【动态规划】之树形DP例题2024/7/10codeforces Div.2 T4《Maximize the Root》

题目大意

You are given a rooted tree, consisting of $n$ vertices. The vertices in the tree are numbered from $1$ to $n$, and the root is the vertex $1$. The value $a_i$ is written at the $i$-th vertex.

You can perform the following operation any number of times (possibly zero): choose a vertex $v$ which has at least one child; increase $a_v$ by $1$; and decrease $a_u$ by $1$ for all vertices $u$ that are in the subtree of $v$ (except $v$ itself). However, after each operation, the values on all vertices should be non-negative.

Your task is to calculate the maximum possible value written at the root using the aforementioned operation.
给你一棵有根的树，由 $n$ 个顶点组成。树中的顶点编号为 $1$ 至 $n$ ，根顶点为 $1$ 。值 $a_i$ 写在第 $i$