309177: CF1637F. Towers
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
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Description
Towers
题意翻译
给定一棵包含 $n$ 个点的树,第 $i$ 个点的高度为 $h_i$。你可以在这 $n$ 个点中建任意多个塔,对于每个塔,你都可以指定其所在的点的编号及其势能。建一个势能为 $e$ 的塔需要花费 $e$ 枚硬币(需要保证 $e>0$)。 对于一个树上的点 $x$,我们称其接收到了信号,当且仅当在树上存在两个建了塔的点 $u,v$(需要保证 $u\neq v$,但不需要保证 $x\neq u$ 或 $x\neq v$),使得 $x$ 在从 $u$ 到 $v$ 的路径上,且 $\min(e_u,e_v)\geqslant h_x$。 请求出最少需要花费多少枚硬币,才能使得树上所有点都能接受到信号。 数据范围: - $2\leqslant n\leqslant 2\times 10^5$。 - $1\leqslant h_i\leqslant 10^9$。 Translated by Eason_AC题目描述
You are given a tree with $ n $ vertices numbered from $ 1 $ to $ n $ . The height of the $ i $ -th vertex is $ h_i $ . You can place any number of towers into vertices, for each tower you can choose which vertex to put it in, as well as choose its efficiency. Setting up a tower with efficiency $ e $ costs $ e $ coins, where $ e > 0 $ . It is considered that a vertex $ x $ gets a signal if for some pair of towers at the vertices $ u $ and $ v $ ( $ u \neq v $ , but it is allowed that $ x = u $ or $ x = v $ ) with efficiencies $ e_u $ and $ e_v $ , respectively, it is satisfied that $ \min(e_u, e_v) \geq h_x $ and $ x $ lies on the path between $ u $ and $ v $ . Find the minimum number of coins required to set up towers so that you can get a signal at all vertices.输入输出格式
输入格式
The first line contains an integer $ n $ ( $ 2 \le n \le 200\,000 $ ) — the number of vertices in the tree. The second line contains $ n $ integers $ h_i $ ( $ 1 \le h_i \le 10^9 $ ) — the heights of the vertices. Each of the next $ n - 1 $ lines contain a pair of numbers $ v_i, u_i $ ( $ 1 \le v_i, u_i \le n $ ) — an edge of the tree. It is guaranteed that the given edges form a tree.
输出格式
Print one integer — the minimum required number of coins.
输入输出样例
输入样例 #1
3
1 2 1
1 2
2 3
输出样例 #1
4
输入样例 #2
5
1 3 3 1 3
1 3
5 4
4 3
2 3
输出样例 #2
7
输入样例 #3
2
6 1
1 2
输出样例 #3
12