Caocao’s Bridges

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 194    Accepted Submission(s): 89

Problem Description Caocao was defeated by Zhuge Liang and Zhou Yu in the battle of Chibi. But he wouldn’t give up. Caocao’s army still was not good at water battles, so he came up with another idea. He built many islands in the Changjiang river, and based on those islands, Caocao’s army could easily attack Zhou Yu’s troop. Caocao also built bridges connecting islands. If all islands were connected by bridges, Caocao’s army could be deployed very conveniently among those islands. Zhou Yu couldn’t stand with that, so he wanted to destroy some Caocao’s bridges so one or more islands would be seperated from other islands. But Zhou Yu had only one bomb which was left by Zhuge Liang, so he could only destroy one bridge. Zhou Yu must send someone carrying the bomb to destroy the bridge. There might be guards on bridges. The soldier number of the bombing team couldn’t be less than the guard number of a bridge, or the mission would fail. Please figure out as least how many soldiers Zhou Yu have to sent to complete the island seperating mission.  

Input There are no more than 12 test cases.

In each test case:

The first line contains two integers, N and M, meaning that there are N islands and M bridges. All the islands are numbered from 1 to N. ( 2 <= N <= 1000, 0 < M <= N
² )

Next M lines describes M bridges. Each line contains three integers U,V and W, meaning that there is a bridge connecting island U and island V, and there are W guards on that bridge. ( U ≠ V and 0 <= W <= 10,000 )

The input ends with N = 0 and M = 0.  

Output For each test case, print the minimum soldier number Zhou Yu had to send to complete the mission. If Zhou Yu couldn’t succeed any way, print -1 instead.  

Sample Input 3 3 1 2 7 2 3 4 3 1 4 3 2 1 2 7 2 3 4 0 0  

Sample Output -1 4  

Source
2013 ACM/ICPC Asia Regional Hangzhou Online  

Recommend liuyiding  

 这题的意思就是求出所有的桥，然后输出桥的权值的最小值。

但是坑点比较多。

如果一开始是不连通的，输出0.

图有重边，需要处理。

还有如果取到的最小值是0的话，要输出1，表示要派一个人过去。

  1 /* ***********************************************
  2 Author        :kuangbin
  3 Created Time  :2013/9/15 星期日 12:11:49
  4 File Name     :2013杭州网络赛\1001.cpp
  5 ************************************************ */
  6 
  7 #pragma comment(linker, "/STACK:1024000000,1024000000")
  8 #include <stdio.h>
  9 #include <string.h>
 10 #include <iostream>
 11 #include <algorithm>
 12 #include <vector>
 13 #include <queue>
 14 #include <set>
 15 #include <map>
 16 #include <string>
 17 #include <math.h>
 18 #include <stdlib.h>
 19 #include <time.h>
 20 using namespace std;
 21 const int INF = 0x3f3f3f3f;
 22 /*
 23 *  求 无向图的割点和桥
 24 *  可以找出割点和桥，求删掉每个点后增加的连通块。
 25 *  需要注意重边的处理，可以先用矩阵存，再转邻接表，或者进行判重
 26 */
 27 const int MAXN = 10010;
 28 const int MAXM = 2000010;
 29 struct Edge
 30 {
 31     int to,next;
 32     int w;
 33     bool cut;//是否为桥的标记
 34 }edge[MAXM];
 35 int head[MAXN],tot;
 36 int Low[MAXN],DFN[MAXN],Stack[MAXN];
 37 int Index,top;
 38 bool Instack[MAXN];
 39 bool cut[MAXN];
 40 int add_block[MAXN];//删除一个点后增加的连通块
 41 int bridge;
 42 
 43 void addedge(int u,int v,int w)
 44 {
 45     edge[tot].to = v;edge[tot].next = head[u];edge[tot].cut = false;
 46     edge[tot].w = w;
 47     head[u] = tot++;
 48 }
 49 
 50 
 51 void Tarjan(int u,int pre)
 52 {
 53     int v;
 54     Low[u] = DFN[u] = ++Index;
 55     Stack[top++] = u;
 56     Instack[u] = true;
 57     int son = 0;
 58     int pre_num = 0;
 59     for(int i = head[u];i != -1;i = edge[i].next)
 60     {
 61         v = edge[i].to;
 62         if(v == pre && pre_num == 0)
 63         {
 64             pre_num++;
 65             continue;
 66 
 67         }
 68         if( !DFN[v] )
 69         {
 70             son++;
 71             Tarjan(v,u);
 72             if(Low[u] > Low[v])Low[u] = Low[v];
 73             //桥
 74             //一条无向边(u,v)是桥，当且仅当(u,v)为树枝边，且满足DFS(u)<Low(v)。
 75             if(Low[v] > DFN[u])
 76             {
 77                 bridge++;
 78                 edge[i].cut = true;
 79                 edge[i^1].cut = true;
 80             }
 81             //割点
 82             //一个顶点u是割点，当且仅当满足(1)或(2) (1) u为树根，且u有多于一个子树。
 83             //(2) u不为树根，且满足存在(u,v)为树枝边(或称父子边，
 84             //即u为v在搜索树中的父亲)，使得DFS(u)<=Low(v)
 85             if(u != pre && Low[v] >= DFN[u])//不是树根
 86             {
 87                 cut[u] = true;
 88                 add_block[u]++;
 89             }
 90         }
 91         else if( Low[u] > DFN[v])
 92              Low[u] = DFN[v];
 93     }
 94     //树根，分支数大于1
 95     if(u == pre && son > 1)cut[u] = true;
 96     if(u == pre)add_block[u] = son - 1;
 97     Instack[u] = false;
 98     top--;
 99 }
100 int  solve(int N)
101 {
102     memset(DFN,0,sizeof(DFN));
103     memset(Instack,false,sizeof(Instack));
104     memset(add_block,0,sizeof(add_block));
105     memset(cut,false,sizeof(cut));
106     Index = top = 0;
107     bridge = 0;
108     for(int i = 1;i <= N;i++)
109         if( !DFN[i] )
110             Tarjan(i,i);
111     int ret = INF;
112     for(int u = 1; u <= N;u++)
113         for(int i = head[u]; i != -1;i = edge[i].next)
114             if(edge[i].cut)
115                 ret = min(ret,edge[i].w);
116     if(ret == INF)ret = -1;
117     if(ret == 0)ret++;
118     return ret;
119 }
120 int F[MAXN];
121 int find(int x)
122 {
123     if(F[x] == -1)return x;
124     else return F[x] = find(F[x]);
125 }
126 void init()
127 {
128     memset(F,-1,sizeof(F));
129     tot = 0;
130     memset(head,-1,sizeof(head));
131 }
132 void bing(int u,int v)
133 {
134     int t1 = find(u);
135     int t2 = find(v);
136     if(t1 != t2)F[t1] = t2;
137 }
138 int main()
139 {
140     //freopen("in.txt","r",stdin);
141     //freopen("out.txt","w",stdout);
142     int n,m;
143     while(scanf("%d%d",&n,&m) == 2)
144     {
145         if(n == 0 && m == 0)break;
146         int u,v,w;
147         init();
148         while(m--)
149         {
150             scanf("%d%d%d",&u,&v,&w);
151             if(u == v)continue;
152             addedge(u,v,w);
153             addedge(v,u,w);
154             bing(u,v);
155         }
156         bool flag = true;
157         for(int i = 1; i <= n;i++)
158             if(find(i) != find(1))
159                 flag = false;
160         if(!flag)
161         {
162             printf("0\n");
163             continue;
164         }
165         printf("%d\n",solve(n));
166     }
167     return 0;
168 }