【图：C++】 深度优生成树

/*
数据结构：邻接表存储图
程序说明：为简单起见，设节点的类型为整型，设visited[],num[].low[],parent[]为全局变量，
为求得先序编号num[]，设置全局变量counter并初始化为1。为便于单独处理根节点设置root变量。
*/
#include <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

const int MAX_N = 100;
vector<int> graph[MAX_N];
vector<int> artPoint;
int num[MAX_N], low[MAX_N], parent[MAX_N];
int counter = 1;
int root;
bool visited[MAX_N];

void Init();           //初始化图
void FindArt(int v);   //找到第二类割点
void PrintArtPoint();  //打印所有割点(第一类割点在此单独处理)

int main()
{
    Init();
    FindArt(root);
    PrintArtPoint();
    return 0;
}

void PrintArtPoint()
{
    int rootChild = 0;  //根节点的孩子个数
    for (int i = 0; i < graph[root].size(); i++) //计算根节点的孩子个数
    {
        if (parent[graph[root][i]] == root)
            rootChild++;
    }
    if (rootChild > 1)            //根节点孩子个数大于1则为割点
        artPoint.push_back(root);
    for (int i = 0; i < artPoint.size(); i++)
        printf("%d\n", artPoint[i]);
}

void Init()
{
    int a, b;
    root = 1;
    while (scanf("%d%d", &a, &b) != EOF)
    {
        graph[a].push_back(b);
        graph[b].push_back(a);
        visited[a] = false;
        visited[b] = false;
    }
}
void FindArt(int v)
{
    visited[v] = true;
    low[v] = num[v] = counter++;          //情况(1)
    for (int i = 0; i < graph[v].size(); i++)
    {
        int w = graph[v][i];
        if (!visited[w])           //树边
        {
            parent[w] = v;
            FindArt(w);
            if (low[w] >= num[v] && v != root)
                artPoint.push_back(v);
            low[v] = min(low[v], low[w]);  //情况(3)
        }
        else if (parent[v] != w)           //回退边
        {
            low[v] = min(low[v], num[w]);  //情况(2)
        }
    }
}