poj1236 Network of Schools (Tarjan + condensing point)

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 27058		Accepted: 10670

Description

A number of schools are connected to a computer network. Agreements have been developed among those schools: each school maintains a list of schools to which it distributes software (the “receiving schools”). Note that if B is in the distribution list of school A, then A does not necessarily appear in the list of school B 
You are to write a program that computes the minimal number of schools that must receive a copy of the new software in order for the software to reach all schools in the network according to the agreement (Subtask A). As a further task, we want to ensure that by sending the copy of new software to an arbitrary school, this software will reach all schools in the network. To achieve this goal we may have to extend the lists of receivers by new members. Compute the minimal number of extensions that have to be made so that whatever school we send the new software to, it will reach all other schools (Subtask B). One extension means introducing one new member into the list of receivers of one school. 

Input

The first line contains an integer N: the number of schools in the network (2 <= N <= 100). The schools are identified by the first N positive integers. Each of the next N lines describes a list of receivers. The line i+1 contains the identifiers of the receivers of school i. Each list ends with a 0. An empty list contains a 0 alone in the line.

Output

Your program should write two lines to the standard output. The first line should contain one positive integer: the solution of subtask A. The second line should contain the solution of subtask B.

Sample Input

5
2 4 3 0
4 5 0
0
0
1 0

Sample Output

1
2

Source

ion 1996

 

Subject to the effect

A single set of data, n-points, after 1 ~ n rows each row having an input connected to the point, the end of the 0

Task A: selecting at least a few computers, file transfer so that the computer can receive the n files

Task B: adding at least a few connections (edges), such that any computer by computer reach all n

 

Thinking

Task A: after the degree of shrinkage solver point number 0

Task B: retrusion solver max (the degree of the number of point 0, a point is the number of 0's)

 

 1 #include <cstdio>
 2 #include <vector>
 3 #include <algorithm>
 4 using namespace std;
 5 
 6 const int N=1e2+5;
 7 int low[N],dfn[N],Stack[N],belong[N],rdu[N],cdu[N],vis[N][N];
 8 bool inStack[N];
 9 int n,m,tot,tag,top;
10 vector<int> g[N],vec[N];
11 
12 void tarjan(int u){
13     int v;
14     low[u]=dfn[u]=++tot;
15     Stack[++top]=u;
16     inStack[u]=true;
17     for(int i=0;i<g[u].size();i++){
18         v=g[u][i];
19         if(dfn[v]==0){
20             tarjan(v);
21             low[u]=min(low[u],low[v]);
22         }
23         else if(inStack[v]==true){
24             low[u]=min(low[u],dfn[v]);
25         }
26     }
27     if(dfn[u]==low[u]){
28         tag++;
29         do{
30             v=Stack[top--];
31             inStack[v]=false;
32             belong[v]=tag;
33         }while(u!=v);
34     }
35 }
36 
37 int main(){
38     scanf("%d",&n);
39     for(int i=1;i<=n;i++){
40         int x;
41         while(scanf("%d",&x),x){
42             g[i].push_back(x);
43         }
44     }
45     for(int i=1;i<=n;i++){
46         if(dfn[i]==0){
47             tot=0;
48             tarjan(i);
49         }
50     }
51     if(tag==1){
52         printf("1\n0\n");
53         return 0;
54     }
55     for(int i=1;i<=n;i++){
56         for(int j=0;j<g[i].size();j++){
57             int x=g[i][j],bi=belong[i],bx=belong[x];
58             if(bi!=bx&&vis[bi][bx]==0){
59                 vec[bi].push_back(bx);
60                 vis[bi][bx]=1;
61             }
62         }
63     }
64     for(int i=1;i<=tag;i++){
65         for(int j=0;j<vec[i].size();j++){
66             int x=vec[i][j];
67             cdu[i]++;
68             rdu[x]++;
69         }
70     }
71 //    for(int i=1;i<=tag;i++){
72 //        printf(" %d",i);
73 //        for(int j=0;j<vec[i].size();j++){
74 //            printf(" %d",vec[i][j]);
75 //        }
76 //        printf("\n");
77 //    }
78     int cnta=0,cntb=0;
79     for(int i=1;i<=tag;i++){
80         if(rdu[i]==0){
81             cnta++;
82         }
83         if(cdu[i]==0){
84             cntb++;
85         }
86     }
87     printf("%d\n",cnta);
88     printf("%d\n",max(cnta,cntb));
89 }