| Codeforces Round 813 (Div. 2) |
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| Finished |
A tree is a connected undirected graph without cycles. A weighted tree has a weight assigned to each edge. The degree of a vertex is the number of edges connected to this vertex.
You are given a weighted tree with $$$n$$$ vertices, each edge has a weight of $$$1$$$. Let $$$L$$$ be the set of vertices with degree equal to $$$1$$$.
You have to answer $$$q$$$ independent queries. In the $$$i$$$-th query:
- You are given a positive integer $$$x_i$$$.
- For all $$$u,v \in L$$$ such that $$$u < v$$$, add edge $$$(u, v)$$$ with weight $$$x_i$$$ to the graph (initially the given tree).
- Find the diameter of the resulting graph.
The diameter of a graph is equal to $$$\max\limits_{1 \le u < v \le n}{\operatorname{d}(u, v)}$$$, where $$$\operatorname{d}(u, v)$$$ is the length of the shortest path between vertex $$$u$$$ and vertex $$$v$$$.
The first line contains a single integer $$$n$$$ ($$$3 \le n \le 10^6$$$).
The second line contains $$$n - 1$$$ integers $$$p_2,p_3,\ldots,p_n$$$ ($$$1 \le p_i < i$$$) indicating that there is an edge between vertices $$$i$$$ and $$$p_i$$$. It is guaranteed that the given edges form a tree.
The third line contains a single integer $$$q$$$ ($$$1 \le q \le 10$$$).
The fourth line contains $$$q$$$ integers $$$x_1,x_2,\ldots,x_q$$$ ($$$1 \le x_i \le n$$$). All $$$x_i$$$ are distinct.
Print $$$q$$$ integers in a single line — the answers to the queries.
4 1 2 2 4 1 2 3 4
1 2 2 2
7 1 2 3 4 2 1 7 2 1 3 7 5 6 4
3 3 4 5 5 5 4
3 1 2 1 1
1
The graph in the first test after adding the edges:
