如果这个图是欧拉路，则每个顶点的出度等于入度。
即out[i] = in[i]
如果这个图是半欧拉图，
则起点的出度比入度大1，终点的入度比出度大1.
其余顶点的出度等于入度。
如果满足上述条件，就可以将所有单词链接起来，
否则不能。
当然，在判断出度入度的时候还有一点需要注意，
那就是除了起点终点以外的顶点，
出度必须等于入度（出度入度可以同时为2，即环），
但是起点和终点必须保证出度和入度之差为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.

3

2

acm

ibm

3

acm

malform

mouse

2

ok

ok

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[fy]=fx;

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]++; //入度和出度分别加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])//如果这个图是欧拉路，则每个顶点的出度等于入度。即outd[i] = ind[i]

52             {

53                 ans.push_back(i);

54             }

55             if(ans.size()>2)/*如果这个图是半欧拉图，

56                             则起点的出度比入度大1，终点的入度比出度大1.

57                             其余顶点的出度等于入度。*/

58             {

59                 flag=0;

60                 break;

61             }

62             if((ind[i]||outd[i])&&pre[i]==i) //如果不同源，则非同根

63                 cnt++; //计算连通分支个数

64             if(cnt>1) //是否构成欧拉图

65             {

66                 flag=0;

67                 break;

68             }

69         }

70         if(ans.size()==2)

71         {

72             /*

73             那就是除了起点终点以外的顶点，

74             出度必须等于入度（出度入度可以同时为2，即环），

75             但是起点和终点必须保证出度和入度之差为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 }