[BZOJ1002] [FJOI2007] 轮状病毒 (基尔霍夫矩阵)

 1 #include <cstring>
 2 #include <iostream>
 3 #include <algorithm>
 4 using namespace std;
 5 struct bigint
 6 {
 7     int a[55];
 8  
 9     bigint()
10     {
11         memset(a, 0, sizeof(a));
12     }
13  
14     bigint operator + (int rhs)
15     {
16         bigint ans;
17         for(int i = 0; i <= a[0]; i++)
18             ans.a[i] = a[i];
19         ans.a[0]++, ans.a[1] += rhs;
20         for(int i = 1; i < ans.a[0]; i++)
21         {
22             ans.a[i + 1] += ans.a[i] / 10;
23             ans.a[i] %= 10;
24         }
25         while(!ans.a[ans.a[0]])
26             ans.a[0]--;
27         return ans;
28     }
29  
30     bigint operator - (bigint rhs)
31     {
32         bigint ans;
33         ans.a[0] = a[0];
34         for(int i = 1; i <= ans.a[0]; i++)
35             ans.a[i] = a[i] - rhs.a[i];
36         for(int i = 1; i < ans.a[0]; i++)
37             if(ans.a[i] < 0)
38             {
39                 ans.a[i] += 10;
40                 ans.a[i + 1] -= 1;
41             }
42         while(!ans.a[ans.a[0]])
43             ans.a[0]--;
44         return ans;
45     }
46  
47     bigint operator * (int rhs)
48     {
49         bigint ans;
50         ans.a[0] = a[0] + 1;
51         for(int i = 1; i <= ans.a[0]; i++)
52             ans.a[i] = a[i] * rhs;
53         for(int i = 1; i < ans.a[0]; i++)
54         {
55             ans.a[i + 1] += ans.a[i] / 10;
56             ans.a[i] %= 10;
57         }
58         while(!ans.a[ans.a[0]])
59             ans.a[0]--;
60         return ans;
61     }
62  
63 }f[105];
64  
65 int main()
66 {
67     int n;
68     cin >> n;
69     f[1].a[1] = 1, f[2].a[1] = 5;
70     f[1].a[0] = f[2].a[0] = 1;
71     for(int i = 3; i <= n; i++)
72         f[i] = f[i - 1] * 3 - f[i - 2] + 2;
73     for(int i = f[n].a[0]; i; i--)
74         cout << f[n].a[i];
75     cout << endl;
76     return 0;
77 }