Air Raid——最小路径覆盖

题目链接:https://cn.vjudge.net/problem/HDU-1151

Consider a town where all the streets are one-way and each street leads from one intersection to another. It is also known that starting from an intersection and walking through town's streets you can never reach the same intersection i.e. the town's streets form no cycles.

With these assumptions your task is to write a program that finds the minimum number of paratroopers that can descend on the town and visit all the intersections of this town in such a way that more than one paratrooper visits no intersection. Each paratrooper lands at an intersection and can visit other intersections following the town streets. There are no restrictions about the starting intersection for each paratrooper.

Input

Your program should read sets of data. The first line of the input file contains the number of the data sets. Each data set specifies the structure of a town and has the format:

no_of_intersections
no_of_streets
S1 E1
S2 E2
......
Sno_of_streets Eno_of_streets

The first line of each data set contains a positive integer no_of_intersections (greater than 0 and less or equal to 120), which is the number of intersections in the town. The second line contains a positive integer no_of_streets, which is the number of streets in the town. The next no_of_streets lines, one for each street in the town, are randomly ordered and represent the town's streets. The line corresponding to street k (k <= no_of_streets) consists of two positive integers, separated by one blank: Sk (1 <= Sk <= no_of_intersections) - the number of the intersection that is the start of the street, and Ek (1 <= Ek <= no_of_intersections) - the number of the intersection that is the end of the street. Intersections are represented by integers from 1 to no_of_intersections.

There are no blank lines between consecutive sets of data. Input data are correct.

Output

The result of the program is on standard output. For each input data set the program prints on a single line, starting from the beginning of the line, one integer: the minimum number of paratroopers required to visit all the intersections in the town.

Sample Input

2
4
3
3 4
1 3
2 3
3
3
1 3
1 2
2 3

Sample Output

2
1

题目翻译

一个城镇有n个路口，由一些单向马路连接。现在要安排一些伞兵降落在某些路口上，清查所有的路口。一个伞兵可以沿着马路一路清查过去。清查过程中不能有两个伞兵同时清查一个路口（应该是为了防止暴露）。给定城镇的线路，求最少需要几个人伞兵就能清查所有的路口。

第一个整数表示测试数据的组数。
对于每组测试数据，第一行一个整数n表示路口数量。
第三行一个整数m表示马路的数量
接下来m行，每行两个整数表示一条单向路径

输出最少需要的伞兵数量

 

题意很好理解，二分图也很好建(拆点)，关键在于要知道有向无环图的最小路径覆盖的定理。DAG的最小路径覆盖=节点数n-最大匹配数。

#include 
#include
#include
#include
using namespace std;
vector G[127];
int visited[127],nxt[127];
int n,m;
int find(int x){
	for(int i = 0;i>ncase;
    while(ncase--){
    	for(int i = 0;i<=157;++i) G[i].clear();
    	cin>>n>>m;
    	for(int i = 0;i>x>>y;
    		G[x].push_back(y);
		}
		cout<

有关二分图匹配的知识和资料可以参考我的这篇文章：https://blog.csdn.net/qq_43472263/article/details/96831025