判断无向图是否存在欧拉回路，就是看度数为奇数的点有多少个，如果有两个，那么以那分别两个点为起点和终点，可以构造出一条欧拉回路，如果没有，就任意来，否则，欧拉回路不存在。

首先用并查集判断连通，然后统计度数。

#include
     
      #include
      
       #include
       
        //#include
        
         //#define localusing namespace std;const int maxl = 26;const int maxn = 1e3 + 3;int p[maxl];bool used[maxl];//出现过的字符char s[maxn];int Find(int x) {
   return p[x] == x ? x : p[x] = Find(p[x]); }char last(char *p){   while(*(++p));   return *(p-1);}int deg[maxl];//出度 - 入度#define ID(c) (c-'a')int main(){#ifdef local    freopen("in10129.txt","r",stdin);#endif // local   int T,N;   scanf("%d",&T);   while(T--) {      memset(used,false,sizeof(used));      memset(deg,0,sizeof(deg));      int cc = 26;      for(int i = 0; i < maxl; i ++) { p[i] = i; }      scanf("%d", &N);      while(N--){         scanf("%s",s);         int u = ID(*s), v = ID(last(s));         deg[u]++; deg[v]--;         used[u] = used[v] = true;         int s1 = Find(u), s2 = Find(v);         if(s1 != s2) {            p[s1] = s2; cc--;         }      }      bool ok = false;      for(int i = 0; i < maxl; i ++) {         if(!used[i]) cc--;      }      int odd[maxl] = {
   0},top = 0;      if(cc == 1){         for(int i = 0; i < maxl; i ++) if(deg[i]) {            odd[top++] = deg[i];         }         if(top == 2 && (odd[0] == 1 || odd[1] == 1) ) ok = true;//入度sum = 出度sum         else if(top == 0) ok = true;      }      if(ok) printf("Ordering is possible.\n");      else printf("The door cannot be opened.\n");   }   return 0;}