题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=2256
题意:计算(sqrt(2)+sqrt(3))^(2n)%1024。
思路:令x=(sqrt(2)+sqrt(3))^2.
x=5+2*sqrt(6.0) -> (5*2-1)%1024=9
x^2=49+20*sqrt(6.0) -> (49*2-1)%1024=97
x^3=485+198*sqrt(6.0) -> (485*2-1)%1024=969
得到规律: 49=5*5+2*12 20=5*2+2*5
485=49*5+20*12 198=49*2+20*5
令2*2的矩阵为a={5,12,2,5}。对于n求a^(n-1)。
#include <iostream>
#include <cstdio>
#include <string.h>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <string>
#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define abs(x) ((x)>=0?(x):-(x))
#define i64 long long
#define u32 unsigned int
#define u64 unsigned long long
#define clr(x,y) memset(x,y,sizeof(x))
#define CLR(x) x.clear()
#define ph(x) push(x)
#define pb(x) push_back(x)
#define Len(x) x.length()
#define SZ(x) x.size()
#define PI acos(-1.0)
#define sqr(x) ((x)*(x))
#define FOR0(i,x) for(i=0;i<x;i++)
#define FOR1(i,x) for(i=1;i<=x;i++)
#define FOR(i,a,b) for(i=a;i<=b;i++)
#define DOW0(i,x) for(i=x;i>=0;i--)
#define DOW1(i,x) for(i=x;i>=1;i--)
#define DOW(i,a,b) for(i=a;i>=b;i--)
using namespace std;
void RD(int &x){scanf("%d",&x);}
void RD(i64 &x){scanf("%lld",&x);}
void RD(u64 &x){scanf("%llu",&x);}
void RD(u32 &x){scanf("%u",&x);}
void RD(double &x){scanf("%lf",&x);}
void RD(int &x,int &y){scanf("%d%d",&x,&y);}
void RD(i64 &x,i64 &y){scanf("%lld%lld",&x,&y);}
void RD(u64 &x,u64 &y){scanf("%llu%llu",&x,&y);}
void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}
void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}
void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}
void RD(i64 &x,i64 &y,i64 &z){scanf("%lld%lld%lld",&x,&y,&z);}
void RD(u64 &x,u64 &y,u64 &z){scanf("%llu%llu%llu",&x,&y,&z);}
void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}
void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}
void RD(char &x){x=getchar();}
void RD(char *s){scanf("%s",s);}
void RD(string &s){cin>>s;}
void PR(int x) {printf("%d\n",x);}
void PR(i64 x) {printf("%lld\n",x);}
void PR(u64 x) {printf("%llu\n",x);}
void PR(u32 x) {printf("%u\n",x);}
void PR(double x) {printf("%lf\n",x);}
void PR(char x) {printf("%c\n",x);}
void PR(char *x) {printf("%s\n",x);}
void PR(string x) {cout<<x<<endl;}
const int mod=1024;
const int INF=2000000000;
const int N=105;
int C,num=0;
int n,m;
class Matrix
{
public:
int a[N][N];
void init(int x)
{
int i;
if(!x) clr(a,0);
else
{
clr(a,0);
FOR0(i,N) a[i][i]=1;
}
}
void read(int n)
{
int i,j;
FOR1(i,n) FOR1(j,n)
{
RD(a[i][j]);
a[i][j]%=mod;
}
}
Matrix operator*(Matrix b)
{
int i,j,k;
Matrix p;
p.init(0);
FOR0(i,2) FOR0(j,2) FOR0(k,2)
{
(p.a[i][j]+=(i64)a[i][k]*b.a[k][j]%mod)%=mod;
}
return p;
}
Matrix power(int t)
{
Matrix ans,p=*this;
ans.init(1);
while(t)
{
if(t&1) ans=ans*p;
p=p*p;
t>>=1;
}
return ans;
}
void print(int n)
{
int i,j;
FOR0(i,n)
{
FOR0(j,n) printf("%d ",a[i][j]);
puts("");
}
}
};
Matrix a,b;
int main()
{
RD(C);
while(C--)
{
scanf("%d",&n);
if(n==1)
{
puts("9");
continue;
}
a.a[0][0]=5;
a.a[0][1]=12;
a.a[1][0]=2;
a.a[1][1]=5;
a=a.power(n-1);
int ans=(a.a[0][0]*5+a.a[0][1]*2)%mod;
printf("%d\n",(ans*2-1)%mod);
}
return 0;
}