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HDU 1083 Courses 二分匹配匈牙利演算法模板

題目連結:http://acm.hdu.edu.cn/showproblem.php?pid=1083

Problem Description 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

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.

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.

An example of program input and output:  

Sample Input 2 3 3 3 1 2 3 2 1 2 1 1 3 3 2 1 3 2 1 3 1 1  

Sample Output YES NO  

Source Southeastern Europe 2000

一共有 p 門課,每門課都有若干的學生,現在要為每個課程選一名課代表,

每個學生只能擔任一門課的課代表,如果每個課都能找到課代表,

every student in the committee represents a different course (a student can represent a course if he/she visits that course) 

則輸出"YES",否則"NO"。

二分圖最大匹配,對課程—學生關係建立一個圖,進行二分圖的最大匹配,

如果最大匹配數等於課程數,說明能夠滿足要求,否則不能。

一開始wa了好幾發,因為我看到every student in the committee represents a different course (a student can represent a course if he/she visits that course) 這句話裡的different 以為是每個學生代表的課程是不同的,這樣的話一開始接受的m和n都相等。。。。。

去掉就過了。。。迷,難道不是這麼理解嗎qaq

因為 很迷所以補個題,希望dalao和我說一下。

#include<iostream>
#include<cstdio>
#include<vector>
#include<cstring>
using namespace std;

const int MAXN = 1000;
int n,m,nl,nr;
vector<int> g[MAXN];
int from[MAXN],tot;
int to[MAXN];
bool use[MAXN];

bool match(int x){
	for(int i = 0;i < g[x].size();i++)
		if(!use[g[x][i]]){
			use[g[x][i]] = true;
			if(from[g[x][i]] == -1||match(from[g[x][i]])){
				from[g[x][i]] = x;
				to[x] = g[x][i];                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
				return true;
			}
		}
	return false;
}
int hungary(){
	tot = 0;
	memset(from,255,sizeof(from));
	for(int i = 1;i <= n;i++){
		memset(use,0,sizeof(use));
		if(match(i))
			++tot;
	}
	return tot;
}

void build(){
	
	int tmp1,tmp2;
	for(int i = 1;i <= m;i++){
		scanf("%d",&tmp1);
		for(int j = 0;j < tmp1;j++){
			scanf("%d",&tmp2);
			g[i].push_back(tmp2);
		}
	}
	return;
}
void init(){
	for(int i = 0;i < MAXN;i++){
		g[i].clear();
	}
	return;
}
int main(){
	int t;
	scanf("%d",&t);
	while(t--){
		scanf("%d%d",&m,&n);
	/*	if(n != m){
			printf("NO\n");
			continue;
		}
	*/
		init();
		build();
		if(hungary() == m)printf("YES\n");
		else printf("NO\n");
	}
	
	return 0;
}