][j-1])%mod;
	}
    for(int i=1;i<=n*n+n;i++)fac[i]=1ll*fac[i-1]*i%mod;
    inv[n*n+n]=qpow(fac[n*n+n],mod-2);
    for(int i=n*n+n-1;i>=1;i--)inv[i]=1ll*inv[i+1]*(i+1)%mod;
    for(int i=1;i<=n;i++)
    {
    	for(int j=1;j<=n;j++)g[i][j]=C(i*j+n-1,n);
	}
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=n;j++)
		{
			f[i][j]=g[i][j];
			for(int k=1;k<j;k++)
			{
				if((k-j)&1)Add(f[i][j],mod-1ll*c[j][k]*g[i][k]%mod);
				else Add(f[i][j],1ll*c[j][k]*g[i][k]%mod); 
			} 
		}
	}
	for(int j=1;j<=n;j++)
	{
		for(int i=1;i<=n;i++)
		{
			dp[i][j]=f[i][j];
			for(int k=1;k<i;k++)
			{
				if((k-i)&1)Add(dp[i][j],mod-1ll*c[i][k]*f[k][j]%mod);
				else Add(dp[i][j],1ll*c[i][k]*f[k][j]%mod);
			}
		}
	}
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)g[i][j]=dp[n-i][n-j];
	}
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)
		{
			f[i][j]=g[i][j];
			for(int k=j+1;k<n;k++)
			{
				if((k-j)&1)Add(f[i][j],mod-1ll*c[k][j]*g[i][k]%mod);
				else Add(f[i][j],1ll*c[k][j]*g[i][k]%mod); 
			} 
		}
	}
	for(int j=0;j<n;j++)
	{
		for(int i=0;i<n;i++)
		{
			dp[i][j]=f[i][j];
			for(int k=i+1;k<n;k++)
			{
				if((k-i)&1)Add(dp[i][j],mod-1ll*c[k][i]*f[k][j]%mod);
				else Add(dp[i][j],1ll*c[k][i]*f[k][j]%mod);
			}
		}
	}
	for(int i=0;i<n;i++)
	{
		for(int j=0;j<n;j++)cout<<dp[i][j]<<' ';
		cout<<'\n';
	}
	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: 7684kb

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: 1ms
memory: 7696kb

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: 1ms
memory: 7812kb

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: 1ms
memory: 7676kb

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: 0ms
memory: 7800kb

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: 1ms
memory: 7940kb

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: 1ms
memory: 7812kb

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: 1ms
memory: 7808kb

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: 1ms
memory: 7968kb

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: 1ms
memory: 7908kb

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: 3ms
memory: 7904kb

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: 7ms
memory: 7980kb

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: 7ms
memory: 8060kb

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: 7ms
memory: 7824kb

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: 7ms
memory: 7872kb

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: 725ms
memory: 9548kb

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: 734ms
memory: 9632kb

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: 738ms
memory: 9564kb

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: 742ms
memory: 9584kb

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: 743ms
memory: 9648kb

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