题目描述:
Consider a group of N students and P courses. Each student visits zero, one or more than one courses. Your task is to determine whether it is possible to form a committee of exactly P students that satisfies simultaneously the conditions:
. every student in the committee represents a different course (a student can represent a course if he/she visits that course)
. each course has a representative in the committee
Your program should read sets of data from a text file. The first line of the input file contains the number of the data sets. Each data set is presented in the following format:
P N
Count1 Student1 1 Student1 2 ... Student1 Count1
Count2 Student2 1 Student2 2 ... Student2 Count2
......
CountP StudentP 1 StudentP 2 ... StudentP CountP
输入:
The first line in each data set contains two positive integers separated by one blank: P (1 <= P <= 100) - the number of courses and N (1 <= N <= 300) - the number of students. The next P lines describe in sequence of the courses . from course 1 to course P, each line describing a course. The description of course i is a line that starts with an integer Count i (0 <= Count i <= N) representing the number of students visiting course i. Next, after a blank, you'll find the Count i students, visiting the course, each two consecutive separated by one blank. Students are numbered with the positive integers from 1 to N.
There are no blank lines between consecutive sets of data. Input data are correct.
输出:
The result of the program is on the standard output. For each input data set the program prints on a single line "YES" if it is possible to form a committee and "NO" otherwise. There should not be any leading blanks at the start of the line.
样例输入:
2
3 3
3 1 2 3
2 1 2
1 1
3 3
2 1 3
2 1 3
1 1
样例输出:
YES
NO
code:
很明显,这是一个入门级的二分图匹配问题
需要使用模板即可
不过要注意输入的序号
#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<vector>
using namespace std;
const int maxn=650;
int n,m;
vector<int> g[maxn];
int match[maxn];
bool used[maxn];
void init(){
int number=n+m;
for(int i=0;i<=number;i++){
g[i].clear();
}
}
void add_edge(int u,int v){
g[u].push_back(v);
g[v].push_back(u);
}
bool dfs(int v){
used[v]=true;
for(int i=0;i<g[v].size();i++){
int u=g[v][i],w=match[u];
if(w<0||!used[w]&&dfs(w)){
match[v]=u;
match[u]=v;
return true;
}
}
return false;
}
int findd(){
int res=0;
memset(match,-1,sizeof(match));
// init();
int number=n+m;
for(int v=1;v<=number;v++){
if(match[v]<0){
memset(used,0,sizeof(used));
if(dfs(v))res++;
}
}
return res;
}
int main()
{
int ttt;
scanf("%d",&ttt);
while(ttt--){
scanf("%d%d",&n,&m);
int t;
init();
for(int i=1;i<=n;i++){
scanf("%d",&t);
while(t--){
int jiang;
scanf("%d",&jiang);
add_edge(jiang+n,i);
}
}
int what=findd();
if(what>=n)printf("YES\n");
else printf("NO\n");
}
return 0;
}
或者,匈牙利算法走一波
#include<iostream>
#include<string.h>
#include<stdio.h>
#include<vector>
using namespace std;
int n,m;
const int maxn=350;
int pre[maxn];
vector<int> match[maxn];
int visit[maxn];
void init(){
for(int i=0;i<maxn;i++){
match[i].clear();
}
memset(pre,0,sizeof(pre));
}
bool dfs(int x){
for(int i=0;i<match[x].size();i++){
int j=match[x][i];
if(visit[j]==0){
visit[j]=1;
if(pre[j]==0||dfs(pre[j])){
pre[j]=x;
return true;
}
}
}
return false;
}
int findd(){
int sum=0;
for(int i=1;i<=n;i++){
memset(visit,0,sizeof(visit));
if(dfs(i))sum++;
}
return sum;
}
int main()
{
int ttt;
scanf("%d",&ttt);
while(ttt--){
init();
scanf("%d%d",&n,&m);
for(int i=1;i<=n;i++){
int t,y;
scanf("%d",&t);
while(t--){
scanf("%d",&y);
match[i].push_back(y);
}
}
int num=findd();
if(num==n)printf("YES\n");
else printf("NO\n");
}
return 0;
}