1509: Hamiltonian Cycle（深搜）

Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	427	99	Standard

A few definitions first:

Definition 1

A graph G = (V, E) is called ``dense'' if for each pair of non-adjacent vertices u and v , where n = | V | and denotes the degree of the vertex .

Definition 2

A ``Hamiltonian cycle'' on G is a sequence of vertices ( ) such that for all and { v _{i l} , v _{i l} } is an edge of G.

The problem is: write a program that, given a dense graph G = (V; E) as input, deter- mines whether G admits a Hamiltonian cycle on G and outputs that cycle, if there is one, or outputs ``N '' if there is none.

Input

A file containing descriptions of graphs, each one ending with a %, in the form:

n ₁

%

n ₂

%

where n _i is the number of vertices and are integers between 1 and n indicating that there exists an edge between vertex u _{i h} and u _{i l}

Output

The output file must contain the sequence of vertices that form a Hamiltonian cycle in the form:

or containing:

N

Sample Input

 

4

1 2

2 3

2 4

3 4

3 1

%

6

1 2

1 3

1 6

3 2

3 4

5 2

5 4

6 5

6 4

%

Sample Output

 

1 2 4 3 1

1 2 3 4 5 6 1









#include<iostream>

#include<cstdio>

#include<cstring>

using namespace std;

int map[100][100];

int n,vis[100];

char str[10];

int ans[100];

int j;

bool flag;

void dfs(int x,int y)//第x层解答树，第y个取值

{

   ans[x]=y;//先进行处理

   vis[y]=1;

   if(x==n)

   {

       if(map[ans[x]][ans[1]])

       {

           cout<<ans[1];

           for(int i=2;i<=n;i++)

           cout<<" "<<ans[i];

           cout<<" "<<ans[1]<<endl;

           flag=true;

           return;

       }

   }

   else

   {

       for(int i=1;i<=n;i++)

       {

           if(map[y][i]&&!vis[i])

           {

               dfs(x+1,i);

           }

       }

   }

   vis[y]=0;//注意

}

int main()

{

    int i;

    while(cin>>n)

    {

        getchar();

        memset(vis,0,sizeof(vis));

        memset(map,0,sizeof(map));

        while(1)

        {  gets(str);

           if(strcmp(str,"%")==0) break;

           int x=str[0]-'0';

           int y=str[2]-'0';

           map[x][y]=1;

           map[y][x]=1;

        }

        flag=false;

        if(n<3)

        {  cout<<"N"<<endl;

           continue;

        }

        else

        {  dfs(1,1);

           if(!flag)

           cout<<"N"<<endl;

        }

    }

    return 0;

}