动态规划--最长回文子序列

$给定一个序列S_{i,j} = \{ c_i, c_{i+1}, ..., c_j \}$

1、

$\qquad设c_k \in S_{i,j},\ c_q \in S_{i,j},\ c_k = c_q\ (i \leq k \leq q \leq j), \ 则$

$$S_{i,j} = \begin{cases} 1, & i \leq k = q \leq j \\ \min\{2+S_{i,j} -\{c_k,c_q\}\}, & i \leq k < q \leq j \\ \end{cases}$$

2、

$$S_{i,j} = \begin{cases} 1, & i = j \\ 2+S_{i+1,j-1}, & c_{i} = c_{j} \\ \max\{S_{i+1,j},\ S_{i,j-1}\}, & c_{i} \neq c_{j} \end{cases}$$