The Settlers of Catan uva dfs+回溯

The Settlers of Catan 

Within Settlers of Catan, the 1995 German game of the year, players attempt to dominate an islandby 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 ofthis 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 linearpath. Therefore, determining the longest road is not trivial (although human players usually see itimmediately).

Compared to the original game, we will solve a simplified problem here: You are given a set ofnodes (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 ()and thenumber of edgesm (). The nextm lines describe the m edges. Each edge is given by thenumbers of the two nodes connected by it. Nodes are numbered from 0 ton-1. Edges areundirected. 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 20 11 215 160 21 22 33 43 54 65 76 87 87 98 109 1110 1211 1210 1312 140 0

Sample Output 

212

解决方案：水题，dfs+回溯

代码：

#include<iostream>#include<cstdio>#include<cstring>using namespace std;int Map[30][30];int n,m,M;int dfs(int no,int sum){    if(sum>M) M=sum;    for(int i=0;i<n;i++){        if(Map[no][i]){           Map[i][no]--;           Map[no][i]--;            dfs(i,sum+1);           Map[i][no]++;           Map[no][i]++;        }    }   return M;}int main(){    while(~scanf("%d%d",&n,&m)&&(n+m)){            memset(Map,0,sizeof(Map));        for(int i=0;i<m;i++)        {            int a,b;            scanf("%d%d",&a,&b);            Map[a][b]++;            Map[b][a]++;        }        int Max=0;        for(int i=0;i<n;i++)        {            M=0;           int temp=dfs(i,0);           if(temp>Max) Max=temp;        }        cout<<Max<<endl;    }return 0;}