Hdu1151_air RAID (bipartite graph/minimum path overwrite = N-maximum match)

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Question:

In a small town, all the streets are one-way. These streets are all from one crossroads to another. It is known that they start from any crossroads and walk along these streets, can not return to the same crossroads, that is, there is no loop.

The town requires a minimum number of paratroopers to attack the town. These paratroopers will travel all the intersections in the town, and each crossroads will only be taken by one paratroopers. Every paratroopers land at a crossroads and can go to other intersections along the street.

Ideas:

Cover the street with the smallest paratroopers, and cover the model with the smallest path. Split each vertex into X1 and Y1 to create a bipartite graph. Minimum path overwrite = N-Maximum number of matches.

#include <iostream>#include <cstring>#include <cstdio>using namespace std;int k,n,m,mmap[1100][1100],vis[1100],pre[1100];int dfs(int x){    for(int i=1;i<=n;i++)    {        if(!vis[i]&&mmap[x][i])        {            vis[i]=1;            if(pre[i]==-1||dfs(pre[i]))            {                pre[i]=x;                return 1;            }        }    }    return 0;}int main(){    int i,j,u,v,a,t;    scanf("%d",&t);    while(t--)    {        memset(pre,-1,sizeof(pre));        memset(mmap,0,sizeof(mmap));        scanf("%d",&n);        scanf("%d",&m);        for(i=1;i<=m;i++)        {            scanf("%d%d",&u,&v);            mmap[u][v]=1;        }        int ans=0;        for(i=1;i<=n;i++)        {            memset(vis,0,sizeof(vis));            ans+=dfs(i);        }        printf("%d\n",n-ans);    }}

Air raid Time Limit: 2000/1000 MS (Java/others) memory limit: 65536/32768 K (Java/Others)
Total submission (s): 3344 accepted submission (s): 2194


Problem descriptionconsider 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 paratrotions.
 
Inputyour program shocould 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.
 
Outputthe 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

2433 41 32 3331 31 22 3

 
Sample output

21