笔记-[JSOI2011]柠檬
\(f_i\) 表示到第 \(i\) 只贝壳最多可以换得的柠檬数。
令 \(c_i=\sum_{h=1}^i[s_h=s_i]\)。
\[\begin{split} f_i=&\max\{f_{j-1}+s_i(c_i-c_j+1)^2\}(s_i=s_j,j\le i)\\\\ f_i=&f_{j-1}+s_i(c_i^2+c_j^2+1-2c_ic_j+2c_i-2c_j)\\\\ f_i=&f_{j-1}+s_ic_i^2+s_ic_j^2+s_i-2s_ic_ic_j+2s_ic_i-2s_ic_j\\\\ f_{j-1}+s_jc_j^2-2s_jc_j=&2s_ic_ic_j+f_i-s_ic_i^2-2s_ic_i-s_i\\\\ \end{split} \\ \therefore \begin{cases} y=f_{j-1}+s_jc_j^2-2s_jc_j\\ k=2s_ic_i\\ x=c_j\\ b=f_i-s_ic_i^2-2s_ic_i-s_i\\ \end{cases} \\ \Huge y=kx+b \]
搞定。
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