【POJ 1523】SPF（Tarjan求割点）

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原文链接：http://www.cnblogs.com/lris-searching/p/9402987.html

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#数据结构与算法

本文介绍了一种基于Tarjan算法求解无向图中的单点故障(SPF)节点的方法，并通过示例输入输出展示了如何确定网络中的关键节点，这些节点一旦失效会导致原本完全连接的网络分裂成多个子网。

SPF

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 8246		Accepted: 3767

Description

Consider the two networks shown below. Assuming that data moves around these networks only between directly connected nodes on a peer-to-peer basis, a failure of a single node, 3, in the network on the left would prevent some of the still available nodes from communicating with each other. Nodes 1 and 2 could still communicate with each other as could nodes 4 and 5, but communication between any other pairs of nodes would no longer be possible.

Node 3 is therefore a Single Point of Failure (SPF) for this network. Strictly, an SPF will be defined as any node that, if unavailable, would prevent at least one pair of available nodes from being able to communicate on what was previously a fully connected network. Note that the network on the right has no such node; there is no SPF in the network. At least two machines must fail before there are any pairs of available nodes which cannot communicate.

Input

The input will contain the description of several networks. A network description will consist of pairs of integers, one pair per line, that identify connected nodes. Ordering of the pairs is irrelevant; 1 2 and 2 1 specify the same connection. All node numbers will range from 1 to 1000. A line containing a single zero ends the list of connected nodes. An empty network description flags the end of the input. Blank lines in the input file should be ignored.

Output

For each network in the input, you will output its number in the file, followed by a list of any SPF nodes that exist.

The first network in the file should be identified as "Network #1", the second as "Network #2", etc. For each SPF node, output a line, formatted as shown in the examples below, that identifies the node and the number of fully connected subnets that remain when that node fails. If the network has no SPF nodes, simply output the text "No SPF nodes" instead of a list of SPF nodes.

Sample Input

Sample Output

Network #1
  SPF node 3 leaves 2 subnets

Network #2
  No SPF nodes

Network #3
  SPF node 2 leaves 2 subnets
  SPF node 3 leaves 2 subnets

Source

Greater New York 2000

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[题意][求一个无向图的中，去掉某一个割点后，图变为几个联通块]

【题解】【Tarjan求割点】

【先求割点，然后有一个结论性的东西】

【如果，i==1&&vis[i]>1，那么联通块的数目为vis[i];如果i!=1&&vis[i],那么联通块的数量为vis[i]+1】

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[1000010],nxt[1000010],p[1010],tot;
int dft[1010],dis[1010],vis[1010],cnt;
int n,t;
inline void add(int x,int y)
{
	tot++; a[tot]=y; nxt[tot]=p[x]; p[x]=tot;
	tot++; a[tot]=x; nxt[tot]=p[y]; p[y]=tot;
}
void tarjan(int x)
{
	dft[x]=dis[x]=++cnt;
	for(int i=p[x];i!=-1;i=nxt[i])
	 if(!dft[a[i]])
	  {
	  	tarjan(a[i]);
	  	dis[x]=min(dis[x],dis[a[i]]);
	  	if(dft[x]<=dis[a[i]]) vis[x]++;
	  }
	 else dis[x]=min(dis[x],dft[a[i]]);
}
int main()
{
//	freopen("int.txt","r",stdin);
//	freopen("my.txt","w",stdout);
	int i,j;
	while(1)
	 {
	 	memset(p,-1,sizeof(p));
	 	memset(dft,0,sizeof(dft));
	    memset(dis,0,sizeof(dis));
	    memset(vis,0,sizeof(vis));
	  	memset(nxt,-1,sizeof(nxt));
	    tot=cnt=0; int n=0; bool b=0;
	    int x,y; t++;
	    while(1)
	     {
	     	scanf("%d",&x);
	     	if(!x) break;
	     	if(n<x) n=x;
	     	b=1;
	     	scanf("%d",&y);
	     	if(n<y) n=y;
	     	add(x,y);
		 }
		if(!b) return 0;
		printf("Network #%d\n",t);
		tarjan(1);
		bool b1=0;
		for(i=1;i<=n;++i)
		 if(i==1&&vis[i]>1)
		  {
		  	b1=1;
		  	printf("  SPF node %d leaves %d subnets\n",i,vis[i]);
		  }
		  else
		   if(i!=1&&vis[i]+1>1)
		    {
		   	    b1=1;
		   	    printf("  SPF node %d leaves %d subnets\n",i,vis[i]+1);
		    }
		if(!b1) puts("  No SPF nodes");
		putchar('\n');
	 }
}

转载于:https://www.cnblogs.com/lris-searching/p/9402987.html