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jeff69

Fast Matrix Multiplication

Sep 17th, 2016
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  1. #include<bits/stdc++.h>
  2. #define ll long long
  3. #define Matrix vector< vector < long long > >
  4. using namespace std;
  5. Matrix D;
  6. long long MOD=1000000007;
  7. void Resize_Matrix(long long n , long long m , Matrix &M){
  8.     M.clear();
  9.     for(int j=0;j<n;j++) {
  10.         M.push_back( vector< long long >() );
  11.         M[j].clear();
  12.         M[j].resize(m);
  13.         for(int i=0;i<m;i++) M[j][i]=0;
  14.     }
  15. }
  16. Matrix Matrix_Multiplication(Matrix A , Matrix B){
  17.     Matrix Ans; long long n , m;
  18.     Resize_Matrix(n=A.size() , m=A[0].size() , Ans);
  19.     for(long long j=0;j<n;j++){
  20.         for(long long i=0;i<n;i++){
  21.             Ans[j][i]=0;
  22.  
  23.             for(long long k=0;k<n;k++){
  24.                 Ans[j][i]+=A[j][k]*B[k][i];
  25.                 Ans[j][i]%=MOD;
  26.             }
  27.         }
  28.     }
  29.     return Ans;
  30. }
  31. Matrix Matrix_Exponentiation(Matrix M , long long power){
  32.     if(power==0)return D;
  33.     if(power==1) return M;
  34.     Matrix ret;
  35.     ret=Matrix_Exponentiation(M , power/2);
  36.     ret=Matrix_Multiplication(ret , ret);
  37.     if(power%2==1) ret=Matrix_Multiplication(ret,M);
  38.     return ret;
  39. }
  40.  
  41. int main()
  42. {
  43. int t;cin>>t;
  44. while(t--)
  45.     {ll k;cin>>k;
  46.     if(k==1){cout<<3<<endl;continue;}
  47.     Matrix F;
  48.     Resize_Matrix(3,3,F);
  49.     Resize_Matrix(3,3,D);
  50.     int q=1;
  51.     for(int i=0;i<3;i++)
  52.     for(int j=0;j<3;j++){
  53.         D[i][j]=1;
  54.         F[j][i]=q;
  55.         q++;
  56.     }
  57.     //for(int i=0;i<3;i++)F[i][i]=1;
  58. ll sum=0;
  59.     Matrix R;
  60.     Resize_Matrix(3,3,R);
  61.     R=Matrix_Exponentiation(F,k-1);
  62.     for(int i=0;i<3;i++)for(int j=0;j<3;j++)sum=(sum%MOD+R[i][j]%MOD)%MOD;
  63.     cout<<sum<<endl;
  64.     }
  65.     return 0;
  66. }
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