$\max$卷积优化

标签：卷积 max sum times 现在 优化

现在有

\[h_i = \sum _ {\max(j,k) = i} f_j\times g_k \]

求\(h\)。
设

\[F_i = \sum_{j = 1} ^ i f_j\\ G_i = \sum_{j = 1} ^ i g_j \]

则

\[\sum_{i = 1} ^ n h_i = F_n \times G_n\\ h_n = F_n \times G_n - F_{n - 1} \times G_{n - 1} \]

标签：卷积,max,sum,times,现在,优化
From： https://www.cnblogs.com/luyiming123blog/p/max_juan_ji.html