A14152. AB Tree
编程题
普及/提高-
知识点
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.
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.
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.
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.
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 #1
9 3 1 2 2 4 4 4 3 1
输出 #1
4 aabbbbbba
说明/提示
The tree from the sample is shown below:
The tree after assigning characters to every node (according to the output) is the following:
Strings for all nodes are the following:
- string of node $1$ is: a
- string of node $2$ is: aa
- string of node $3$ is: aab
- string of node $4$ is: aab
- string of node $5$ is: aabb
- string of node $6$ is: aabb
- string of node $7$ is: aabb
- string of node $8$ is: aabb
- string of node $9$ is: aa
The set of unique strings is $\{\text{a}, \text{aa}, \text{aab}, \text{aabb}\}$ , so the number of distinct strings is $4$ .
The tree after assigning characters to every node (according to the output) is the following:
Strings for all nodes are the following:
- string of node $1$ is: a
- string of node $2$ is: aa
- string of node $3$ is: aab
- string of node $4$ is: aab
- string of node $5$ is: aabb
- string of node $6$ is: aabb
- string of node $7$ is: aabb
- string of node $8$ is: aabb
- string of node $9$ is: aa
The set of unique strings is $\{\text{a}, \text{aa}, \text{aab}, \text{aabb}\}$ , so the number of distinct strings is $4$ .