矩阵优化dp

链接：https://www.luogu.org/problemnew/show/P1939

题解：

矩阵优化dp模板题

搞清楚矩阵是怎么乘的构造一下矩阵就很简单了

代码：

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mo 1000000007
ll t,x;
struct re{
    ll jz[][];
}a,c;
re XX(re x,re y)
{
    re tmp; memset(tmp.jz,,sizeof(tmp.jz));
    for (ll i=;i<=;i++)
      for (ll j=;j<=;j++)
        for (ll k=;k<=;k++)
          tmp.jz[i][k]=(tmp.jz[i][k]+x.jz[i][j]*y.jz[j][k])%mo;
    return(tmp);
}
re fastpow(ll x)
{
    if (x==) return(a);
    re b=fastpow(x/);
    b=XX(b,b);
    if (x%==) b=XX(b,a);
    return(b);
}
int main()
{
    freopen("noip.in","r",stdin);
    freopen("noip.out","w",stdout);
    cin>>t;
    while (t--)
    {
      memset(a.jz,,sizeof(a.jz));
      a.jz[][]=; a.jz[][]=;
      a.jz[][]=; a.jz[][]=;
      cin>>x;
      if (x<=) cout<<<<endl;
      else
      {
         c=fastpow(x-);
           cout<<(c.jz[][]+c.jz[][]+c.jz[][])%mo<<endl;
      }

    }
    return ;
}