Jimmy’s Assignment

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 464    Accepted Submission(s): 224

Problem Description Jimmy is studying Advanced Graph Algorithms at his university. His most recent assignment is to find a maximum matching in a special kind of graph. This graph is undirected, has N vertices and each vertex has degree 3. Furthermore, the graph is 2-edge-connected (that is, at least 2 edges need to be removed in order to make the graph disconnected). A matching is a subset of the graph’s edges, such that no two edges in the subset have a common vertex. A maximum matching is a matching having the maximum cardinality.

  Given a series of instances of the special graph mentioned above, find the cardinality of a maximum matching for each instance.  

Input The first line of input contains an integer number T, representing the number of graph descriptions to follow. Each description contains on the first line an even integer number N (4<=N<=5000), representing the number of vertices. Each of the next 3*N/2 lines contains two integers A and B, separated by one blank, denoting that there is an edge between vertex A and vertex B. The vertices are numbered from 1 to N. No edge may appear twice in the input.  

Output For each of the T graphs, in the order given in the input, print one line containing the cardinality of a maximum matching.  

Sample Input 2 4 1 2 1 3 1 4 2 3 2 4 3 4 4 1 2 1 3 1 4 2 3 2 4 3 4  

Sample Output 2 2  

Author Mugurel Ionut Andreica  

Source
Politehnica University of Bucharest Local Team Contest 2007  

Recommend lcy  

水题来一发

#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <iostream>
using namespace std;

const int MAXN = 5010;//点数的最大值
const int MAXM = 50010;//边数的最大值
struct Edge
{
    int to,next;
}edge[MAXM];
int head[MAXN],tot;
void init()
{
    tot = 0;
    memset(head,-1,sizeof(head));
}
void addedge(int u,int v)
{
    edge[tot].to = v; edge[tot].next = head[u];
    head[u] = tot++;
}
int linker[MAXN];
bool used[MAXN];
int uN;
bool dfs(int u)
{
    for(int i = head[u]; i != -1 ;i = edge[i].next)
    {
        int v = edge[i].to;
        if(!used[v])
        {
            used[v] = true;
            if(linker[v] == -1 || dfs(linker[v]))
            {
                linker[v] = u;
                return true;
            }
        }
    }
    return false;
}
int hungary()
{
    int res = 0;
    memset(linker,-1,sizeof(linker));
    for(int u = 0; u < uN;u++)
    {
        memset(used,false,sizeof(used));
        if(dfs(u))res++;
    }
    return res;
}
int main()
{
    int T;
    int n;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d",&n);
        int m = n*3/2;
        int u,v;
        init();
        uN = n;
        while(m--)
        {
            scanf("%d%d",&u,&v);
            u--; v--;
            addedge(u,v);
            addedge(v,u);
        }
        printf("%d\n",hungary()/2);
    }
    return 0;
}