[POJ3352]Road Construction（缩点，割边，桥，环）

题目链接：http://poj.org/problem?id=3352

给一个图，问加多少条边可以干掉所有的桥。

先找环，然后缩点。标记对应环的度，接着找桥。写几个例子就能知道要添加的边数是桥的个数/2取上整。

这题和3177不一样的地方在于，这个题考虑重边，而我的代码本身，饿哦考虑重边的。

考虑重边：

找出桥，然后缩点。计算缩点后度为1的连通块个数。

 /*
 ━━━━━┒ギリギリ♂ eye！
 ┓┏┓┏┓┃キリキリ♂ mind！
 ┛┗┛┗┛┃＼○／
 ┓┏┓┏┓┃ /
 ┛┗┛┗┛┃ノ)
 ┓┏┓┏┓┃
 ┛┗┛┗┛┃
 ┓┏┓┏┓┃
 ┛┗┛┗┛┃
 ┓┏┓┏┓┃
 ┛┗┛┗┛┃
 ┓┏┓┏┓┃
 ┃┃┃┃┃┃
 ┻┻┻┻┻┻
 */
 #include <algorithm>
 #include <iostream>
 #include <iomanip>
 #include <cstring>
 #include <climits>
 #include <complex>
 #include <fstream>
 #include <cassert>
 #include <cstdio>
 #include <bitset>
 #include <vector>
 #include <deque>
 #include <queue>
 #include <stack>
 #include <ctime>
 #include <set>
 #include <map>
 #include <cmath>
 using namespace std;
 #define fr first
 #define sc second
 #define cl clear
 #define BUG puts("here!!!")
 #define W(a) while(a--)
 #define pb(a) push_back(a)
 #define Rint(a) scanf("%d", &a)
 #define Rll(a) scanf("%lld", &a)
 #define Rs(a) scanf("%s", a)
 #define Cin(a) cin >> a
 #define FRead() freopen("in", "r", stdin)
 #define FWrite() freopen("out", "w", stdout)
 #define Rep(i, len) for(int i = 0; i < (len); i++)
 #define For(i, a, len) for(int i = (a); i < (len); i++)
 #define Cls(a) memset((a), 0, sizeof(a))
 #define Clr(a, x) memset((a), (x), sizeof(a))
 #define Full(a) memset((a), 0x7f7f, sizeof(a))
 #define lp p << 1
 #define rp p << 1 | 1
 #define pi 3.14159265359
 #define RT return
 typedef long long LL;
 typedef long double LD;
 typedef unsigned long long ULL;
 typedef pair<int, int> pii;
 typedef pair<string, int> psi;
 typedef map<string, int> msi;
 typedef vector<int> vi;
 typedef vector<LL> vl;
 typedef vector<vl> vvl;
 typedef vector<bool> vb;

 typedef struct Edge {
     int v;
     bool cut;
     Edge() {}
     Edge(int vv) : v(vv) { cut = ; }
 }Edge;

 const int maxn = ;
 const int maxm = ;
 int n, m;
 int dig[maxn];
 int dfn[maxn], low[maxn], idx;
 vector<Edge> G[maxn];
 bool vis[maxn];
 int st[maxn], top;
 int belong[maxn], bcnt;

 void tarjan(int u, int p) {
     int v;
     low[u] = dfn[u] = ++idx;
     vis[u] = ;
     st[top++] = u;
     Rep(i, G[u].size()) {
         v = G[u][i].v;
         if(v == p) continue;
         if(!dfn[v]) {
             tarjan(v, u);
             low[u] = min(low[u], low[v]);
             if(low[v] > dfn[u]) {
                 G[u][i].cut = ;
                 Rep(j, G[v].size()) {
                     if(G[v][j].v== u) {
                         G[v][j].cut = ;
                         break;
                     }
                 }
             }
         }
         else if(vis[v]) low[u] = min(low[u], dfn[v]);
     }
     if(low[u] == dfn[u]) {
         bcnt++;
         do {
             v = st[--top];
             vis[v] = ;
             belong[v] = bcnt;
         } while(v != u);
     }
 }

 int main() {
     // FRead();
     int u, v;
     while(~Rint(n) && ~Rint(m)) {
         Rep(i, n+) G[i].cl();
         Cls(vis); Cls(dig); Cls(dfn); Cls(low);
         top = ; idx = ; bcnt = ;
         Rep(i, m) {
             Rint(u); Rint(v);
             G[u].pb(Edge(v)); G[v].pb(Edge(u));
         }
         tarjan(, );
         int ret = ;
         For(u, , n+) {
             Rep(i, G[u].size()) {
                 if(G[u][i].cut) {
                     dig[belong[u]]++;
                 }
             }
         }
         For(i, , bcnt+) {
             if(dig[i] == ) ret++;
         }
         printf("%d\n", (ret+)>>);
     }
     RT ;
 }

