233 Matrix
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1190 Accepted Submission(s): 700
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 a0,1 = 233,a0,2 = 2333,a0,3 = 23333...) Besides, in 233 matrix, we got ai,j = ai-1,j +ai,j-1( i,j ≠ 0). Now you have known a1,0,a2,0,...,an,0, could you tell me an,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, a1,0,a2,0,...,an,0(0 ≤ ai,0 < 231).
Output
For each case, output an,m mod 10000007.
Sample Input
1 1
1
2 2
0 0
3 7
23 47 16
Sample Output
234
2799
72937
Hint
我们这样看：已知a11 ,a21 ,a31 ,a41 。。。求后面的
a12 = a11 +233;
a22 = a11 + a21 +233;
a32 = a11 + a21 +a31 +233;
a42 = a11 + a21 +a31 +a41 +233;
.........
同理：后面的列也一样：
a13 = a12 +233;
a23 = a12 + a22 +233;
a33 = a12 + a22 +a32 +233;
a43 = a12 + a22 +a32 +a42 +233;
...........
ss所以有矩阵：
| 233 | a11 |
a21 | a31 | a41 | ... | 3 |
*
| 10 | 1 | 1 | 1 | 1 | ... | 0 |
| 0 | 1 | 1 | 1 | 1 | ... | 0 |
| 0 | 0 | 1 | 1 | 1 | ... | 0 |
| 0 | 0 | 0 | 1 | 1 | ... | 0 |
| 0 | 0 | 0 | 0 | 1 | ... | 0 |
| ... | ... | ... | ... | ... | ... | ... |
| 1 | 0 | 0 | 0 | 0 | ... | 1 |
=
......................................................................................................................................................
z转载请注明出处：
寻找&星空の孩子
题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5015
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<iostream>
#include<algorithm>
using namespace std;
#define LL __int64
#define mod 10000007 LL N,M; struct matrix
{
LL m[][];
};
LL a[]; matrix multiply(matrix x,matrix y)
{
matrix temp;
memset(temp.m,,sizeof(temp.m));
for(int i=; i<N+; i++)
{
for(int j=; j<N+; j++)
{
if(x.m[i][j]==) continue;
for(int k=; k<N+; k++)
{
if(y.m[j][k]==) continue;
temp.m[i][k]+=x.m[i][j]*y.m[j][k]%mod;
temp.m[i][k]%=mod;
}
}
}
return temp;
} matrix quickmod(matrix a,LL n)
{
matrix res;
memset(res.m,,sizeof(res.m));
for(int i=;i<N+;i++) res.m[i][i]=;
while(n)
{
if(n&)
res=multiply(res,a);
n>>=;
a=multiply(a,a);
}
return res;
}
int main()
{
int n,k;
while(scanf("%d%d",&N,&M)!=EOF)
{
a[]=;
a[N+]=;
for(int i=;i<=N;i++)
{
scanf("%d",&a[i]);
} matrix ans;
memset(ans.m,,sizeof(ans.m));
ans.m[][]=;
ans.m[N+][]=;
ans.m[N+][N+]=;
for(int j=;j<=N;j++)
{
for(int i=;i<=j;i++)
{
ans.m[i][j]=;
}
} ans=quickmod(ans,M);//M次幂定位到纵坐标。 LL ant=;
for(int i=;i<N+;i++)//横坐标是N，即，乘以矩阵的N列。
{
ant=(ant+a[i]*ans.m[i][N])%mod;
}
printf("%I64d\n",ant);
}
return ;
}