割點（割頂）：無向連通圖中，刪除某點後，圖變成不連通，稱該點為割點；

橋：無向連通圖中，如果刪除某條邊後，圖變成不連通，則該邊稱為橋；

定理：在無向連通圖的dfs樹中，非根節點u是割點當且僅當u存在一個子節點v使得v及其所有後代都沒有反向邊連回u的祖先（連回u不算）

求割點的Tarjan演算法：

#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<climits>
#include<cctype>
#include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<string>
#define ll long long
#define MAX 1000
#define INF INT_MAX
#define eps 1e-8

using namespace std;

int pre[MAX],mark[MAX],low[MAX],dfs_clock;  //mark[i]用來標記節點是否為割點 

vector<int>G[MAX];

int n;

void init(){
	for (int i=0; i<=n; i++) G[i].clear();
	memset(pre,0,sizeof(pre));
	memset(mark,0,sizeof(mark));
	dfs_clock = 0;
}

int dfs(int u, int fa){
	int lowu = pre[u] = ++dfs_clock;
	int c = 0;
	for (int i=0; i<G[u].size(); i++){
		int v = G[u][i];
		if (!pre[v]){
			c++;
			int lowv = dfs(v,u);
			lowu = min(lowu,lowv);
			if (lowv >= pre[u]){    //判斷節點u是不是存在一子節點v，使得v以及其所有後代都沒有反邊連回u的祖先 
				mark[u] = 1;
			}
		}
		else if (pre[v] < pre[u] && v != fa){  //注意不再考慮連到父親節點的回邊； 
			lowu = min(lowu,pre[v]);
		}
	} 
	if (fa < 0 && c == 1) mark[u] = 0;  //當且僅當根節點有多個孩子節點時才是割點
	low[u] = lowu;
	return lowu; 
}

int main(){
	int m;
	while(scanf("%d%d",&n,&m) != EOF){
		init();
		int u,v;
		for (int i=0; i<m; i++){
			scanf("%d%d",&u,&v);
			G[u].push_back(v);
			G[v].push_back(u);
		}
		dfs(1,-1);
		for (int i=1; i<=n; i++) if (mark[i]) printf("%d ",i); printf("\n");
	}
	return 0;
}

 

#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<climits>
#include<cctype>
#include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<string>
#define ll long long
#define MAX 1000
#define INF INT_MAX
#define eps 1e-8

using namespace std;

struct Edge{
	int u, v;
};

int pre[MAX],low[MAX],dfs_clock; 

vector<int>G[MAX];
vector<Edge> edges;   //記錄橋 

int n;

void init(){
	for (int i=0; i<=n; i++) G[i].clear();
	edges.clear();
	memset(pre,0,sizeof(pre));
	dfs_clock = 0;
}

int dfs(int u, int fa){
	int lowu = pre[u] = ++dfs_clock;
	int c = 0;
	for (int i=0; i<G[u].size(); i++){
		int v = G[u][i];
		if (!pre[v]){
			c++;
			int lowv = dfs(v,u);
			lowu = min(lowu,lowv);
			if (lowv > pre[u]){    //注意和割點的區別，對於u的子節點v，v的後代只能連回自己，則（u，v）為橋 
				edges.push_back((Edge){u,v});
			}
		}
		else if (pre[v] < pre[u] && v != fa){  
			lowu = min(lowu,pre[v]);
		}
	} 
	low[u] = lowu;
	return lowu; 
}

int main(){
	int m;
	while(scanf("%d%d",&n,&m) != EOF){
		init();
		int u,v;
		for (int i=0; i<m; i++){
			scanf("%d%d",&u,&v);
			G[u].push_back(v);
			G[v].push_back(u);
		}
		dfs(1,-1);
		for (int i=0; i<edges.size(); i++){
			printf("%d %d\n",edges[i].u,edges[i].v);
		}
	}
	return 0;
}