题意：有N 个点，M条边，加一条边，求割边最少。（有重边）
链接：点我
先求双连通分量，缩点形成一个生成树，然后求这个的直径，割边-直径即是答案
1 #pragma comment(linker, "/STACK:1024000000,1024000000") 2 #include <stdio.h> 3 #include <string.h> 4 #include <iostream> 5 #include <algorithm> 6 #include <map> 7 #include <vector> 8 using namespace std; 9 10 const int MAXN = 200010;//点数 11 const int MAXM = 2000010;//边数，因为是无向图，所以这个值要*2 12 13 14 15 16 struct Edge 17 { 18 int to,next; 19 bool cut;//是否是桥标记 20 bool cong; 21 }edge[MAXM]; 22 int head[MAXN],tot; 23 int Low[MAXN],DFN[MAXN],Stack[MAXN],Belong[MAXN];//Belong数组的值是1~block 24 int Index,top; 25 int block;//边双连通块数 26 bool Instack[MAXN]; 27 int bridge;//桥的数目 28 29 void addedge(int u,int v,bool pp) 30 { 31 edge[tot].to = v;edge[tot].next = head[u];edge[tot].cut=false; 32 edge[tot].cong = pp; 33 head[u] = tot++; 34 } 35 36 void Tarjan(int u,int pre,bool ff) 37 { 38 int v; 39 Low[u] = DFN[u] = ++Index; 40 Stack[top++] = u; 41 Instack[u] = true; 42 for(int i = head[u];i != -1;i = edge[i].next) 43 { 44 v = edge[i].to; 45 if(v == pre && (!ff))continue; //有重边 46 if( !DFN[v] ) 47 { 48 Tarjan(v,u,edge[i].cong); 49 if( Low[u] > Low[v] )Low[u] = Low[v]; 50 if(Low[v] > DFN[u]) 51 { 52 bridge++; 53 edge[i].cut = true; 54 edge[i^1].cut = true; 55 } 56 } 57 else if( Instack[v] && Low[u] > DFN[v] ) 58 Low[u] = DFN[v]; 59 } 60 if(Low[u] == DFN[u]) 61 { 62 block++; 63 do 64 { 65 v = Stack[--top]; 66 Instack[v] = false; 67 Belong[v] = block; 68 } 69 while( v!=u ); 70 } 71 } 72 void init() 73 { 74 tot = 0; 75 memset(head,-1,sizeof(head)); 76 } 77 78 int du[MAXN];//缩点后形成树，每个点的度数 79 vector<int>vec[MAXN]; 80 int dep[MAXN]; 81 void dfs(int u) 82 { 83 for(int i = 0;i < vec[u].size();i++) 84 { 85 int v = vec[u][i]; 86 if(dep[v]!=-1)continue; 87 dep[v]=dep[u]+1; 88 dfs(v); 89 } 90 } 91 void solve(int n) 92 { 93 memset(DFN,0,sizeof(DFN)); 94 memset(Instack,false,sizeof(Instack)); 95 Index = top = block = 0; 96 Tarjan(1,0,false); 97 for(int i = 1;i <= block;i++) 98 vec[i].clear(); 99 for(int i = 1;i <= n;i++) 100 for(int j = head[i];j != -1;j = edge[j].next) 101 if(edge[j].cut) 102 { 103 vec[Belong[i]].push_back(Belong[edge[j].to]); 104 } 105 memset(dep,-1,sizeof(dep)); 106 dep[1]=0; 107 dfs(1); 108 int k = 1; 109 for(int i = 1;i <= block;i++) 110 if(dep[i]>dep[k]) 111 k = i; 112 memset(dep,-1,sizeof(dep)); 113 dep[k]=0; 114 dfs(k); 115 int ans = 0; 116 for(int i = 1;i <= block;i++) 117 ans = max(ans,dep[i]); 118 printf("%d ",block-1-ans); 119 } 120 struct NN 121 { 122 int u,v; 123 }node[MAXM]; 124 bool cmp(NN a,NN b) 125 { 126 if(a.u != b.u)return a.u<b.u; 127 else return a.v<b.v; 128 } 129 int main() 130 { 131 //freopen("in.txt","r",stdin); 132 //freopen("out.txt","w",stdout); 133 int n,m; 134 int u,v; 135 while(scanf("%d%d",&n,&m)==2) 136 { 137 if(n==0 && m==0)break; 138 init(); 139 for(int i = 0;i < m;i++) 140 { 141 scanf("%d%d",&u,&v); 142 if(u==v)continue; 143 if(u>v)swap(u,v); 144 node[i].u = u; 145 node[i].v = v; 146 } 147 sort(node,node+m,cmp); 148 for(int i = 0;i < m;i++) 149 { 150 if(i == 0 || (node[i].u!=node[i-1].u || node[i].v != node[i-1].v)) 151 { 152 if(i < m-1 && (node[i].u==node[i+1].u && node[i].v == node[i+1].v)) //标记了是否出现重边 153 { 154 addedge(node[i].u,node[i].v,true); 155 addedge(node[i].v,node[i].u,true); 156 } 157 else 158 { 159 addedge(node[i].u,node[i].v,false); 160 addedge(node[i].v,node[i].u,false); 161 } 162 } 163 } 164 solve(n); 165 } 166 return 0; 167 }