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 <cstdio> 2 #include <vector> 3 using namespace std; 4 5 int obj[26]; //obj[i]表示第i+1个字母出现在"<"右端的次数，用于处理关系的方向性 6 int temp[26]; //temp为obj的拷贝，用于拓扑排序时进行修改 7 char relation[3], seq[26]; //relation用于读入对象间关系，seq用于存储得到的序列 8 bool alpha[26]; //alpha用于记录对象是否已经检查 9 int n, m; 10 vector< vector<char> > v; //使用STL的成员vector来存储节点 11 12 //拓扑排序，返回拓扑排序后得到的序列中元素的个数；若发现矛盾则返回-1，无法判断则返回0 13 int toposort( int s ) 14 { 15 int i, j; //j表示当前已读入的未出现在"<"右端的对象 16 int r, cnt; //cnt表示这些对象的个数；r表示得到序列中元素的个数 17 bool flag; //flag为标志变量，表示拓扑排序结束后是否可以得到序列 18 r = 0, cnt = 0; 19 for( i = 0; i < n; i++ ) temp[i] = obj[i]; 20 flag = 1; 21 while( s-- ) 22 { 23 cnt = 0; 24 for( i = 0; i < n; i++ ) 25 { 26 if( temp[i] == 0 ) 27 j = i, cnt++; 28 } 29 if( cnt>=1 ) 30 { 31 //cnt=1表示仅一个对象出现在"<"右端，则该对象必然处于序列最右端 32 if( cnt>1 ) flag = 0; 33 for( i=0; i<v[j].size( ); i++ ) 34 temp[ v[j][i] ]--; //处理完毕后剔除 35 seq[r++] = j + 'A'; 36 temp[j] = -1; seq[r] = 0; 37 } 38 else if( cnt == 0 ) //cnt==0表示当前已读入的对象均出现在"<"右端一次以上 39 return -1; //则必然存在环 40 } 41 if( flag ) return r; 42 else return 0; 43 } 44 45 int main( ) 46 { 47 int i, t, k; //k用于记录关系矛盾或可以得到序列时已处理的关系个数 48 int count; //count用于记录读入的对象个数 49 int determined; //determined用于标记是否可以得到序列 50 //-1表示关系矛盾、0表示无法得到序列、1表示可以得到序列 51 while( scanf( "%d %d", &n, &m ) != EOF && n != 0 && m != 0 ) 52 { 53 memset( obj, 0, sizeof( obj )); //初始化 54 memset( alpha, false, sizeof( alpha )); 55 //删除vector中的元素，并重新调整大小 56 v.clear( ); v.resize( n ); 57 count = 0; determined = 0; 58 for( i=0; i<m; i++ ) 59 { 60 scanf( "%s", relation ); //读入数据 61 obj[ relation[2]-'A' ]++; 62 v[ relation[0]-'A' ].push_back( relation[2]-'A' ); 63 //记录读入的对象个数 64 if( !alpha[ relation[0]-'A' ] ) 65 { 66 count++; alpha[ relation[0]-'A' ] = true; 67 } 68 if( !alpha[ relation[2]-'A' ] ) 69 { 70 count++; alpha[ relation[2]-'A' ] = true; 71 } 72 if( determined==0 ) 73 { 74 t = toposort( count ); 75 if( t==-1 ) 76 determined = -1, k = i + 1; 77 else if( t==n ) 78 determined = 1, k = i + 1; 79 } 80 } 81 if( determined==-1 ) 82 printf( "Inconsistency found after %d relations.\n",k ); 83 else if( determined==0 ) 84 printf( "Sorted sequence cannot be determined.\n" ); 85 else 86 printf( "Sorted sequence determined after %d relations: %s.\n",k,seq ); 87 } 88 return 0; 89 }