308201: CF1481F. AB Tree
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
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Description
AB Tree
题意翻译
给定一棵 $n$ 个节点的树,根为 $1$ ,每个节点会分配到一个字符 `a` 或 `b`。 要求整棵树中字符 `a` 的数量为 $x$ ,字符 `b` 的数量为 $n-x$ 。 定义节点 $v$ 上的字符串: - 若 $v$ 是根节点,则 $v$ 的上的字符串为根节点分配到的字符。 - 否则,$v$ 上的字符串为父节点上的字符串的末尾加上 $v$ 分配到的字符。 请为每个节点分配字符,在满足字符 `a` ,`b` 数量要求的前提下,使得所有节点上的字符串的种类最少。 注:本翻译基于 [**fanfansann**](https://www.luogu.com.cn/user/262605) 的翻译修改。题目描述
Kilani and Abd are neighbors for 3000 years, but then the day came and Kilani decided to move to another house. As a farewell gift, Kilani is going to challenge Abd with a problem written by their other neighbor with the same name Abd. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1481F/8cce3829ad0fff29931f8889a2e2e36a655644b6.png)The problem is: You are given a connected tree rooted at node $ 1 $ . You should assign a character a or b to every node in the tree so that the total number of a's is equal to $ x $ and the total number of b's is equal to $ n - x $ . Let's define a string for each node $ v $ of the tree as follows: - if $ v $ is root then the string is just one character assigned to $ v $ : - otherwise, let's take a string defined for the $ v $ 's parent $ p_v $ and add to the end of it a character assigned to $ v $ . You should assign every node a character in a way that minimizes the number of distinct strings among the strings of all nodes.输入输出格式
输入格式
The first line contains two integers $ n $ and $ x $ ( $ 1 \leq n \leq 10^5 $ ; $ 0 \leq x \leq n $ ) — the number of vertices in the tree the number of a's. The second line contains $ n - 1 $ integers $ p_2, p_3, \dots, p_{n} $ ( $ 1 \leq p_i \leq n $ ; $ p_i \neq i $ ), where $ p_i $ is the parent of node $ i $ . It is guaranteed that the input describes a connected tree.
输出格式
In the first line, print the minimum possible total number of distinct strings. In the second line, print $ n $ characters, where all characters are either a or b and the $ i $ -th character is the character assigned to the $ i $ -th node. Make sure that the total number of a's is equal to $ x $ and the total number of b's is equal to $ n - x $ . If there is more than one answer you can print any of them.
输入输出样例
输入样例 #1
9 3
1 2 2 4 4 4 3 1
输出样例 #1
4
aabbbbbba