Sorting It All Out Time Limit: 1000MS Memory Limit: 10000K
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. 题意：输入n代表26个大写字母中的前n个参与，有m个关系 分出三种情况： 1.有环，不能确定拓扑序列 2.无环，能确定拓扑序列，但序列不唯一，是由于由于关系不够造成的 3.能确定唯一拓扑序列 思路： 1 就是题目要求的知道是第几个确定的结果，因此每个关系都要进行拓扑排序。 2.若有环的出现，那么最后的字符串肯定没有环中的字母，那么字符串个数就肯定小于n。 3.如果一个队列里面的元素超过1的话，就说明拓扑序列当前可以有多个起点，那么拓扑序列就是不唯一的
#include<iostream> #include<string> #include<vector> #include<queue> #include<cstring> using namespace std; const int Max=10000; int n,m; string s[Max],t; vector<int>G[Max];//邻接表 int indeg[Max];//入度 int tp() { queue<int>que; int book=0; for(int i=0;i<n;i++) { if(indeg[i]==0) que.push(i); } int indeg2[Max]; memcpy(indeg2,indeg,sizeof indeg); while(!que.empty()) { if(que.size()>1)book=1; int now=que.front(); que.pop(); t+=now+'A'; int SIZE=G[now].size(); for(int i=0;i<SIZE;i++) { int to=G[now][i]; --indeg2[to]; if(indeg2[to]==0) { que.push(to); } } } if(t.size()<n)return -1; else if(book)return 0; else return 1; } int main() { while(cin>>n>>m&&(n||m)) { memset(indeg,0,sizeof indeg); for(int i=0;i<Max;i++) { G[i].clear(); } for(int i=1;i<=m;i++) { cin>>s[i]; } int id; int flag=1; for(int i=1;i<=m;i++) { t=""; int x=s[i][0]-'A',y=s[i][2]-'A'; ++indeg[y]; G[x].push_back(y); flag=tp(); if(flag==-1) { cout<<"Inconsistency found after "<<i<<" relations."<<endl; break; } else if(flag==1) { cout<<"Sorted sequence determined after "<<i<<" relations: "<<t<<"."<<endl; break; } } if(flag==0)cout<<"Sorted sequence cannot be determined."<<endl; } }