CodeForces 185A. Plant（矩阵快速幂）

题目链接：http://codeforces.com/problemset/problem/185/A

Dwarfs have planted a very interesting plant, which is a triangle directed "upwards". This plant has an amusing feature. After one year a triangle plant directed "upwards" divides into four triangle plants: three of them will point "upwards" and one will point "downwards". After another year, each triangle plant divides into four triangle plants: three of them will be directed in the same direction as the parent plant, and one of them will be directed in the opposite direction. Then each year the process repeats. The figure below illustrates this process.

Help the dwarfs find out how many triangle plants that point "upwards" will be in n years.

Input

The first line contains a single integer n (0 ≤ n ≤ 1018) — the number of full years when the plant grew.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64dspecifier.

Output

Print a single integer — the remainder of dividing the number of plants that will point "upwards" in n years by 1000000007 (109 + 7).

Sample test(s)

input

1

output

3

input

2

output

10

Note

The first test sample corresponds to the second triangle on the figure in the statement. The second test sample corresponds to the third one.

PS:

上三角个数：△-> 3*△ +1*▽

下三角个数：▽-> 1*△ +3*▽

矩阵快速幂；

等比矩阵为：

3 1

1 3

代码如下：

#include 
#include 
#include 
#include 
using namespace std;
#define LL __int64
struct Matrix
{
    LL  m[5][5];
} I,A,B,T;

LL a, b, n;
int ssize = 2;
#define mod 1000000007
Matrix Mul(Matrix a,Matrix b)
{
    int i, j, k;
    Matrix c;
    for(i = 1; i <= ssize; i++)
    {
        for(j = 1; j <= ssize; j++)
        {
            c.m[i][j]=0;
            for(k = 1; k <= ssize; k++)
            {
                c.m[i][j]+=(a.m[i][k]*b.m[k][j]);
                c.m[i][j]%=mod;
            }
        }
    }
    return c;
}

Matrix quickpagow(LL n)
{
    Matrix m = A, b = I;
    while(n)
    {
        if(n & 1)
            b = Mul(b,m);
        n = n >> 1;
        m = Mul(m,m);
    }
    return b;
}
int main()
{
    //a1 向下，b1向上
    LL c;
    while(~scanf("%I64d",&n))
    {
        memset(I.m,0,sizeof(I.m));
        memset(A.m,0,sizeof(A.m));
        memset(B.m,0,sizeof(B.m));
        for(int i = 1; i <= ssize; i++)
        {
            //单位矩阵
            I.m[i][i]=1;
        }
        B.m[1][1] = 0, B.m[2][1] = 1;
        A.m[1][1] = 3;//初始化等比矩阵
        A.m[1][2] = 1;
        A.m[2][1] = 1;
        A.m[2][2] = 3;
        T = quickpagow(n);
        T = Mul(B,T);
        printf("%I64d\n",T.m[2][1]%mod);
    }
    return 0;
}
/*
1
2
3
1000000
1000000000000000000
10
*/