Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 29855		Accepted: 10341

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>
using namespace std;
int map[27][27];
int point_num,edge_num;
int degree[27];
char order[27];
int top_sort(){
    int flag=1;
    int p=-1;
    for(int j=0;j<27;j++){
        degree[j]=0;
        order[j]='';
    }
    for(int i=0;i<point_num;i++){
        for(int j=0;j<point_num;j++){
            if(map[i][j])degree[j]++;
        }
    }

    for(int i=0;i<point_num;i++){
        p=-1;
        for(int j=0;j<point_num;j++){
            if(degree[j]==0){
                if(p==-1) p=j;
                else flag=0;
            }
        }
        if(p==-1) return 0;
        degree[p]=-1;
        order[i]=p+'A';
        for(int j=0;j<point_num;j++)
         {
            if(map[p][j]) degree[j]--;
         }
    }
    if(flag) return 1;
    else return 2;
}
int main() {
    cin>>point_num>>edge_num;
    while(point_num&&edge_num){
        int flag=0;
        for(int i=0;i<27;i++){
            for(int j=0;j<27;j++){
                map[i][j]=0;
            }
        }
        for(int i=0;i<edge_num;i++){
            char a,b,c;
            cin>>a>>b>>c;
            if(flag) continue;
            map[a-'A'][c-'A']=1;
            int result=top_sort();
            if(result==0){
                 cout<<"Inconsistency found after "<<i+1<<" relations.
";
                 flag=1;
             }
            else if(result==1)
             {
                 cout<<"Sorted sequence determined after "<<i+1<<" relations: "<<order<<".
";
                 flag=1;
             }
         }
         if(!flag) cout<<"Sorted sequence cannot be determined.
";
         cin>>point_num>>edge_num;
    }
    return 0;
}