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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#782328 | #9782. NonZero PrefSuf Sums | grass8cow | AC ✓ | 22ms | 8740kb | C++17 | 1.5kb | 2024-11-25 19:46:09 | 2024-11-25 19:46:10 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
int mod,c[110][110],g[110][110][110];
int qpow(int a,int b){
int c=1;
for(;b;b>>=1){
if(b&1)c=1ll*a*c%mod;
a=1ll*a*a%mod;
}
return c;
}
void ad(int &x,int y){
x+=y;if(x>=mod)x-=mod;
}
int F(int n,int m){
int ans=0;
for(int i=1;i<n;i++){
for(int s=1;s<i;s++){
if(i-s-1<=m)
ad(ans,1ll*c[n][i]*g[n-i][s][i-s-1]%mod),
ad(ans,mod-1ll*c[n][i]*g[n-i][s][m+1]%mod);
}
//sum<i,mx>=i-sum-1
}
return ans;
}
int n,m,f[20100],h[20100];
int main(){
scanf("%d%d%d",&n,&m,&mod);
f[n*m]=1;
for(int i=1;i<=n;i++){
memset(h,0,sizeof(h));
for(int j=1;j<=n*m*2;j++)(f[j]+=f[j-1])%=mod;
for(int j=0;j<=n*m*2;j++){
h[j]=f[min(j+m,n*m*2)];
if(j-m>0)ad(h[j],mod-f[j-m-1]);
}
for(int j=0;j<=n*m*2;j++)f[j]=h[j];
}
g[0][0][0]=1;
for(int i=0;i<n;i++)
for(int j=0;j<=n;j++)
for(int k=0;k<=n;k++)if(g[i][j][k])
for(int l=1;j+l<=n;l++)
ad(g[i+1][j+l][max(k,l)],g[i][j][k]);
for(int i=0;i<n;i++)
for(int j=0;j<=n;j++)
for(int k=n-1;k>=0;k--)
ad(g[i][j][k],g[i][j][k+1]);
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-1]+c[i-1][j])%mod;
}
int ans=f[n*m];
for(int i=0;i<=n;i++){
if(i&&n-i<2){if(n-i==1)(ans+=1ll*m*n*2%mod)%=mod;}
else{for(int l=1,r;l<=m;l=r+1)r=m/(m/l),(ans+=2ll*F(n-i,m/l)*c[n][i]%mod*(r-l+1)%mod)%=mod;}
}
ans=(qpow(m*2+1,n)+mod-ans)%mod;
printf("%d",ans);
return 0;
}
//枚举k,然后做长度为n,m除掉k
//sum>0 正数=1 最小的负数<=-(sum-1)
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 4008kb
input:
2 1 998244353
output:
2
result:
ok single line: '2'
Test #2:
score: 0
Accepted
time: 8ms
memory: 6372kb
input:
69 42 696969697
output:
378553557
result:
ok single line: '378553557'
Test #3:
score: 0
Accepted
time: 0ms
memory: 3864kb
input:
2 1 998244353
output:
2
result:
ok single line: '2'
Test #4:
score: 0
Accepted
time: 8ms
memory: 6332kb
input:
69 42 696969697
output:
378553557
result:
ok single line: '378553557'
Test #5:
score: 0
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time: 4ms
memory: 5812kb
input:
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output:
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Test #6:
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memory: 4200kb
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output:
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time: 0ms
memory: 6340kb
input:
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output:
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memory: 3912kb
input:
3 2 503002109
output:
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memory: 3924kb
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output:
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output:
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memory: 4060kb
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output:
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memory: 4368kb
input:
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output:
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memory: 4016kb
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output:
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memory: 4012kb
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output:
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memory: 4080kb
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output:
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memory: 4680kb
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37 18 833753929
output:
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result:
ok single line: '592917251'
Test #22:
score: 0
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time: 1ms
memory: 4092kb
input:
11 3 998773403
output:
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result:
ok single line: '860630017'
Test #23:
score: 0
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time: 1ms
memory: 4064kb
input:
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output:
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ok single line: '347188409'
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score: 0
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memory: 3876kb
input:
3 3 844621907
output:
270
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memory: 3928kb
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memory: 4064kb
input:
4 1 637268377
output:
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Test #28:
score: 0
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memory: 3960kb
input:
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output:
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Test #29:
score: 0
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memory: 3988kb
input:
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output:
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score: 0
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memory: 3860kb
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Test #31:
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Test #32:
score: 0
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memory: 3976kb
input:
6 8 417027509
output:
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Test #33:
score: 0
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memory: 3996kb
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Test #34:
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memory: 3924kb
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score: 0
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score: 0
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score: 0
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memory: 4028kb
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score: 0
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memory: 4056kb
input:
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score: 0
Accepted
time: 10ms
memory: 7852kb
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score: 0
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memory: 4840kb
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Test #48:
score: 0
Accepted
time: 3ms
memory: 5232kb
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ok single line: '135425620'
Test #49:
score: 0
Accepted
time: 1ms
memory: 4020kb
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ok single line: '102703562'
Test #50:
score: 0
Accepted
time: 22ms
memory: 8740kb
input:
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output:
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result:
ok single line: '313377809'
Extra Test:
score: 0
Extra Test Passed