HDU 5015 233 Matrix --矩阵快速幂

题意：

ai,j = a i-1,j +a i,j-1( i,j > 0) , a0,i=23333...., i+1个3，ai，0为输入的数值

给出n，m，给出（a0，1 ）， （ a0，n）

求an，m

思路：

我们知道这是NXM的矩阵

试着画出该矩阵，想推出ai，j发现推不出来，但是可以推出下一列

应该一目了然了吧

#include<bits/stdc++.h>#define N  10000007using namespace std;struct node{long long a[12][12];};const node A={          {     {1,1 ,0,0,0,0,0,0,0,0,0,0},            {0,10,1,1,1,1,1,1,1,1,1,1},{0,0 ,1,1,1,1,1,1,1,1,1,1},{0,0 ,0,1,1,1,1,1,1,1,1,1},{0,0 ,0,0,1,1,1,1,1,1,1,1},{0,0 ,0,0,0,1,1,1,1,1,1,1},{0,0 ,0,0,0,0,1,1,1,1,1,1},{0,0 ,0,0,0,0,0,1,1,1,1,1},{0,0 ,0,0,0,0,0,0,1,1,1,1},{0,0 ,0,0,0,0,0,0,0,1,1,1},{0,0 ,0,0,0,0,0,0,0,0,1,1},{0,0 ,0,0,0,0,0,0,0,0,0,1}    }             };const node B={          {          {3,233,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0}          }             };node cheng(node a,node b,bool f){node c;memset(c.a,0,sizeof(c.a));for(int i=0;i<12;i++){if(f&&i==1) break;for(int j=0;j<12;j++)for(int k=0;k<12;k++)c.a[i][j]=(c.a[i][j]+(a.a[i][k]*b.a[k][j])%N)%N;}return c;}int main(){int t,n,m,sum;node a,b;while(~scanf("%d%d",&n,&m))    {    if(n==m&&n==0)    {    printf("0\n");    continue;    }    a=A;    b=B;    for(int i=0;i<n;i++)    scanf("%lld",&(b.a[0][2+i]));        while(m)    {    if(m&1) b=cheng(b,a,true);    m>>=1;    a=cheng(a,a,false);    }    printf("%lld\n",(b.a[0][n+1]%N+N)%N);    }return 0;}