> 首先变形为:
> a[i + 1] = 2 * a[i] - a[i - 1] + 2 * c[i]
> 
> 比如
> a[2] = 2 * a[1] - a[0] + 2 * c[1]
> 发现它是a[1]的线性组合，猜想a[3]也是a[1]的线性组合
> 
> 那么设
> a[i] = p[i] * a[1] + q[i]
> 则
> a[i + 1] = 2 * a[i] - a[i - 1] + 2 * c[i]
>          = 2 * (p[i] * a[1] + q[i]) - (p[i - 1] * a[1] + q[i - 1]) + 2 * c[i]
>          = (2 * p[i] - p[i - 1]) * a[1] + (2 * q[i] - q[i - 1] + 2 * c[i])
> 即
> p[i + 1] = 2 * p[i] - p[i - 1]
> q[i + 1] = 2 * q[i] - q[i - 1] + 2 * c[i]
> 由此递推得到a[n + 1]关于a[1]的线性表达式，即可求解
> 
> 

• UP&ORZ moretimes (0) Tune 2013-03-10 16:43:07