| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 24354 | Accepted: 8417 |
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.
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.
/*
此题要注意优先级，当在输入的过程中出现环或拓扑排序成功时可以直接输出，但当前驱结点不唯一时不能直接输出，因为后面的输入可能导致出现环，这时候就应该输出矛盾而不是拓扑序列不唯一了，所以判拓扑序列不唯一时应放在输入完毕后；wa了好多次，有想哭的冲动；
*/
1 #include<stdio.h> 2 #include<string.h> 3 int n,m,cnt; 4 int degree[30]; 5 bool map[30][30],vis[30]; 6 char topo[30]; 7 8 int toposort() 9 { 10 memset(vis,0,sizeof(vis)); 11 int indegree[30];//函数内部设一个记录入度的数组，尝试着进行拓扑，因为记录入度的外部数组不能随意更改； 12 int i,j,k,m; 13 for(i = 0; i < 26; i++) 14 indegree[i] = degree[i]; 15 cnt = 0; 16 m = 0;//判断是否有多个前驱结点，注意初始化放在外循环外面； 17 int count = 0;//记录前驱结点的个数； 18 for(i = 0; i < n; i++) 19 { 20 21 for(j = 0; j < n; j++) 22 { 23 if(indegree[j] == 0 && !vis[j]) 24 { 25 vis[j] = 1;//把该入度为0的结点删除，这里标记为1； 26 topo[cnt++] = j+'A';//进拓扑序列； 27 count++;//找到一个前驱结点，计数器加1； 28 29 for(k = j+1; k < n; k++) 30 { 31 if(indegree[k] == 0 && !vis[k]) 32 m = 1;//m=1说明有多个前驱结点，拓扑序列不唯一； 33 } 34 for(k = 0; k < n; k++) 35 { 36 if(map[j][k] == 1) 37 indegree[k]--;//与j相连的结点入度减一； 38 } 39 break; 40 } 41 42 } 43 } 44 topo[cnt] = ' '; 45 if(count < n) 46 return -1;//若n次循环后前驱结点数小于n说明有环； 47 else if(m == 1) return 0;//m=1说明有多个前驱结点，拓扑序列不唯一； 48 else return 1; 49 } 50 int main() 51 { 52 int i,res; 53 char u,v; 54 while(~scanf("%d %d",&n,&m)) 55 { 56 if(n == 0 && m == 0) 57 break; 58 getchar(); 59 memset(map,0,sizeof(map)); 60 memset(degree,0,sizeof(degree)); 61 62 int ok = 0; 63 for(i = 1; i <= m; i++) 64 { 65 if(ok == 0) 66 { 67 scanf("%c<%c",&u,&v); 68 getchar(); 69 degree[v-'A']++; 70 map[u-'A'][v-'A'] = 1; 71 res = toposort(); 72 if(res == -1) 73 { 74 printf("Inconsistency found after %d relations. ",i); 75 ok = 1; 76 continue; 77 } 78 else if(res == 1) 79 { 80 printf("Sorted sequence determined after %d relations: ",i); 81 printf("%s. ",topo); 82 ok = 1; 83 continue; 84 } 85 } 86 else 87 { 88 scanf("%c<%c",&u,&v); 89 getchar(); 90 } 91 } 92 if(ok == 0) 93 printf("Sorted sequence cannot be determined. "); 94 } 95 return 0; 96 }