POJ1523 SPF 【求割点Tarjan】

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. 

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.

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.

1 2
5 4
3 1
3 2
3 4
3 5
0

1 2
2 3
3 4
4 5
5 1
0

1 2
2 3
3 4
4 6
6 3
2 5
5 1
0

0

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

Greater New York 2000

#include <stdio.h>
#include <string.h>
#define maxn 1002
#define maxm maxn * maxn
/*
** vertex[i]用来存储若i为割点时能将图分割的块数
** sec是时间戳
** dfn[]存储到达节点的时间
** low[]存储节点i能到达的最早节点的时间
** sta[]存储点双连通分支
*/
int head[maxn], id, cas = 1, vertex[maxn], sec;
int dfn[maxn], low[maxn], n, sta[maxn], id2;
struct Node{
    int to, next;
} E[maxm];

int max(int a, int b){
    return a > b ? a : b;
}

int min(int a, int b){
    return a < b ? a : b;
}

void initial()
{
    id = n = id2 = sec = 0;
    memset(head, -1, sizeof(head));
    memset(vertex, 0, sizeof(vertex));
    memset(dfn, 0, sizeof(dfn));
    memset(low, 0, sizeof(low));
}

void addEdge(int u, int v)
{
    E[id].to = v; E[id].next = head[u];
    head[u] = id++; E[id].to = u;
    E[id].next = head[v]; head[v] = id++;
}

void Tarjan(int pos, int father)
{
    dfn[pos] = low[pos] = ++sec;
    sta[id2++] = pos; int i;
    for(i = head[pos]; i != -1; i = E[i].next){
        if(E[i].to == father) continue; //过滤
        if(!dfn[E[i].to]){
            Tarjan(E[i].to, pos);
            low[pos] = min(low[pos], low[E[i].to]); //更新low
            if(dfn[pos] <= low[E[i].to]){
                while(sta[--id2] != E[i].to) ; //同一分支出栈
                ++vertex[pos]; //子树+1
            }
        }else low[pos] = min(low[pos], low[E[i].to]); //更新low
    }
}

void solve(int n)
{
    int i, u, v, ok = 0;
    Tarjan(1, 0); --vertex[1]; //根节点分支数要-1，输出时再+1
    printf("Network #%d\n", cas++);    
    for(i = 1; i <= n; ++i){
        if(vertex[i] > 0){
            printf("  SPF node %d leaves %d subnets\n", i, vertex[i] + 1);
            ok = 1;
        }
    }
    if(ok == 0) printf("  No SPF nodes\n");
    printf("\n");
}

int main()
{
    //freopen("stdin.txt", "r", stdin);
    int u, v; initial();
    while(scanf("%d%d", &u, &v) != EOF){
        n = max(u, n);
        n = max(v, n);
        if(0 == u){
            solve(n); if(!v) break;
            initial(); scanf("%d", &u);
            n = max(u, n);
        }
        addEdge(u, v);
    }
    return 0;
}