FZU 1683 纪念SlingShot 矩阵快速幂

  1 // File Name: temp.cpp
  2 // Author: darkdream
  3 // Created Time: 2014年09月17日 星期三 11时35分45秒
  4 
  5 #include<vector>
  6 #include<list>
  7 #include<map>
  8 #include<set>
  9 #include<deque>
 10 #include<stack>
 11 #include<bitset>
 12 #include<algorithm>
 13 #include<functional>
 14 #include<numeric>
 15 #include<utility>
 16 #include<sstream>
 17 #include<iostream>
 18 #include<iomanip>
 19 #include<cstdio>
 20 #include<cmath>
 21 #include<cstdlib>
 22 #include<cstring>
 23 #include<ctime>
 24 #define LL long long
 25 #define m 2009
 26 using namespace std;
 27 int n ; 
 28 struct Matrix
 29 {
 30    int  mat[4][4];
 31    void clear()
 32    {
 33       memset(mat,0,sizeof(mat));
 34    }
 35    void output()
 36    {
 37      for(int i =0  ;i < n ;i ++)
 38      {
 39        for(int j = 0 ;j < n ;j ++)
 40            printf("%d ",mat[i][j]);
 41      printf("\n");
 42      }
 43    }
 44    void init()
 45    {
 46       clear();
 47       n = 4 ;
 48       mat[0][0] = 3; 
 49       mat[0][1] = 2; 
 50       mat[0][2] = 7;
 51       mat[1][0] = 1;
 52       mat[2][1] = 1;
 53       mat[3][0] = 1;
 54       mat[3][3] = 1;
 55    }
 56    Matrix operator *(const Matrix &b) const
 57    {
 58        Matrix ret;
 59        ret.clear();
 60        for(int i = 0 ;i < n ;i ++)
 61            for(int j = 0;j < n;j ++)
 62            {
 63                for(int k = 0 ;k < n ;k ++)
 64                {
 65                  ret.mat[i][j] =(ret.mat[i][j] + mat[i][k] * b.mat[k][j]) % m ; // 第I 行  第J  列        
 66                }
 67            }
 68        return ret;
 69    }
 70 };
 71 Matrix Pow( Matrix a ,LL t )
 72 {
 73   Matrix ret;
 74   ret.clear();
 75   for(int i = 0 ;i < n ;i ++)
 76        ret.mat[i][i] = 1;
 77   Matrix tmp = a; 
 78   while(t)
 79   {
 80       if(t&1) ret = ret * tmp;
 81       tmp = tmp * tmp;
 82       t >>=1;
 83   }
 84   return ret;
 85 }
 86 int main(){
 87     int l ;
 88     int ca = 0 ;
 89     int t ;
 90     scanf("%d",&t);
 91     while(t--)
 92     {
 93         ca ++;
 94         scanf("%d",&l);
 95         int tt[] = {4,1,3,5};
 96         if(l <= 2)
 97         {
 98           if(l == 0 )
 99            printf("Case %d: 1\n",ca);
100           if(l == 1 )
101            printf("Case %d: 4\n",ca);
102           if(l == 2 )
103            printf("Case %d: 9\n",ca);
104            continue;
105         }
106         Matrix  a;
107         a.init();
108         a = Pow(a,l - 1);
109         //a.output();
110         int ans = 0 ; 
111         for(int i = 0 ;i < n;i ++)
112         {
113            ans = (ans + a.mat[3][i] *tt[3-i] )%m ;
114         }
115         printf("Case %d: %d\n",ca,ans);
116     }
117     return 0;
118 }