[UVA315]Network（tarjan, 求割点）

Posted 2020-07-09

题目链接：https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=251

求割点，除了输入用strtok和sscanf处理输入以外，对于求割点的tarjan算法有了进一步理解。

特别注意88行，如果u是根并且至少两个儿子，那它一定是割点无误，还有第二个情况用如图代表：

这个例子里显然：low[4]=2,dfn[4]=4，dfn[3]=3。现dfs到3点位置了，4是3的儿子，假如3是割点，那删掉3后4和2依然连通，因此3不是割点。判断依据可以是low[4]<dfn[3]。

假如low[4]>=dfn[3]的话，那3就是割点了。

  1 /*
  2 ━━━━━┒ギリギリ♂ eye！
  3 ┓┏┓┏┓┃キリキリ♂ mind！
  4 ┛┗┛┗┛┃＼○／
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 
 36 using namespace std;
 37 
 38 #define fr first
 39 #define sc second
 40 #define cl clear
 41 #define BUG puts("here!!!")
 42 #define W(a) while(a--)
 43 #define pb(a) push_back(a)
 44 #define Rint(a) scanf("%d", &a)
 45 #define Rll(a) scanf("%lld", &a)
 46 #define Rs(a) scanf("%s", a)
 47 #define Cin(a) cin >> a
 48 #define FRead() freopen("in", "r", stdin)
 49 #define FWrite() freopen("out", "w", stdout)
 50 #define Rep(i, len) for(int i = 0; i < (len); i++)
 51 #define For(i, a, len) for(int i = (a); i < (len); i++)
 52 #define Cls(a) memset((a), 0, sizeof(a))
 53 #define Clr(a, x) memset((a), (x), sizeof(a))
 54 #define Full(a) memset((a), 0x7f7f, sizeof(a))
 55 #define lrt rt << 1
 56 #define rrt rt << 1 | 1
 57 #define pi 3.14159265359
 58 #define RT return
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef map<string, int> msi;
 65 typedef vector<int> vi;
 66 typedef vector<LL> vl;
 67 typedef vector<vl> vvl;
 68 typedef vector<bool> vb;
 69 
 70 const int maxn = 220;
 71 char str[66666];
 72 int n, m, rt, bcnt;
 73 int G[maxn][maxn];
 74 int dfn[maxn], low[maxn], vis[maxn];
 75 int in[maxn];
 76 bool cut[maxn];
 77 vi e[maxn];
 78 int bridge[maxn][3];
 79 
 80 void dfs(int u, int d) {
 81     int son = 0;
 82     vis[u] = 1; dfn[u] = low[u] = d;
 83     Rep(i, e[u].size()) {
 84         int v = e[u][i];
 85         if(!vis[v]) {
 86             dfs(v, d+1); son++;
 87             low[u] = min(low[u], low[v]);
 88             if((u==rt&&son>1)||(u!=rt&&low[v]>=dfn[u])) cut[u] = 1;
 89         }
 90         else low[u] = min(low[u], dfn[v]);
 91     }
 92 }
 93 
 94 int main() {
 95     // FRead();
 96     int u, v;
 97     while(~Rint(n) && n) { 
 98         Cls(G); Cls(dfn); Cls(low); Cls(in);
 99         Cls(vis); Cls(bridge); Cls(cut); bcnt = 0;
100         Rep(i, n+5) e[i].cl();
101         getchar();
102         while(gets(str) && strcmp("0", str)) {
103             char* p = strtok(str, " ");
104             sscanf(p, "%d", &u);
105             p = strtok(NULL, " ");
106             while(p) {
107                 sscanf(p, "%d", &v);
108                 p = strtok(NULL, " ");
109                 G[u][v] = G[v][u] = 1;
110             }
111         }
112         For(i, 1, n+1) {
113             For(j, i+1, n+1) {
114                 if(G[i][j]) {
115                     e[i].push_back(j);
116                     e[j].push_back(i);
117                 }
118             }
119         }
120         rt = 1;
121         int ret = 0;
122         dfs(1, 0);
123         For(i, 1, n+1) if(cut[i]) ret++;
124         printf("%d\\n", ret);
125     }
126     RT 0;
127 }