HDU multi-school competition 9th games HDU 4965 Fast Matrix Calculation [matrix calculation + mathematical knowledge]

Difficulty, indeed, is not difficult

The problem is that there is a matrix operation optimization.

The question is to give matrix A of N * k to matrix B of K * n (1 <= n <= 1000 & 1 = <k <= 6 ), multiply them into a C matrix and calculate C ^ (N * n)

Equivalent

Ababababababab... = (AB) ^ (N * n)

Worse

A (BA) ^ (N * N-1) B

Because the BA multiplied K * k matrix, K is relatively small.

 

 

#include <cstdio>#include <cstdlib>#include <cstring>#include <cmath>#include <algorithm>#include <iostream>using namespace std;int a[1111][1111];int b[1111][1111];int c[1111][1111];int tmp[1111][1111];int sum[1111][1111];void TIMES(int K,int N,int M,int aa[][1111],int bb[][1111],int cc[][1111]){memset(tmp,0,sizeof(tmp));for(int i=1;i<=K;i++){for(int j=1;j<=M;j++){for(int k=1;k<=N;k++){tmp[i][j]=(tmp[i][j]+aa[i][k]*bb[k][j]%6)%6;}}}for(int i=1;i<=K;i++)for(int j=1;j<=M;j++)cc[i][j]=tmp[i][j]%6;}void quick(int cc[][1111],int mi,int n){for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)if(i==j) sum[i][j]=1;else sum[i][j]=0;while(mi){if(mi&1)TIMES(n,n,n,cc,sum,sum);TIMES(n,n,n,cc,cc,cc);mi>>=1;}}int main(){#ifndef ONLINE_JUDGEfreopen("G:/in.txt","r",stdin);//freopen("G:/myout.txt","w",stdout);#endifint N,K;while(~scanf("%d%d",&N,&K)){if(N==0 && K==0) return 0;for(int i=1;i<=N;i++){for(int j=1;j<=K;j++){scanf("%d",&a[i][j]);}}for(int i=1;i<=K;i++){for(int j=1;j<=N;j++){scanf("%d",&b[i][j]);}}TIMES(K,N,K,b,a,c);quick(c,N*N-1,K);TIMES(N,K,K,a,sum,sum);TIMES(N,K,N,sum,b,sum);int ans=0;for(int i=1;i<=N;i++)for(int j=1;j<=N;j++)ans+=sum[i][j];cout<<ans<<endl;}}