HDU1151- 最小路径覆盖

墨蓝 2022-07-12 05:03 192阅读 0赞

# Air Raid #

**Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)  
Total Submission(s): 5072    Accepted Submission(s): 3419**

Problem Description

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

题目大意：

给你一张b个点m条边的有向五环图，求最少的顶点是得从该些顶点出发能经过所有的边

题目思路：

因为是有向无环图，所以可以建立二分图模型，所以题目就是要求二分图上的最小路径覆盖，

而最小路径覆盖 = 顶点数-最大匹配数

AC代码：

#include<cstring>
    #include<cstdio>
    
    const int maxn = 2e2+10;
    
    bool vis[maxn],mp[maxn][maxn];
    int link[maxn];
    
    int n,m,k;
    
    bool dfs(int u){
        for(int i=1;i<=n;i++){
            if(!vis[i]&&mp[u][i]){
                vis[i]=true;
                if(link[i]==-1||dfs(link[i])){
                    link[i]=u;
                    return true;
                }
            }
        }
        return false;
    }
    
    int main()
    {
        int t;scanf("%d",&t);
        while(t--){
            scanf("%d%d",&n,&m);
            memset(link,-1,sizeof(link));
            memset(mp,false,sizeof(mp));
            for(int i=1;i<=m;i++){
                int b,c;scanf("%d%d",&b,&c);
                mp[b][c]=true;
            }
            int ans = 0;
            for(int i=1;i<=n;i++){
                memset(vis,false,sizeof(vis));
                if(dfs(i))ans++;
            }
            printf("%d\n",n-ans);
        }
        return 0;
    }