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.

 1 #include<iostream>  2 #include<cstdio>  3 #include<cstring>  4 #include<algorithm>  5 #include<map>  6 #include<set>  7 #include<stack>  8 #include<queue>  9 #include<vector> 10 using namespace std; 11 const int ms=26; 12 int n,m; 13 bool appear[ms]; 14 char output[ms+1]; 15 int cnt[ms]; 16 int tmp[ms]; 17 vector<vector<char> > v; 18 int topo_sort(int s) 19 { 20 int i,j,k,flag=1; 21 int total=0,r=0; 22 for(i=0;i<n;i++) 23 tmp[i]=cnt[i]; 24 while(s--) 25  { 26 total=0; 27 for(i=0;i<n;i++) 28 if(appear[i]&&tmp[i]==0) 29  { 30 j=i; 31 total++; 32  } 33 if(total>=1) 34  { 35 if(total>1) 36 flag=0; 37 for(i=0;i<v[j].size();i++) 38 tmp[v[j][i]]--; 39 tmp[j]=-1; 40 output[r++]=j+'A'; 41 output[r]=0; 42  } 43 else 44 return -1; 45  } 46 if(flag) 47 return r; 48 return 0; 49 } 50 int main() 51 { 52 int i,j,k,judge,det; 53 char str[4]; 54 while(scanf("%d%d",&n,&m)==2&&(n+m)) 55  { 56 judge=0; 57 det=0; 58 int sum=0; 59  v.clear();v.resize(n); 60 memset(cnt,0,sizeof(cnt)); 61 memset(appear,false,sizeof(appear)); 62 for(i=1;i<=m;i++) 63  { 64 scanf("%s",str); 65 cnt[str[2]-'A']++; 66 v[str[0]-'A'].push_back(str[2]-'A'); 67 if(!appear[str[0]-'A']) 68  { 69 sum++; 70 appear[str[0]-'A']=1; 71  } 72 if(!appear[str[2]-'A']) 73  { 74 sum++; 75 appear[str[2]-'A']=1; 76  } 77 if(judge==0) 78  { 79 det=topo_sort(sum); 80 if(det==-1) 81  { 82 judge=-1;k=i; 83  } 84 else if(det==n) 85  { 86 judge=1; 87 k=i; 88  } 89  } 90  } 91 if(judge==-1) 92 printf("Inconsistency found after %d relations.\n",k); 93 else if(judge==0) 94 printf("Sorted sequence cannot be determined.\n"); 95 else 96 printf("Sorted sequence determined after %d relations: %s.\n",k,output); 97  } 98 return 0; 99 }