A11566. Coloring a Tree
编程题
普及/提高-
知识点
题目描述
You are given a rooted tree with $n$ vertices. The vertices are numbered from $1$ to $n$ , the root is the vertex number $1$ .
Each vertex has a color, let's denote the color of vertex $v$ by $c_{v}$ . Initially $c_{v}=0$ .
You have to color the tree into the given colors using the smallest possible number of steps. On each step you can choose a vertex $v$ and a color $x$ , and then color all vectices in the subtree of $v$ (including $v$ itself) in color $x$ . In other words, for every vertex $u$ , such that the path from root to $u$ passes through $v$ , set $c_{u}=x$ .
It is guaranteed that you have to color each vertex in a color different from $0$ .
You can learn what a rooted tree is using the link: <a>https://en.wikipedia.org/wiki/Tree\_(graph\_theory)</a>.
Each vertex has a color, let's denote the color of vertex $v$ by $c_{v}$ . Initially $c_{v}=0$ .
You have to color the tree into the given colors using the smallest possible number of steps. On each step you can choose a vertex $v$ and a color $x$ , and then color all vectices in the subtree of $v$ (including $v$ itself) in color $x$ . In other words, for every vertex $u$ , such that the path from root to $u$ passes through $v$ , set $c_{u}=x$ .
It is guaranteed that you have to color each vertex in a color different from $0$ .
You can learn what a rooted tree is using the link: <a>https://en.wikipedia.org/wiki/Tree\_(graph\_theory)</a>.
输入格式
The first line contains a single integer $n$ ( $2<=n<=10^{4}$ ) — the number of vertices in the tree.
The second line contains $n-1$ integers $p_{2},p_{3},...,p_{n}$ ( $1<=p_{i}<i$ ), where $p_{i}$ means that there is an edge between vertices $i$ and $p_{i}$ .
The third line contains $n$ integers $c_{1},c_{2},...,c_{n}$ ( $1<=c_{i}<=n$ ), where $c_{i}$ is the color you should color the $i$ -th vertex into.
It is guaranteed that the given graph is a tree.
The second line contains $n-1$ integers $p_{2},p_{3},...,p_{n}$ ( $1<=p_{i}<i$ ), where $p_{i}$ means that there is an edge between vertices $i$ and $p_{i}$ .
The third line contains $n$ integers $c_{1},c_{2},...,c_{n}$ ( $1<=c_{i}<=n$ ), where $c_{i}$ is the color you should color the $i$ -th vertex into.
It is guaranteed that the given graph is a tree.
输出格式
Print a single integer — the minimum number of steps you have to perform to color the tree into given colors.
输入输出样例
输入 #1
6 1 2 2 1 5 2 1 1 1 1 1
输出 #1
3
输入 #2
7 1 1 2 3 1 4 3 3 1 1 1 2 3
输出 #2
5
说明/提示
The tree from the first sample is shown on the picture (numbers are vetices' indices):
On first step we color all vertices in the subtree of vertex $1$ into color $2$ (numbers are colors):
On seond step we color all vertices in the subtree of vertex $5$ into color $1$ :
On third step we color all vertices in the subtree of vertex $2$ into color $1$ :
The tree from the second sample is shown on the picture (numbers are vetices' indices):
On first step we color all vertices in the subtree of vertex $1$ into color $3$ (numbers are colors):
On second step we color all vertices in the subtree of vertex $3$ into color $1$ :
On third step we color all vertices in the subtree of vertex $6$ into color $2$ :
On fourth step we color all vertices in the subtree of vertex $4$ into color $1$ :
On fith step we color all vertices in the subtree of vertex $7$ into color $3$ :
On first step we color all vertices in the subtree of vertex $1$ into color $2$ (numbers are colors):
On seond step we color all vertices in the subtree of vertex $5$ into color $1$ :
On third step we color all vertices in the subtree of vertex $2$ into color $1$ :
The tree from the second sample is shown on the picture (numbers are vetices' indices):
On first step we color all vertices in the subtree of vertex $1$ into color $3$ (numbers are colors):
On second step we color all vertices in the subtree of vertex $3$ into color $1$ :
On third step we color all vertices in the subtree of vertex $6$ into color $2$ :
On fourth step we color all vertices in the subtree of vertex $4$ into color $1$ :
On fith step we color all vertices in the subtree of vertex $7$ into color $3$ :
