# POJ 1094 Sorting It All Out （拓扑排序）

Sorting It All Out

 Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 34275 Accepted: 12017

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.

### AC 代码

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<vector>
#include<queue>
#include<set>
using namespace std;
#define M 30
vector<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;
}