如果這個圖是尤拉路，則每個頂點的出度等於入度。
即out[i] = in[i]
如果這個圖是半尤拉圖，
則起點的出度比入度大1，終點的入度比出度大1.
其餘頂點的出度等於入度。
如果滿足上述條件，就可以將所有單詞連結起來，
否則不能。
當然，在判斷出度入度的時候還有一點需要注意，
那就是除了起點終點以外的頂點，
出度必須等於入度（出度入度可以同時為2，即環），
但是起點和終點必須保證出度和入度之差為1。

Some of the secret doors contain a very interesting word puzzle. The team of archaeologists has to solve it to open that doors. Because there is no other way to open the doors, the puzzle is very important for us.

There is a large number of magnetic plates on every door. Every plate has one word written on it. The plates must be arranged into a sequence in such a way that every word begins with the same letter as the previous word ends. For example, the word ``acm'' can be followed by the word ``motorola''. Your task is to write a computer program that will read the list of words and determine whether it is possible to arrange all of the plates in a sequence (according to the given rule) and consequently to open the door.

InputThe input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case begins with a line containing a single integer number Nthat indicates the number of plates (1 <= N <= 100000). Then exactly Nlines follow, each containing a single word. Each word contains at least two and at most 1000 lowercase characters, that means only letters 'a' through 'z' will appear in the word. The same word may appear several times in the list.

OutputYour program has to determine whether it is possible to arrange all the plates in a sequence such that the first letter of each word is equal to the last letter of the previous word. All the plates from the list must be used, each exactly once. The words mentioned several times must be used that number of times.
If there exists such an ordering of plates, your program should print the sentence "Ordering is possible.". Otherwise, output the sentence "The door cannot be opened.".
Sample Input

3
2
acm
ibm
3
acm
malform
mouse
2
ok
ok

Sample Output

The door cannot be opened.
Ordering is possible.
The door cannot be opened.

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<map>
 4 #include<vector>
 5 #include<cstring>
 6 using namespace std;
 7 int ind[30];
 8 int outd[30];
 9 int pre[30];
10 void init()
11 {
12     for(int i=0;i<26;i++)
13         pre[i]=i;
14 }
15 int find(int x)
16 {
17     return x==pre[x]?x:find(pre[x]);
18 }
19 void merge(int x,int y)
20 {
21     int fx=find(x);
22     int fy=find(y);
23     pre[fx]=fy;
24 }
25 int main()
26 {
27     int t;
28     scanf("%d",&t);
29     while(t--)
30     {
31         memset(ind,0,sizeof(ind));
32         memset(outd,0,sizeof(outd));
33         int n;
34         scanf("%d",&n);
35         init();
36         for(int i=0;i<n;i++)
37         {
38             char s[1005];
39             scanf("%s",s);
40             int u=s[0]-'a';
41             int v=s[strlen(s)-1]-'a';
42             ind[u]++; //入度和出度分別加1
43             outd[v]++;
44             merge(u,v);
45         }
46         vector<int> ans;
47         int cnt=0;
48         int flag=1;
49         for(int i=0;i<26;i++)
50         {
51             if(ind[i]!=outd[i])//如果這個圖是尤拉路，則每個頂點的出度等於入度。即outd[i] = ind[i] 
52             {
53                 ans.push_back(i);
54             }
55             if(ans.size()>2)/*如果這個圖是半尤拉圖，
56                             則起點的出度比入度大1，終點的入度比出度大1.
57                             其餘頂點的出度等於入度。*/
58             {
59                 flag=0;
60                 break;
61             }
62             if((ind[i]||outd[i])&&pre[i]==i) //如果不同源，則非同根
63                 cnt++; //計算連通分支個數
64             if(cnt>1) //是否構成尤拉圖 
65             {
66                 flag=0;
67                 break;
68             }
69         }
70         if(ans.size()==2)
71         {
72             /*
73             那就是除了起點終點以外的頂點，
74             出度必須等於入度（出度入度可以同時為2，即環），
75             但是起點和終點必須保證出度和入度之差為1。
76             */
77             int a=ans[0],b=ans[1];
78             if((ind[a]+ind[b]==outd[a]+outd[b])&&(outd[a]-ind[a]==1||outd[a]-ind[a]==-1))
79                 flag=1;
80             else flag=0;
81         }
82         if(!flag)
83             cout<<"The door cannot be opened."<<endl;
84         else cout<<"Ordering is possible."<<endl;
85     }
86 }