Sorting It All Out

Description

An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.

Input

Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. the first value indicated the number of objects to sort, where 2 <= n <= 26. The objects to be sorted will be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters: an uppercase letter, the character "<" and a second uppercase letter. No letter will be outside the range of

the first n letters of the alphabet. Values of n = m = 0 indicate end of input.

Output

For each problem instance, output consists of one line. This line should be one of the following three:
Sorted sequence determined after xxx relations: yyy...y. Sorted sequence cannot be determined. Inconsistency found after xxx relations.
where xxx is the number of relations processed at the time either a sorted sequence is determined or an inconsistency is found, whichever comes first, and yyy...y is the sorted, ascending sequence.

Sample Input

4 6
A<B
A<C
B<C
C<D
B<D
A<B
3 2
A<B
B<A
26 1
A<Z
0 0

Sample Output

Sorted sequence determined after 4 relations: ABCD.
Inconsistency found after 2 relations.
Sorted sequence cannot be determined.

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<map>
 #include<set>
 #include<stack>
 #include<queue>
 #include<vector>
 using namespace std;
 const int ms=;
 int n,m;
 bool appear[ms];
 char output[ms+];
 int cnt[ms];
 int tmp[ms];
 vector<vector<char> > v;
 int topo_sort(int s)
 {
     int i,j,k,flag=;
     int total=,r=;
     for(i=;i<n;i++)
         tmp[i]=cnt[i];
     while(s--)
     {
         total=;
         for(i=;i<n;i++)
             if(appear[i]&&tmp[i]==)
             {
                 j=i;
                 total++;
             }
         if(total>=)
         {
             if(total>)
                 flag=;
             for(i=;i<v[j].size();i++)
                 tmp[v[j][i]]--;
             tmp[j]=-;
             output[r++]=j+'A';
             output[r]=;
         }
         else
             return -;
     }
     if(flag)
         return r;
     return ;
 }
 int main()
 {
     int i,j,k,judge,det;
     char str[];
     while(scanf("%d%d",&n,&m)==&&(n+m))
     {
         judge=;
         det=;
         int sum=;
         v.clear();v.resize(n);
         memset(cnt,,sizeof(cnt));
         memset(appear,false,sizeof(appear));
         for(i=;i<=m;i++)
         {
             scanf("%s",str);
             cnt[str[]-'A']++;
             v[str[]-'A'].push_back(str[]-'A');
             if(!appear[str[]-'A'])
             {
                 sum++;
                 appear[str[]-'A']=;
             }
             if(!appear[str[]-'A'])
             {
                 sum++;
                 appear[str[]-'A']=;
             }
             if(judge==)
             {
                 det=topo_sort(sum);
                 if(det==-)
                 {
                     judge=-;k=i;
                 }
                 else if(det==n)
                 {
                     judge=;
                     k=i;
                 }
             }
         }
         if(judge==-)
             printf("Inconsistency found after %d relations.\n",k);
         else if(judge==)
             printf("Sorted sequence cannot be determined.\n");
         else
             printf("Sorted sequence determined after %d relations: %s.\n",k,output);
     }
     return ;
 }