pku 2762 Going from u to v or from v to u?

强联通+拓扑排序判断~~

题目大意:给定一个有向图，问该图是不是半连通图.

所谓半连通图即是指 在连通图中任意给出两个点a,b，要保证至少存在一条从a到b，或者从b到a的边。

解题思路:先用强联通进行缩点，之后再重新建图，再用拓扑排序进行判断：当某一时刻存在两个或两个以上入度为0的点则输出No,否则输出Yes！

为了学习双联通不得不学习了tarjan，先用tarjan把这个题给A了。之后不太过瘾，又用Kosaraju给A了下，结果发现Kosaraju要比tarjan更快。。很神奇。。

可能是因为我写的tarjan太丑陋了！！ 或者是我写的Kosaraju更风骚一点。。 ^_^。。 不过我感觉还是后者比较容易理解一点，我写的也比较清晰！！

分别贴下两种方法的代码：

tarjan：

 

View Code

  1 # include<stdio.h>
  2 # include<string.h>
  3 # include<stack>
  4 using namespace std;
  5 # define N 1005
  6 # define M 6005
  7 struct node{
  8     int from,to,next;
  9 }edge[M],edge1[M];
 10 int tol,head[N],visit[N],dfn[N],low[N],n,m,vis[N],cnt,flag,Belong[N],count,degree[N],tol1,head1[N];
 11 //int adj[N][N];
 12 stack<int>S;
 13 void add(int a,int b)
 14 {
 15     edge[tol].from=a;edge[tol].to=b;edge[tol].next=head[a];head[a]=tol++;
 16 }
 17 void add1(int a,int b)
 18 {
 19     edge1[tol1].from=a;edge1[tol1].to=b;edge1[tol1].next=head1[a];head1[a]=tol1++;
 20 }
 21 int min(int a,int b)
 22 {
 23     return a<b?a:b;
 24 }
 25 void tarjan(int u)
 26 {
 27     int j,v;
 28     dfn[u]=low[u]=cnt++;
 29     visit[u]=vis[u]=1;
 30     S.push(u);
 31     for(j=head[u];j!=-1;j=edge[j].next)
 32     {
 33         v=edge[j].to;
 34         if(!visit[v])
 35         {
 36             tarjan(v);
 37             low[u]=min(low[u],low[v]);
 38         }
 39         else if(vis[v]) low[u]=min(low[u],dfn[v]);
 40     }
 41     if(low[u]==dfn[u])
 42     {
 43         count++;
 44         do{
 45             v=S.top();
 46             S.pop();
 47             vis[v]=0;
 48             Belong[v]=count;
 49         }while(v!=u);
 50     }
 51 }
 52 int main()
 53 {
 54     int i,ncase,count1,index,a,b,index1,j;
 55     scanf("%d",&ncase);
 56     while(ncase--)
 57     {
 58         scanf("%d%d",&n,&m);
 59         memset(head,-1,sizeof(head));
 60         tol=0;
 61         for(i=1;i<=m;i++)
 62         {
 63             scanf("%d%d",&a,&b);
 64             add(a,b);
 65         }
 66         memset(visit,0,sizeof(visit));
 67         memset(vis,0,sizeof(vis));
 68         cnt=0;
 69         count=0;
 70         for(i=1;i<=n;i++)
 71             if(!visit[i]) tarjan(i);
 72         //    memset(adj,0,sizeof(adj));
 73             memset(degree,0,sizeof(degree));
 74             tol1=0;
 75             memset(head1,-1,sizeof(head1));
 76         for(i=0;i<tol;i++)
 77         {
 78             a=edge[i].from;
 79             b=edge[i].to;
 80             if(Belong[a]!=Belong[b])
 81             {
 82                 //if(!adj[Belong[a]][Belong[b]])
 83                 //{
 84                 //    adj[Belong[a]][Belong[b]]=1;
 85                     add1(Belong[a],Belong[b]);
 86                     degree[Belong[b]]++;
 87                 //}
 88             }
 89         }
 90         count1=0;
 91         for(i=1;i<=count;i++)
 92         {
 93             if(degree[i]==0) {count1++;index=i;}
 94         }
 95         if(count1!=1) {printf("No\n");continue;}
 96         flag=0;
 97         while(1)
 98         {
 99             count1=0;
100             /*for(i=1;i<=count;i++)
101             {
102                 if(adj[index][i]) 
103                 {
104                     degree[i]--;
105                     if(degree[i]==0)
106                     {
107                         count1++;
108                         index1=i;
109                     }
110                 }
111             }*/
112             for(j=head1[index];j!=-1;j=edge1[j].next)
113             {
114                 i=edge1[j].to;
115                 degree[i]--;
116                 if(degree[i]==0)
117                 {
118                     count1++;
119                     index1=i;
120                 }
121             }
122             if(count1>1) {flag=1;break;}
123             else if(count1==0) break;
124             index=index1;
125         }
126         if(flag) printf("No\n");
127         else printf("Yes\n");
128     }
129     return 0;
130 }

