uva 539 The Settlers of Catan

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本文介绍了一个经典的图论问题——寻找给定网络中最长的道路。问题来源于UVA在线评测系统的一个竞赛题目，要求找出连接城市间最长的路径，允许重复访问节点但不能重复使用边。文章提供了详细的题目描述、输入输出样例以及一种基于深度优先搜索的解决方案。

题目地址：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=108&page=show_problem&problem=480

题目描述：

The Settlers of Catan

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.

o        o -- o        o
 \      /      \      /
  o -- o        o -- o
 /      \      /      \
o        o -- o        o -- o
               \      /
                o -- o

Input

The input file will contain one or more test cases.

The first line of each test case contains two integers: the number of nodes n ( $2 \le n \le 25$ ) and the number of edges m ( $1 \le m \le 25$ ). 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

Sample Output

2
12

题意：找存在的最长的欧拉回路。

题解：暴力深搜。

代码：

/*

topcoder codeforce acm

uva 10474 - Where is the Marble?

no repeat edges between two vertexs

*/
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<time.h>
#include<iostream>
#include<string>
#include<algorithm>
#include<map>
#include<vector>
using namespace std;

typedef struct Points
{
	int start;
	int end;
	bool used;
	Points()
	{
		start=0;
		end=0;
		used=false;
	}
}Points,*PointsLink;
Points List[200+5];

bool Graph[25+5][25+5]={false};//true is connected

int n=0;//the count of the nodes,the node number begin with 0
int m=0;//the count of the edges
int MaxLen=0;

/*DFS the graph and find the euler path*/
int DFS(int cur,int Len)
{
	if(Len>MaxLen)
	{
		MaxLen=Len;
	}
	int i=0,j=0;
	for(i=0;i<=n-1;i++)
	{
		if(Graph[cur][i])//connected
		{
			//not used
			for(j=0;j<=m-1;j++)
			{
				if((cur==List[j].start&&i==List[j].end)||(cur==List[j].end&&i==List[j].start))
				{
					if(List[j].used==false)
					{
						List[j].used=true;
						DFS(i,Len+1);
						List[j].used=false;
						break;//has found so it is no need to continue to find
					}
				}
			}
		}
	}
	return(0);
}

/*for test*/
int test()
{
	return(0);
}

/*main process*/
int MainProc()
{
	while(scanf("%d%d",&n,&m)!=EOF&&(n>0||m>0))
	{
		int i=0;
		int Start=0,End=0;
		memset(Graph,false,sizeof(Graph));
		MaxLen=0;
		for(i=0;i<=m-1;i++)
		{
			scanf("%d%d",&Start,&End);
			Graph[Start][End]=true;
			Graph[End][Start]=true;
			List[i].start=Start;
			List[i].end=End;
			List[i].used=false;
		}
		if(m<=1)
		{
			printf("%d\n",m);
		}
		else
		{
			int Len=0;
			for(i=0;i<=n-1;i++)
			{
				Len=0;
				DFS(i,Len);
			}
			printf("%d\n",MaxLen);
		}
	}
	return(0);
}

int main()
{
	MainProc();
	return(0);
}