笔记-P6302 [NOI2019] 回家路线 加强版

\[f_i = \min\limits(f_{j} + A(p_i - q_j)^2 + B(p_i - q_j) + C) \]

\[f_i = \min\limits(f_j + Aq_j^2 - Bq_j - 2Ap_i q_j) + C + Ap_i^2 + Bp_i \]

让 \(d_j = f_j + A q_j^2 - Bq_j\)

\[f_i = \min\limits(d_j - 2Ap_i q_j) + C + Ap_i^2 + Bp_i \]

如果对于 \(q_{j} < q_{k}\)，\(k\) 比 \(j\) 优秀：

\[d_j - 2Ap_i q_j > d_k - 2Ap_i q_k \]

\[2Ap_i q_k - 2Ap_i q_j > d_k - d_j \]

\[2A p_i > \frac{d_k - d_j}{q_k - q_j} \]

斜率优化？？？