hdu 5015 233 Matrix （矩阵高速幂）

Posted 2020-09-27 cxchanpin

233 Matrix

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 749    Accepted Submission(s): 453

Problem Description

In our daily life we often use 233 to express our feelings. Actually, we may say 2333, 23333, or 233333 ... in the same meaning. And here is the question: Suppose we have a matrix called 233 matrix. In the first line, it would be 233, 2333, 23333... (it means a_0,1 = 233,a_0,2 = 2333,a_0,3 = 23333...) Besides, in 233 matrix, we got a_i,j = a_i-1,j +a_i,j-1( i,j ≠ 0). Now you have known a_1,0,a_2,0,...,a_n,0, could you tell me a_n,m in the 233 matrix?

 

Input

There are multiple test cases. Please process till EOF.

For each case, the first line contains two postive integers n,m(n ≤ 10,m ≤ 10⁹). The second line contains n integers, a_1,0,a_2,0,...,a_n,0(0 ≤ a_i,0 < 2³¹).

 

Output

For each case, output a_n,m mod 10000007.

 

Sample Input

1 1
1
2 2
0 0
3 7
23 47 16

 

Sample Output

234
2799
72937

Hint

思路：

第一列元素为：

0

a1

a2

a3

a4

转化为：

23

a1

a2

a3

a4

3

则第二列为：

23*10+3

23*10+3+a1

23*10+3+a1+a2

23*10+3+a1+a2+a3

23*10+3+a1+a2+a3+a4

3

依据前后两列的递推关系，有等式可得矩阵A的元素为：   

#include"iostream"
#include"stdio.h"
#include"string.h"
#include"algorithm"
#include"queue"
#include"vector"
using namespace std;
#define N 15
#define LL __int64
const int mod=10000007;
int n;
int b[N];
struct Mat
{
    LL mat[N][N];
}a,ans;
Mat operator*(Mat a,Mat b)
{
    int i,j,k;
    Mat c;
    memset(c.mat,0,sizeof(c.mat));
    for(i=0; i<=n+1; i++)
    {
        for(j=0; j<=n+1; j++)
        {
            c.mat[i][j]=0;
            for(k=0; k<=n+1; k++)
            {
                if(a.mat[i][k]&&b.mat[k][j])
                {
                    c.mat[i][j]+=a.mat[i][k]*b.mat[k][j];
                    c.mat[i][j]%=mod;
                }
            }
        }
    }
    return c;
}
void mult(int k)
{
    int i;
    memset(ans.mat,0,sizeof(ans.mat));
    for(i=0;i<=n+1;i++)
        ans.mat[i][i]=1;
    while(k)
    {
        if(k&1)
            ans=ans*a;
        k>>=1;
        a=a*a;
    }
}
void inti()
{
    int i,j;
    b[0]=23;
    b[n+1]=3;
    for(i=1; i<=n; i++)
        scanf("%d",&b[i]);
    memset(a.mat,0,sizeof(a.mat));
    for(i=0; i<=n; i++)
    {
        a.mat[i][0]=10;
        a.mat[i][n+1]=1;
    }
    a.mat[n+1][n+1]=1;
    for(i=1; i<n+1; i++)
    {
        for(j=1; j<=i; j++)
        {
            a.mat[i][j]=1;
        }
    }
}
int main()
{
    int i,m;
    while(scanf("%d%d",&n,&m)!=-1)
    {
        inti();
        mult(m);
        LL s=0;
        for(i=0;i<=n+1;i++)
            s=(s+(ans.mat[n][i]*b[i])%mod)%mod;
        printf("%I64d\n",s);
    }
    return 0;
}