Kosaraju：

View Code

  1 # include<stdio.h>
  2 # include<string.h>
  3 # define N 1005
  4 # define M 6005
  5 struct node{
  6     int from,to,next;
  7 }edge1[M],edge2[M],edge[M];
  8 int head1[N],visit1[N],visit2[N],head2[N],T[N],Belong[N],head[N],degree[N];
  9 int tol1,tol2,tol,Tcnt,Bcnt,n,m;
 10 void add1(int a,int b)
 11 {
 12     edge1[tol1].from=a;edge1[tol1].to=b;edge1[tol1].next=head1[a];head1[a]=tol1++;
 13     edge2[tol2].from=b;edge2[tol2].to=a;edge2[tol2].next=head2[b];head2[b]=tol2++;
 14 }
 15 void add(int a,int b)
 16 {
 17     edge[tol].from=a;edge[tol].to=b;edge[tol].next=head[a];head[a]=tol++;
 18 }
 19 void dfs1(int i)
 20 {
 21     int j,u;
 22     visit1[i]=1;
 23     for(j=head1[i];j!=-1;j=edge1[j].next)
 24     {
 25         u=edge1[j].to;
 26         if(!visit1[u]) dfs1(u);
 27     }
 28     T[Tcnt++]=i;
 29 }
 30 void dfs2(int i)
 31 {
 32     int j,u;
 33     visit2[i]=1;
 34     Belong[i]=Bcnt;
 35     for(j=head2[i];j!=-1;j=edge2[j].next)
 36     {
 37         u=edge2[j].to;
 38         if(!visit2[u]) dfs2(u);
 39     }
 40 }
 41 int main()
 42 {
 43     int i,j,ncase,count,index,a,b;
 44     scanf("%d",&ncase);
 45     while(ncase--)
 46     {
 47         scanf("%d%d",&n,&m);
 48         tol1=tol2=0;
 49         Bcnt=Tcnt=0;
 50         memset(head1,-1,sizeof(head1));
 51         memset(head2,-1,sizeof(head2));
 52         memset(visit1,0,sizeof(visit1));
 53         memset(visit2,0,sizeof(visit2));
 54         for(i=1;i<=m;i++)
 55         {
 56             scanf("%d%d",&a,&b);
 57             add1(a,b);
 58         }
 59         for(i=1;i<=n;i++)
 60             if(!visit1[i]) dfs1(i);
 61             for(i=Tcnt-1;i>=0;i--)
 62             {
 63                 if(!visit2[T[i]])
 64                 {
 65                     dfs2(T[i]);
 66                     Bcnt++;
 67                 }
 68             }
 69             memset(head,-1,sizeof(head));
 70             memset(degree,0,sizeof(degree));
 71             tol=0;
 72             for(i=0;i<tol1;i++)
 73             {
 74                 a=edge1[i].from;
 75                 b=edge1[i].to;
 76                 if(Belong[a]!=Belong[b])
 77                 {
 78                     add(Belong[a],Belong[b]);
 79                     degree[Belong[b]]++;
 80                 }
 81             }
 82             count=0;
 83             for(i=0;i<Bcnt;i++)
 84             {
 85                 if(degree[i]==0)
 86                 { 
 87                     count++;
 88                     index=i;
 89                 }
 90             }
 91             if(count>1) {printf("No\n");continue;}
 92             while(1)
 93             {
 94                 count=0;
 95                 for(j=head[index];j!=-1;j=edge[j].next)
 96                 {
 97                     i=edge[j].to;
 98                     degree[i]--;
 99                     if(degree[i]==0)
100                     {
101                         count++;
102                         index=i;
103                     }
104                 }
105                 if(count>1) {printf("No\n");break;}
106                 else if(count==0) {printf("Yes\n");break;}
107             }
108     }
109     return 0;
110 }