POJ 1236 Network of Schools

Network of Schools

Time Limit: 1000ms

Memory Limit: 10000KB

This problem will be judged on PKU. Original ID: 1236
64-bit integer IO format: %lld      Java class name: Main

 

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

IOI 1996

 

解题：强连通缩点，求入度为0的块数，和出度为0的块数。

 

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <climits>
#include <vector>
#include <queue>
#include <cstdlib>
#include <string>
#include <set>
#include <stack>
#define LL long long
#define pii pair<int,int>
#define INF 0x3f3f3f3f
using namespace std;
const int maxn = 110;
vector<int>g[maxn];
stack<int>stk;
int dfn[maxn],low[maxn],belong[maxn],cnt,scc;
int n,in[maxn],out[maxn];
bool instack[maxn];
void tarjan(int u){
    dfn[u] = low[u] = ++cnt;
    instack[u] = true;
    stk.push(u);
    for(int i = 0; i < g[u].size(); i++){
        if(!dfn[g[u][i]]){
            tarjan(g[u][i]);
            low[u] = min(low[u],low[g[u][i]]);
        }else if(dfn[g[u][i]] && instack[g[u][i]]) low[u] = min(low[u],dfn[g[u][i]]);
    }
    if(dfn[u] == low[u]){
        scc++;
        int v;
        do{
            v = stk.top();
            instack[v] = false;
            stk.pop();
            belong[v] = scc;
        }while(v != u);
    }
}
int main(){
    int i,j,v;
    while(~scanf("%d",&n)){
        for(i = 0; i <= n; i++){
            dfn[i] = low[i] = belong[i] = 0;
            in[i] = out[i] = 0;
            instack[i] = false;
            g[i].clear();
        }
        while(!stk.empty()) stk.pop();
        cnt = scc = 0;
        for(i = 1; i <= n; i++)
            while(scanf("%d",&v),v) g[i].push_back(v);
        for(i = 1; i <= n; i++) if(!dfn[i]) tarjan(i);
        for(i = 1; i <= n; i++){
            for(j = 0; j < g[i].size(); j++){
                if(belong[i] != belong[g[i][j]]){
                    in[belong[g[i][j]]]++;
                    out[belong[i]]++;
                }
            }
        }
        int ans1 = 0,ans2 = 0;
        for(i = 1; i <= scc; i++){
            if(!in[i]) ans1++;
            if(!out[i]) ans2++;
        }
        printf("%d\n%d\n",ans1,scc == 1?0:max(ans1,ans2));
    }
    return 0;
}