Hdu_4965 Fast Matrix Calculation 2014 multi-School 9 matrix Rapid power + witty matrix combination Law

At first, I thought this question was a raw question about the rapid power of the matrix,

Later it was found that it would time out, and the super would exceed M = C ^ (N * n). This operation, and the C itself is a matrix of N * n, with N at the maximum of 1000.

But here is a clever place: the source of C is actually = a * B. A is a matrix of N * k, and B is a matrix of K * n, K is up to 10. Here is the breakthrough. The combination Law of the matrix should be used.

That is to say, I will not combine a * B first. I will first combine B * A. Isn't m required to be C ^ N * n, calculate the N x n (B x A) values, multiply the value of 10x10 by the value of logn x n. Then multiply A and B at the two ends.

I did not expect the combination of law.

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#define LL __int64using namespace std;LL matA[1010][10],matB[10][1010];LL matC[1010][10];LL MM[1010][1010];int n,k;struct Mat{    LL mat[10][10];}E;Mat operator *(Mat a,Mat b){    Mat c;    for (int i=0;i<k;i++)    for (int j=0;j<k;j++){        c.mat[i][j]=0;        for (int w=0;w<k;w++){            c.mat[i][j]+=a.mat[i][w]*b.mat[w][j];            c.mat[i][j]%=6;        }    }    return c;}Mat operator ^(Mat a,int x){    Mat c=E;    for (int i=x;i;i>>=1){        if (i&1){            c=c*a;        }        a=a*a;    }    return c;}int main(){    memset(E.mat,0,sizeof E.mat);    for (int i=0;i<10;i++) E.mat[i][i]=1;    while (scanf("%d%d",&n,&k)!=EOF)    {        if (n==0 && k==0) break;        for (int i=0;i<n;i++)            for (int j=0;j<k;j++) scanf("%I64d",&matA[i][j]);        for (int i=0;i<k;i++)            for (int j=0;j<n;j++) scanf("%I64d",&matB[i][j]);        Mat a;        for (int i=0;i<k;i++)            for (int j=0;j<k;j++){               a.mat[i][j]=0;               for (int w=0;w<n;w++){                 a.mat[i][j]+=matB[i][w]*matA[w][j];               }               //cout<<i<<" aaa "<<j<<" "<<a.mat[i][j]<<endl;            }        Mat M=a^(n*n-1);        for (int i=0;i<n;i++)        for (int j=0;j<k;j++){            matC[i][j]=0;            for (int w=0;w<k;w++)                 matC[i][j]+=matA[i][w]*M.mat[w][j];           // cout<<matC[i][j]<<" Matc "<<endl;        }        int ans=0;        for (int i=0;i<n;i++)        for (int j=0;j<n;j++){            MM[i][j]=0;            for (int w=0;w<k;w++){                MM[i][j]+=matC[i][w]*matB[w][j];            }           // cout<<MM[i][j]<<" qwe "<<endl;            ans+=MM[i][j]%6;        }        printf("%d\n",ans);    }    return 0;}

　　

Hdu_4965 Fast Matrix Calculation 2014 multi-School 9 matrix Rapid power + witty matrix combination Law