POJ 1094 Sorting It All Out （拓扑排序）

2019-11-10 17:39:26

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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 6A<BA<CB<CC<DB<DA<B3 2A<BB<A26 1A<Z0 0

Sample Output

Sorted sequence determined after 4 relations: ABCD.Inconsistency found after 2 relations.Sorted sequence cannot be determined.

题意

依序给出一些字母之间的大小关系，判断并输出它能否唯一确定一个序列满足这一关系。

思路

依旧是一道拓扑排序的题目。

无法唯一确定一个序列当且仅当在所有关系输入完毕之后，进行拓扑排序的时候存在一个以上入度为0的点。

序列不存在会在图中存在环的情况下出现。

于是，每输入一组关系，进行一次拓扑排序，对此次拓扑排序的结果判断并做出相应的选择。

AC 代码

#include<iostream>#include<stdio.h>#include<string.h>#include<algorithm>#include<vector>#include<queue>#include<set>using namespace std;#define M 30vector<int>G[M];int in[M],n,m;char ans[M];int solve(){ int res=1,h[M],top=0; memcpy(h,in,sizeof(h)); //copy 入度数组 queue<int>sk; for(int i=0; i<n; i++) //入度为0的点压入队列 if(h[i]==0) sk.push(i); while(!sk.empty()) { int p=sk.front(); sk.pop(); ans[top++]=p+'A'; if(sk.size()>0) //如果入度为0的点同时存在一个以上，说明无法唯一确定序列 res=0; for(int i=0; i<(int)G[p].size(); i++) //消除当前点，临界点入度-1 { int j=G[p][i]; if(--h[j]==0) sk.push(j); } } if(top<n)res=-1; //图中存在环 ans[top]=0; return res;}int main(){ while(~scanf("%d%d%*c",&n,&m)&&(n||m)) { char a,b; int flag=0; memset(in,0,sizeof(in)); for(int i=0; i<M; i++) G[i].clear(); for(int i=0; i<m; i++) { scanf("%c%*c%c%*c",&a,&b); if(flag)continue; a-='A'; b-='A'; G[(int)a].push_back((int)b); ++in[(int)b]; //入度 flag=solve(); //拓扑排序 if(flag==1) printf("Sorted sequence determined after %d relations: %s./n",i+1,ans); if(flag==-1) printf("Inconsistency found after %d relations./n",i+1); } if(!flag) printf("Sorted sequence cannot be determined./n"); } return 0;}

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