HDU 5927 Auxiliary Set（树上搞事）

最新推荐文章于 2018-08-23 15:16:19 发布

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最新推荐文章于 2018-08-23 15:16:19 发布

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分类专栏：树链剖分+树上乱搞

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本文介绍了一种解决树形结构中辅助集大小查询问题的算法。通过深度优先搜索（DFS）预处理树的深度及子节点数量，再对每个查询进行排序处理，最终计算出在去除指定不重要节点后的辅助集大小。

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思路：考虑对于每一个询问的点按照深度排序，如果该不重要的点的儿子有两个，那么就证明可以贡献一个答案，如果该不重要的点没有儿子了，那么对于该点的父节点的儿子数减一

#include<bits/stdc++.h>
using namespace std;
const int maxn = 100000+7;
vector<int>e[maxn];
int dep[maxn],fa[maxn],son[maxn];
int a[maxn];
int b[maxn];
void dfs(int u,int f,int d)
{
	dep[u]=d;
	fa[u]=f;
	int len = e[u].size();
	for(int i= 0;i<len;i++)
	{
		int v = e[u][i];
		if(v==f)continue;
		dfs(v,u,d+1);
        son[u]++;
	}
}
bool cmp(int a,int b)
{
	return dep[a]>dep[b];
}
int main()
{
	int T,cas=1;
	scanf("%d",&T);
	while(T--)
	{
		printf("Case #%d:\n",cas++);
		int n,q;
		scanf("%d%d",&n,&q);
		for(int i =0;i<=n;i++)e[i].clear();
		memset(son,0,sizeof(son));
		memset(a,0,sizeof(a));
		memset(b,0,sizeof(b));
		for(int i = 1;i<=n-1;i++)
		{
			int u,v;
			scanf("%d%d",&u,&v);
			e[u].push_back(v);
			e[v].push_back(u);
		}
		dfs(1,-1,0);
		while(q--)
		{
			int num;
			scanf("%d",&num);
			int ans = n-num;
			for(int i = 0;i<num;i++)
				scanf("%d",&a[i]);
			sort(a,a+num,cmp);
            for(int i = 0;i<num;i++)b[a[i]]=son[a[i]];
            for(int i = 0;i<num;i++)
			{
				if(b[a[i]]>=2)ans++;
				else if (b[a[i]]==0)b[fa[a[i]]]--;
			}
			printf("%d\n",ans);
		}
	}
}

Description

Given a rooted tree with n vertices, some of the vertices are important.

An auxiliary set is a set containing vertices satisfying at least one of the two conditions：

It is an important vertex

It is the least common ancestor of two different important vertices.

You are given a tree with n vertices (1 is the root) and q queries.

Each query is a set of nodes which indicates the unimportant vertices in the tree. Answer the size (i.e. number of vertices) of the auxiliary set for each query.

Input

The first line contains only one integer T (

), which indicates the number of test cases.

For each test case, the first line contains two integers n (

), q (

).

In the following n -1 lines, the i-th line contains two integers

indicating there is an edge between

i and

in the tree.

In the next q lines, the i-th line first comes with an integer

indicating the number of vertices in the query set.Then comes with mi different integers, indicating the nodes in the query set.

It is guaranteed that

.

It is also guaranteed that the number of test cases in which

is no more than 10.

Output

For each test case, first output one line "Case #x:", where x is the case number (starting from 1).

Then q lines follow, i-th line contains an integer indicating the size of the auxiliary set for each query.

Sample Input

Sample Output

Case #1:
3
6
3

Hint


         
   
    
  


         
  

For the query {1，2, 3}:
•node 4, 5, 6 are important nodes For the query {5}：
•node 1，2, 3, 4, 6 are important nodes
•node 5 is the lea of node 4 and node 3 For the query {3, 1，4}:
• node 2, 5, 6 are important nodes