http://poj.org/problem?id=3734
题解:矩阵快速幂
构造初始矩阵:
{0,1,0,1}
{0,0,0,0}
{0,0,0,0}
{0,0,0,0}
构造转移矩阵:
{3,1,3,1}
{1,3,1,3}
{0,0,0,0}
{0,0,0,0}
/*
*@Author: STZG
*@Language: C++
*/
//#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
#define endl "\n"
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=10+10;
const int M=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,p,l,r,u,v,x,y;
int ans,cnt,flag,temp,sum;
int s[N][N];
int b[N][N];
int a[N][N];
char str;
struct node{};
void Matrix(ll a[N][N],ll b[N][N]){
ll c[N][N];
memset(c,0,sizeof(c));
for(int i=0;i<4;i++){
for(int j=0;j<4;j++){
for(int k=0;k<4;k++){
c[i][j]=(c[i][j]+a[i][k]*b[k][j])%10007;
}
}
}
for(int i=0;i<4;i++){
for(int j=0;j<4;j++){
a[i][j]=c[i][j];
}
}
}
ll power(int k){
ll b[N][N]={{3,1,3,1},
{1,3,1,3},
{0,0,0,0},
{0,0,0,0}};
ll a[N][N]={{0,1,0,1},
{0,0,0,0},
{0,0,0,0},
{0,0,0,0}};
while(k){
if(k&1)Matrix(a,b);
Matrix(b,b);
k>>=1;
}
return (a[0][1]+a[0][3])%10007;
}
int main()
{
#ifdef DEBUG
freopen("input.in", "r", stdin);
//freopen("output.out", "w", stdout);
#endif
//ios::sync_with_stdio(false);
//cin.tie(0);
//cout.tie(0);
scanf("%d",&t);
while(t--){
scanf("%d",&n);
cout<<power(n-1)<<endl;
}
#ifdef DEBUG
printf("Time cost : %lf s\n",(double)clock()/CLOCKS_PER_SEC);
#endif
//cout << "Hello world!" << endl;
return 0;
}