HDU 2281 Square Number Pell方程

http://acm.hdu.edu.cn/showproblem.php?pid=2281

又是一道Pell方程 

化简构造以后的Pell方程为 

求出其前15个解,但这些解不一定满足等式,判断后只有5个满足的情况,直接判断即可

求法可以参照上一篇日志: http://www.cnblogs.com/Felix-F/p/3223323.html

 

 

struct matrix
{
    LL ma[2][2];
};
int n = 2;
LL nn[20],xx[20];
matrix operator * (matrix a,matrix b)
{
    matrix temp;
    memset(temp.ma,0,sizeof(temp.ma));
    for(int i = 0; i < n ; i++)
        for(int j = 0; j < n ; j++)
            for(int k = 0 ; k < n ; k++)
                temp.ma[i][j] = temp.ma[i][j] + (a.ma[k][i] * b.ma[j][n-k-1]);
    return temp;
}
matrix operator + (matrix a,matrix b)
{
    for(int i = 0; i < n ; i++)
        for(int j = 0; j < n ; j++)
            a.ma[i][j] = (a.ma[i][j] + b.ma[i][j]) ;
    return a;
}
void init()
{
    matrix a;
    a.ma[0][0] = 1;
    a.ma[0][1] = 7;
    a.ma[1][0] = 7;
    a.ma[1][1] = 48;
    matrix temp = a;
    nn[0] = 1;
    xx[0] = 1;
    int cnt = 1;
    for(int i = 1 ;i <= 18 ; i++)
    {
        if(i%2 == 0)
        {
            LL s1 = temp.ma[0][1] * 7 + temp.ma[1][1] * 1;
            nn[cnt] = (s1 - 3) / 4;
            LL s2 = temp.ma[0][0] * 7 + temp.ma[1][0] * 1;
            xx[cnt++] = s2;
        }
        temp = temp*a;
    }
}
int main()
{
    init();
    LL N;
    while(cin>>N && N)
    {
        for(int i = 7 ; i >= 0 ; i--)
        {
            if(N >= nn[i])
            {
                cout<<nn[i]<<" "<<xx[i]<<endl;
                break;
            }
        }
    }
    return 0;
}