不考虑重边：

 /*
 ━━━━━┒ギリギリ♂ eye！
 ┓┏┓┏┓┃キリキリ♂ mind！
 ┛┗┛┗┛┃＼○／
 ┓┏┓┏┓┃ /
 ┛┗┛┗┛┃ノ)
 ┓┏┓┏┓┃
 ┛┗┛┗┛┃
 ┓┏┓┏┓┃
 ┛┗┛┗┛┃
 ┓┏┓┏┓┃
 ┛┗┛┗┛┃
 ┓┏┓┏┓┃
 ┃┃┃┃┃┃
 ┻┻┻┻┻┻
 */
 #include <algorithm>
 #include <iostream>
 #include <iomanip>
 #include <cstring>
 #include <climits>
 #include <complex>
 #include <fstream>
 #include <cassert>
 #include <cstdio>
 #include <bitset>
 #include <vector>
 #include <deque>
 #include <queue>
 #include <stack>
 #include <ctime>
 #include <set>
 #include <map>
 #include <cmath>
 using namespace std;
 #define fr first
 #define sc second
 #define cl clear
 #define BUG puts("here!!!")
 #define W(a) while(a--)
 #define pb(a) push_back(a)
 #define Rint(a) scanf("%d", &a)
 #define Rll(a) scanf("%lld", &a)
 #define Rs(a) scanf("%s", a)
 #define Cin(a) cin >> a
 #define FRead() freopen("in", "r", stdin)
 #define FWrite() freopen("out", "w", stdout)
 #define Rep(i, len) for(int i = 0; i < (len); i++)
 #define For(i, a, len) for(int i = (a); i < (len); i++)
 #define Cls(a) memset((a), 0, sizeof(a))
 #define Clr(a, x) memset((a), (x), sizeof(a))
 #define Full(a) memset((a), 0x7f7f, sizeof(a))
 #define lp p << 1
 #define rp p << 1 | 1
 #define pi 3.14159265359
 #define RT return
 typedef long long LL;
 typedef long double LD;
 typedef unsigned long long ULL;
 typedef pair<int, int> pii;
 typedef pair<string, int> psi;
 typedef map<string, int> msi;
 typedef vector<int> vi;
 typedef vector<LL> vl;
 typedef vector<vl> vvl;
 typedef vector<bool> vb;

 const int maxn = ;
 const int maxm = ;
 int n, m;
 int dig[maxn];
 int pre[maxn], dfn[maxn], low[maxn];
 vector<int> G[maxn];
 bool vis[maxn];

 void dfs(int u, int p) {
     vis[u] = ;
     pre[u] = p;
     dfn[u] = low[u] = u;
     Rep(i, G[u].size()) {
         int v = G[u][i];
         if(!vis[v]) dfs(v, u);
         else if(v != p) low[u] = min(low[u], dfn[v]);
     }
 }

 void update(int u) {
     int d = low[u];
     while(u != d && u != ) {
         low[u] = d;
         u = pre[u];
     }
 }

 int main() {
     // FRead();
     int u, v;
     while(~Rint(n) && ~Rint(m)) {
         Rep(i, n+) G[i].cl();
         Cls(vis); Cls(dig); Cls(dfn); Cls(low); Cls(pre);
         Rep(i, m) {
             Rint(u); Rint(v);
             G[u].pb(v); G[v].pb(u);
         }
         For(i, , n+) if(!vis[i]) dfs(i, );
         For(i, , n+) if(dfn[i] != low[i]) update(i);
         For(u, , n+) {
             Rep(i, G[u].size()) {
                 int v = G[u][i];
                 if(low[u] != low[v]) {
                     dig[low[u]]++; dig[low[v]]++;
                 }
             }
         }
         int ret = ;
         For(i, , n+) dig[i] /= ;
         For(i, , n+) if(low[i] == i && dig[low[i]] == ) ret++;
         printf("%d\n", ret %  ==  ? ret /  : ret /  + );
     }
     RT ;
 }