【模板】割点(割顶)

嘟嘟嘟

dfs后,如果 low[v] >= dfn[u],则 u 就是割点。

不过如果 u 是搜索树的根节点的话,还要判断他至少有两个出边,而且这个判断必须加在v没有被走到的前提下。这样就表示有一些点只能通过根节点走到,那么如果这种点多于1个的话,根节点就是割点了。

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<cmath>
 4 #include<algorithm>
 5 #include<cstring>
 6 #include<cstdlib>
 7 #include<cctype>
 8 #include<vector>
 9 #include<stack>
10 #include<queue>
11 using namespace std;
12 #define enter puts("") 
13 #define space putchar(' ')
14 #define Mem(a) memset(a, 0, sizeof(a))
15 typedef long long ll;
16 typedef double db;
17 const int INF = 0x3f3f3f3f;
18 const db eps = 1e-8;
19 const int maxn = 1e5 + 5;
20 inline ll read()
21 {
22     ll ans = 0;
23     char ch = getchar(), last = ' ';
24     while(!isdigit(ch)) {last = ch; ch = getchar();}
25     while(isdigit(ch)) {ans = ans * 10 + ch - '0'; ch = getchar();}
26     if(last == '-') ans = -ans;
27     return ans;
28 }
29 inline void write(ll x)
30 {
31     if(x < 0) x = -x, putchar('-');
32     if(x >= 10) write(x / 10);
33     putchar(x % 10 + '0');
34 }
35 
36 int n, m;
37 vector<int> v[maxn];
38 
39 int dfn[maxn], low[maxn], cnt = 0;
40 bool cut[maxn];
41 int root, ccnt = 0;
42 void tarjan(int now)
43 {
44     dfn[now] = low[now] = ++cnt;
45     int flg = 0;
46     for(int i = 0; i < (int)v[now].size(); ++i)
47     {
48         if(!dfn[v[now][i]])
49         {
50             tarjan(v[now][i]);
51             low[now] = min(low[now], low[v[now][i]]);
52             if(low[v[now][i]] >= dfn[now])
53             {
54                 flg++;
55                 if(now != root || flg > 1)
56                 {
57                     if(!cut[now]) ccnt++;
58                     cut[now] = 1;
59                 }                 
60             } 
61         }
62         else low[now] = min(low[now], dfn[v[now][i]]);
63     }
64     
65 }
66 
67 int main()
68 {
69     n = read(); m = read();
70     for(int i = 1; i <= m; ++i)
71     {
72         int x = read(), y = read();
73         if(x == y) continue;
74         v[x].push_back(y); v[y].push_back(x);
75     }
76     for(int i = 1; i <= n; ++i) if(!dfn[i]) root = i, tarjan(i);
77     write(ccnt); enter;
78     for(int i = 1; i <= n; ++i) if(cut[i]) write(i), space; enter;
79     return 0;
80 }
View Code
原文地址:https://www.cnblogs.com/mrclr/p/9619814.html