POJ1422 空降兵【二分图-最小路径覆盖】

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

最小路径覆盖

定义：在一个ＰＸＰ的有向无环图中，路径覆盖就是在图中找一些路经，使之覆盖了图中的所有顶点，且任何一个顶点有且只有一条路径与之关联
定理：最小路径覆盖＝｜总点数｜－最大匹配数
POJ1422
一个地图上有n个小镇，以及连接着其中两个小镇的有向边，而且这些边无法形成回路。现在选择一些小镇空降士兵（1个小镇最多1个士兵），士兵能沿着边走到尽头，问最少空降几个士兵，能遍历完所有的小镇

建图后直接找最大匹配数，点数-最大匹配数即为所求

#include
#include
#include
const int MAX = 210;
using namespace std;
int map[MAX][MAX];
int match[MAX];
int vis[MAX];
int n, k;
bool dfs(int u)
{
    for (int v = 1; v <= n; v++)
    {
        if (map[u][v] && !vis[v])
        {
            vis[v] = true;
            if (match[v] == -1 || dfs(match[v]))
            {
                match[v] = u;
                return true;
            }
        }
    }
    return false;
}
int main()
{
    int T, j, x, y;
    scanf("%d", &T);
    while (T--)
    {
        scanf("%d%d", &n, &k);
        memset(map, 0, sizeof(map));
        for (int i = 0; i < k; i++)
        {
            scanf("%d%d", &x, &y);
            map[x][y] = 1;
        }
        //存图建边

        int sum = 0;
        memset(match, -1, sizeof(match));
        for (int i = 1; i <= n; i++)
        {
            memset(vis, 0, sizeof(vis));
            if (dfs(i))
                sum++;
        }

        //点数-最大匹配数即为所求
        printf("%d\n", n - sum);
    }
}