When register on a social network, you are always asked to specify your hobbies in order to find some potential friends with the same hobbies. A social cluster is a set of people who have some of their hobbies in common. You are supposed to find all the clusters.
Input Specification:
Each input file contains one test case. For each test case, the first line contains a positive integer N (≤1000), the total number of people in a social network. Hence the people are numbered from 1 to N. Then N lines follow, each gives the hobby list of a person in the format:
Ki: hi[1] hi[2] ... hi[Ki]
where Ki (>0) is the number of hobbies, and hi[j] is the index of the j-th hobby, which is an integer in [1, 1000].
Output Specification:
For each case, print in one line the total number of clusters in the network. Then in the second line, print the numbers of people in the clusters in non-increasing order. The numbers must be separated by exactly one space, and there must be no extra space at the end of the line.
Sample Input:
8
3: 2 7 10
1: 4
2: 5 3
1: 4
1: 3
1: 4
4: 6 8 1 5
1: 4
Sample Output:
3
4 3 1题目大意：根据爱好将人们划分为群落。
思路：本题有多种方法，DFS，BFS遍历即可，以及非常好用的并查集；以下为三种解法。
DFS遍历：
#include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#include<cstdio>
using namespace std;
int n,sum;
std::vector<int> visit;
std::vector<std::vector<int> > hobby(1005),people(1005);
std::vector<int> result;
void dfs(int root){
visit[root]=1;
sum++;
for(int i=0;i<people[root].size();i++){
int t=people[root][i];
for(int j=0;j<hobby[t].size();j++){
if(visit[hobby[t][j]]==0)
dfs(hobby[t][j]);
}
}
}
int main(){
scanf("%d",&n);
visit.resize(n,0);
for(int i=0;i<n;i++){
int k;
scanf("%d: ",&k);
for(int j=0;j<k;j++){
int temp;
scanf("%d",&temp);
people[i].push_back(temp);
hobby[temp].push_back(i);
}
}
for(int i=0;i<n;i++){
sum=0;
if(visit[i]==0){
dfs(i);
result.push_back(sum);
}
}
sort(result.begin(), result.end());
printf("%d\n",result.size());
if(result.size()>0)
printf("%d",result[result.size()-1]);
for(int i=result.size()-2;i>=0;i--){
printf(" %d",result[i]);
}
system("pause");
}BFS遍历：
#include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#include<cstdio>
using namespace std;
int n;
std::vector<int> visit;
std::vector<std::vector<int> > hobby(1005),people(1005);
std::vector<int> result;
void bfs(int root){
int sum=0;
queue<int>q;
q.push(root);
visit[root]=1;
while(!q.empty()){
int front=q.front();
for(int i=0;i<people[front].size();i++){
int t=people[front][i];
for(int j=0;j<hobby[t].size();j++){
if(visit[hobby[t][j]]==0)
q.push(hobby[t][j]);
visit[hobby[t][j]]=1;
}
}
q.pop();
sum++;
}
result.push_back(sum);
}
int main(){
scanf("%d",&n);
visit.resize(n,0);
for(int i=0;i<n;i++){
int k;
scanf("%d: ",&k);
for(int j=0;j<k;j++){
int temp;
scanf("%d",&temp);
people[i].push_back(temp);
hobby[temp].push_back(i);
}
}
for(int i=0;i<n;i++){
if(visit[i]==0){
bfs(i);
}
}
sort(result.begin(), result.end());
printf("%d\n",result.size());
if(result.size()>0)
printf("%d",result[result.size()-1]);
for(int i=result.size()-2;i>=0;i--){
printf(" %d",result[i]);
}
}并查集：
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int cmp(int a,int b){
return a>b;
}
int father[1005];
std::vector<int> hobby[1005];
vector<int>numpart(1005,0),result;
int findfather(int x){
int a=x;
while(x!=father[x])
x=father[x];
while(a!=father[a]){
int z=a;
a=father[a];
father[z]=x;
}
return x;
}
void Union(int a,int b){
int faa=findfather(a);
int fab=findfather(b);
if(faa!=fab)
father[faa]=fab;
}
int main(){
int n,m=0;
scanf("%d",&n);
for(int i=0;i<n;i++){
father[i]=i;
int k;
scanf("%d: ",&k);
for(int j=0;j<k;j++){
int temp;
scanf("%d",&temp);
if(temp>m)
m=temp;
hobby[temp].push_back(i);
}
}
for(int i=0;i<=m;i++){
for(int j=1;j<hobby[i].size();j++){
Union(hobby[i][j],hobby[i][j-1]);
}
}
for(int i=0;i<n;i++)
numpart[findfather(i)]++;
sort(numpart.begin(), numpart.end(),cmp);
for(int i=0;i<=n;i++){
if(numpart[i]==0)
break;
result.push_back(numpart[i]);
}
if(result.size()==0){
cout<<'0';
return 0;
}
printf("%d\n%d",result.size(),result[0]);
for(int i=1;i<result.size();i++)
printf(" %d",result[i]);
system("pause");
}