（POJ - 2258）The Settlers of Catan

（POJ - 2258）The Settlers of Catan

Time Limit: 1000MS Memory Limit: 65536K

Total Submissions: 1297 Accepted: 850

Description

Within Settlers of Catan, the 1995 German game of the year, players attempt to dominate an island by building roads, settlements and cities across its uncharted wilderness.
You are employed by a software company that just has decided to develop a computer version of this game, and you are chosen to implement one of the game’s special rules:

When the game ends, the player who built the longest road gains two extra victory points.
The problem here is that the players usually build complex road networks and not just one linear path. Therefore, determining the longest road is not trivial (although human players usually see it immediately).
Compared to the original game, we will solve a simplified problem here: You are given a set of nodes (cities) and a set of edges (road segments) of length 1 connecting the nodes.
The longest road is defined as the longest path within the network that doesn’t use an edge twice. Nodes may be visited more than once, though.

Example: The following network contains a road of length 12.

Input

The input will contain one or more test cases.
The first line of each test case contains two integers: the number of nodes n (2<=n<=25) and the number of edges m (1<=m<=25). The next m lines describe the m edges. Each edge is given by the numbers of the two nodes connected by it. Nodes are numbered from 0 to n-1. Edges are undirected. Nodes have degrees of three or less. The network is not neccessarily connected.
Input will be terminated by two values of 0 for n and m.

Output

For each test case, print the length of the longest road on a single line.

Sample Input

3 2
0 1
1 2
15 16
0 2
1 2
2 3
3 4
3 5
4 6
5 7
6 8
7 8
7 9
8 10
9 11
10 12
11 12
10 13
12 14
0 0

Sample Output

2
12

题目大意：给出一个图：有n个点，m条边，每条边长为1。点可以重复走，边不可以重复重复走。问最长的一条路有多长。

思路：遍历每一个点，爆搜（dfs）寻找最长的那条路并记录下答案。
这与之前那一题很像，先给出链接：单元最长权路径

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int INF=0x3f3f3f3f;
const int maxn=30;
bool G[maxn][maxn],vis[maxn][maxn];
int ans,n,m;

void dfs(int u,int sum)
{
    for(int v=0;v<n;v++)
    {
        if(G[u][v]&&!vis[u][v])
        {
            vis[u][v]=vis[v][u]=1;
            dfs(v,sum+1);
            vis[u][v]=vis[v][u]=0;//回溯 
        }
    }
    ans=max(ans,sum);
}

int main()
{
    int u,v;
    while(scanf("%d%d",&n,&m)!=EOF&&n&&m)
    {
        memset(G,0,sizeof(G));
        for(int i=0;i<m;i++)
        {
            scanf("%d%d",&u,&v);
            G[u][v]=G[v][u]=1;
        }
        ans=-INF;
        for(int i=0;i<n;i++)
        {
            memset(vis,0,sizeof(vis));
            dfs(i,0);
        }
        printf("%d\n",ans);
    }
    return 0;
}