UVALive - 3902 Network-优快云博客

本文链接：https://blog.youkuaiyun.com/acm_1361677193/article/details/40922749

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Description

Consider a tree network with n nodes where the internal nodes correspond to servers and the terminal nodes correspond to clients. The nodes are numbered from 1 to n . Among the servers, there is an original server S which provides VOD (Video On Demand) service. To ensure the quality of service for the clients, the distance from each client to the VOD server S should not exceed a certain value k . The distance from a node u to a node v in the tree is defined to be the number of edges on the path from u to v . If there is a nonempty subset C of clients such that the distance from each u in C to S is greater than k , then replicas of the VOD system have to be placed in some servers so that the distance from each client to the nearest VOD server (the original VOD system or its replica) is k or less.

Given a tree network, a server S which has VOD system, and a positive integer k , find the minimum number of replicas necessary so that each client is within distance k from the nearest server which has the original VOD system or its replica.

For example, consider the following tree network.

$\epsfbox{p3902.eps}$

In the above tree, the set of clients is {1, 6, 7, 8, 9, 10, 11, 13}, the set of servers is {2, 3, 4, 5, 12, 14}, and the original VOD server is located at node 12.

For k = 2 , the quality of service is not guaranteed with one VOD server at node 12 because the clients in {6, 7, 8, 9, 10} are away from VOD server at distance > k . Therefore, we need one or more replicas. When one replica is placed at node 4, the distance from each client to the nearest server of {12, 4} is less than or equal to 2. The minimum number of the needed replicas is one for this example.

Input

Your program is to read the input from standard input. The input consists of T test cases. The number of test cases ( T ) is given in the first line of the input. The first line of each test case contains an integer n(3 $\le$ n $\le$ 1, 000) which is the number of nodes of the tree network. The next line contains two integers s(1 $\le$ s $\le$ n) and k(k $\ge$ 1) where s is the VOD server and k is the distance value for ensuring the quality of service. In the following n - 1 lines, each line contains a pair of nodes which represent an edge of the tree network.

Output

Your program is to write to standard output. Print exactly one line for each test case. The line should contain an integer that is the minimum number of the needed replicas.

Sample Input

Sample Output

1 
0

Source

Regionals 2007 >> Asia - Seoul

分析：

2007年亚洲区域赛首尔赛区的题目，难度在区域赛中应该算简单的。刘汝佳大白书里的题。就是无根树转为有根树，然后是点的覆盖问题。

代码：

#include <iostream>
#include<cstdio>
#include<vector>
#include<cstring>
#include<algorithm>
using namespace std;

const int maxn=1000+10;
vector<int> gr[maxn],nodes[maxn];
int n,s,k,fa[maxn];
bool convered[maxn];

void dfs(int u,int f,int d)
{
fa[u]=f;
int nc=gr[u].size();
if(nc==1&&d>k) nodes[d].push_back(u);
for(int i=0;i<nc;i++)
{
int v=gr[u][i];
if(v!=f) dfs(v,u,d+1);
}
}

void dfs2(int u,int f,int d)
{
convered[u]=true;
int nc=gr[u].size();
for(int i=0;i<nc;i++)
{
int v=gr[u][i];
if(v!=f&&d<k) dfs2(v,u,d+1);
}
}

int solve()
{
int ans=0;
memset(convered,0,sizeof(convered));
for(int d=n-1;d>k;d--)
for(int i=0;i<nodes[d].size();i++)
{
int u=nodes[d][i];
if(convered[u]) continue;
int v=u;
for(int j=0;j<k;j++)
v=fa[v];
dfs2(v,-1,0);
ans++;
}
return ans;
}

int main()
{
int t;
scanf("%d",&t);
while(t--)
{
scanf("%d%d%d",&n,&s,&k);
for(int i=0;i<=n;i++)
{
gr[i].clear();
nodes[i].clear();
}
for(int i=0;i<n-1;i++)
{
int a,b;
scanf("%d%d",&a,&b);
gr[a].push_back(b);
gr[b].push_back(a);
}
dfs(s,-1,0);
printf("%d\n",solve());
}
return 0;
}