poj 1094 Sorting It All Out 拓补排序
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.
题意：给一些大写字母的偏序关系。判断是否存在唯一的关系，或者他们的关系是矛盾的,即造成了回路，或者到最后不能确定他们的关系。
用拓扑排序：
1.拓扑排序可以用栈来实现，每次入栈的是入度为0的节点。
1.拓扑排序的结果一般分为三种情况：1、可以判断 2、有环出现了矛盾 3、条件不足，不能判断.
2.这道题不仅需要判断这三种情况，而且还要判断在处理第几个关系时出现前两种情况，对于本道题来说三种情况是有优先级的。前两种情况是平等的谁先出现先输出谁的相应结果，对于第三种情况是在前两种情况下都没有的前提下输出相应结果的.
1 #include <iostream> 2 #include <cstdio> 3 #include <stack> 4 #include <cstring> 5 using namespace std; 6 const int maxn=30; 7 int n,m; 8 int pb[maxn][maxn],rd[maxn],list[maxn]; 9 int toposort() 10 { 11 int i,j=0; 12 int in[maxn]; 13 memcpy(in,rd,sizeof(rd)); //复制入度数组，以防改变原数组 14 stack <int> s; 15 for(i=0; i<n; i++) //入度为0的入栈 16 { 17 if(!in[i]) 18 s.push(i); 19 } 20 bool flag=false; 21 while(!s.empty()) 22 { 23 if(s.size()>1) 24 flag=true; 25 int t=s.top(); // 记录出栈数字 26 s.pop(); 27 list[j++]=t; 28 for(i=0; i<n; i++) 29 { 30 if(pb[t][i]) 31 { 32 in[i]--; //入度减一 33 if(!in[i]) 34 s.push(i); //入度为0的继续入栈 35 } 36 } 37 } 38 if(j!=n) //存在回路 39 return 1; 40 else if(flag) //有多重排序方式 41 return 2; 42 return 0; 43 } 44 int main() 45 { 46 while(cin>>n>>m,n||m) 47 { 48 memset(pb,0,sizeof(pb)); 49 memset(rd,0,sizeof(rd)); 50 char a,b; 51 int frist,scend; 52 frist=scend=0; 53 for(int i=1; i<=m; i++) 54 { 55 getchar(); 56 scanf("%c<%c",&a,&b); 57 if(!frist && !scend) 58 { 59 if(pb[b-'A'][a-'A']==1) //存在反向边 60 { 61 scend=1; 62 printf("Inconsistency found after %d relations.\n",i); 63 continue; 64 } 65 if(!pb[a-'A'][b-'A']) 66 { 67 pb[a-'A'][b-'A']=1; 68 rd[b-'A']++; 69 } 70 int res=toposort(); //进行拓扑排序 71 if(res==0) //序列能够唯一被确定 72 { 73 printf("Sorted sequence determined after %d relations: ",i); 74 for(int j=0; j<n; j++) 75 printf("%c",list[j]+'A'); 76 printf(".\n"); 77 frist=1; 78 } 79 else if(res==1) //存在回路 80 { 81 scend=1; 82 printf("Inconsistency found after %d relations.\n",i); 83 } 84 } 85 86 } 87 if(!frist&&!scend) //即不能唯一约定，又不构成回路 88 printf("Sorted sequence cannot be determined.\n"); 89 } 90 return 0; 91 }
