USACO 2023 February Contest, Gold: Problem 2. Fertilizing Pastures

Problems and Contests
#1

Hi all, I was looking at the editorial of the problem but can’t really understand why.

USACO 2023 February Contest, Gold: Problem 2. Fertilizing Pastures Problem Link Editorial Link

I understand the part where it says "If Farmer John visits the subtree of child v at time t, it takes dp(v) + sum(v) ⋅t fertilizer."

However, when it moves into talking about minimizing the total fertilizers using greedy methods, the sum part disappears. Is the sum * t part not important when considering the order of the children?

Thank you.

#2

A lot of places where the editorial has a_{v_i} should be \text{sum}_{v_i} instead. Will update the analysis.

#3

Thank you!