Hdu--5015（数学，矩阵快速幂）

2014-09-15 16:20:10

思路：由于n<=10，所以用矩阵存下初始列，然后一列一列地推是可行的。

 1 /*************************************************************************
 2     > File Name: 5015.cpp
 3     > Author: Nature
 4     > Mail: 564374850@qq.com 
 5     > Created Time: Sun 14 Sep 2014 11:26:51 PM CST
 6 ************************************************************************/
 7 
 8 #include <cstdio>
 9 #include <cstring>
10 #include <cstdlib>
11 #include <cmath>
12 #include <vector>
13 #include <queue>
14 #include <iostream>
15 #include <algorithm>
16 using namespace std;
17 typedef long long ll;
18 const int INF = 1 << 29;
19 const ll mod = 10000007;
20 
21 int n,m;
22 
23 struct Mx{
24     ll a[15][15];
25     void clear(){
26         memset(a,0,sizeof(a));
27     }
28     void stand(){
29         memset(a,0,sizeof(a));
30         for(int i = 0; i <= n + 1; ++i)
31             a[i][i] = 1;
32     }
33     Mx operator * (const Mx &b){
34         Mx c; c.clear();
35         for(int i = 0; i <= n + 1; ++i)
36         for(int j = 0; j <= n + 1; ++j)
37         for(int k = 0; k <= n + 1; ++k){
38             c.a[i][j] = (c.a[i][j] + a[i][k] * b.a[k][j]) % mod;
39         }
40         return c;
41     }
42 };
43 
44 Mx Mx_pow(int v){
45     Mx res; res.stand();
46     Mx t; t.clear();
47     t.a[0][0] = 10; t.a[0][n + 1] = 1;
48     for(int i = 1; i <= n; ++i){
49         for(int j = 0; j <= i; ++j){
50             t.a[i][j] = 1;
51         }
52     }
53     t.a[n + 1][n + 1] = 1;
54     while(v){
55         if(v & 1){
56             res = res * t;
57         }
58         t = t * t;
59         v >>= 1;
60     }
61     return res;
62 }
63 
64 int main(){
65     while(scanf("%d%d",&n,&m) != EOF){
66         Mx res; res.clear();
67         res.a[0][0] = 233;
68         for(int i = 1; i <= n; ++i){
69             scanf("%I64d",&res.a[i][0]);
70         }
71         res.a[n + 1][0] = 3;
72         res = Mx_pow(m) * res;
73         printf("%I64d\n",res.a[n][0] % mod);
74     }
75     return 0;
76 }

 

posted @ 2014-09-15 16:21  Naturain  阅读(171)  评论(0)    收藏  举报