HDU 4965 Fast matrix calculation (using matrix operation properties)

Test instructions: Give the n*k matrix A and K*n B, for (AB) ^ (n*n) result matrix of the sum of the elements of Module 6. (n<=1000,k<=6)

Idea: The matrix of a*b is the matrix of N*n (1000*1000), and then the fast power is sure to time out, using multiplication to bind the law a^ (n*n) * b^ (n*n) = A*b*a*b*a*b*a = A * (b*a) * (b*a), The matrix of b*a 6*6 can be quickly power

62MS 1716K 1968 B C + + #include <cstdio> #include <iostream> #include <cstring> #include <algorithm&
Gt


using namespace Std;
    struct Mat {int a[10][10];
    int r,c;
        Mat () {memset (a,0,sizeof (a));
    r=c=0;


} void Mem () {memset (a,0,sizeof (a));}};
int n,l;
Mat I;


int a[1010][10],b[10][1010];
    Mat Mul (Mat m1,mat m2) {mat ans; for (int i=1;i<=l;i++) for (int. j=1;j<=l;j++) if (M1.a[i][j]) for (int k=1;k<=l;k
    + +) ans.a[i][k]= (ans.a[i][k]+m1.a[i][j]*m2.a[j][k])%6;
return ans;
    } Mat Quickmul (Mat m,int k) {mat ans;
    for (int i=1;i<=l;i++) ans.a[i][i]=1;
        while (k) {if (k&1) Ans=mul (ans,m);
        M=mul (M,M);
    k>>=1;
} return ans;

} int ans[1010][10];
    void Ini () {memset (ans,0,sizeof (Ans));
I.mem (); } int main () {while (scanf ("%d%d", &n,&l), (n| |
        L)) {ini (); for (int i=1;i<=n; i++) for (int j=1;j<=l;j++) scanf ("%d", &a[i][j]);

        for (int i=1;i<=l;i++) for (int j=1;j<=n;j++) scanf ("%d", &b[i][j]); for (int i=1;i<=l;i++)//Calculate b*a matrix for (int j=1;j<=n;j++) if (b[i][j]) fo

        R (int k=1;k<=l;k++) i.a[i][k]= (i.a[i][k]+b[i][j]*a[j][k])%6; 
        
        Mat Tmp=quickmul (i,n*n-1);
                    for (int. i=1;i<=n;i++)//a* (b*a) ^ (n-1) for (int j=1;j<=l;j++) if (A[i][j])
        for (int k=1;k<=l;k++) ans[i][k]= (ans[i][k]+a[i][j]*tmp.a[j][k])%6;
        int ans=0; for (int. i=1;i<=n;i++)//a* (b*a) ^ (n-1) ^b= (a*b) ^n for (int j=1;j<=n;j++) {int
                Tmp=0;
                for (int k=1;k<=l;k++) {tmp+=ans[i][k]*b[k][j];
   } ans+= (tmp%6);         } printf ("%d\n", ans);
} return 0; }