# kuangbin topic 19 uva111551 basic matrix

Posted by topsub on Thu, 30 Apr 2020 23:58:42 +0200

Title:
Given a sequence of numbers, each number corresponds to a transformation, which is the sum of some positions of the original sequence, and the sequence after r-th transformation is asked.
Explanation:
I really didn't expect to construct 01 matrix to express power. Their methods are all water problems. It's related, that is, the position of addition is + 1 in 01 matrix, and then fast power can be used. But how can I not expect to get the result after matrix transformation? Why? Is it really because I failed to study linear algebra? Oh. The big guy explained to me.... ORZ

```#include<stdio.h>
#include<string.h>
#define LL long long int
const int MOD=1000;
struct node
{
int m;
node()
{
memset(m,0,sizeof(m));
}
};
int n,m;
int s,s2;
node cla(node a,node b){
node c;
for(int i=0;i<n;i++)
for(int j=0;j<n;j++)
for(int k=0;k<n;k++)
if(a.m[i][k]&&b.m[k][j])//Prune (add conditions, set threshold), improve efficiency, one is 0, multiplication must be 0
{
c.m[i][j]+=a.m[i][k]*b.m[k][j];
c.m[i][j]%=MOD;
}
return c;
}
node POW(node a)
{
node c;
for(int i=0;i<n;i++) c.m[i][i]=1;
while(m)
{
if(m%2) c=cla(c,a);
a=cla(a,a);
m/=2;
}
return c;
}
int main()
{
int t;
scanf("%d",&t);
while(t--)
{
scanf("%d%d",&n,&m);
node a;
memset(s,0,sizeof(s));
memset(s2,0,sizeof(s2));
for(int i=0;i<n;i++)
scanf("%d",&s[i]);
for(int i=0;i<n;i++)
{
int x;
scanf("%d",&x);
for(int j=0;j<x;j++)
{
int v;
scanf("%d",&v);
a.m[i][v]++;
}
}
a=POW(a);

for(int i=0;i<n;i++)
for(int k=0;k<n;k++)
if(a.m[i][k]&&s[k])//Prune (add conditions, set threshold), improve efficiency, there is a 0, multiply must be 0
{
s2[i]+=a.m[i][k]*s[k];
s2[i]%=MOD;
}

for(int i=0;i<n-1;i++)
printf("%d ",s2[i]);
printf("%d\n",s2[n-1]);
}
} ```