矩阵构造

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一个  数列，a[1]=1,给出a[2],            a[n]=2*a[2]*a[n-1]-a[n-2],求这个数列的平方和模M

数据范围：1<=a[2],M<=1000000000(9次方)，2<=N<=1000000000(9次方)

思路：

一看 n的范围是9次方只能想log的算法（构造矩阵，二分幂）

最后构造的结果是

(s[n]代表的是前n项的和)

a[n],a[n-1]*a[n-1],a[n-1]*a[n-2],s[n-1]              2*a[2]*a[2]          1          0              1

                                                                      1-4*a[2]*a[2]          0        2*a[2]        0

                                                                               4*a[2]            0        -1               0

                                                                                0                   0          0              1

构造的过程

s[n]=s[n-1]+a[n]*a[n]

a[n]+2*a[2]*2*a[2]*a[n-1]*a[n-1]+a[n-2]*a[n-2]-2*2*a[2]*a[n-1]*a[n-2]

2*2*a[2]*a[n]*a[n-1]=2*2*a[2]*2*a[2]*a[n-1]*a[n-1]-2*2*a[n-1]*a[n-2]

矩阵构造

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原文地址：http://www.cnblogs.com/ACWQYYY/p/4563447.html