Courses(hdu 1083)

本文探讨了二分图匹配问题,特别是在学生课程选择场景下的应用。通过详细解释问题背景和输入输出要求,介绍了两种解决该问题的方法:一种是基于模板的算法实现,另一种是采用匈牙利算法。代码示例清晰展示了如何处理输入数据,进行匹配,并判断是否能形成满足条件的委员会。

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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;
}

 

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