POJ 1094：Sorting It All Out：拓扑排序的较为繁琐的逻辑变形

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 26852		Accepted: 9262

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.

Source

East Central North America 2001

该问题的难度在于，你不仅要确定在每一步能否确定拓扑序列（成或者不成），还在于三种状态的优先及分类一定要清晰。需要没加入一条边，就进行一次拓扑排序。判断现有的边能否组成拓扑序列，或者一定组不成拓扑序列（存在有向回路），或者无法确定拓扑序列，只有第三种情况，才会对后面添加的边继续进行拓扑排序。前两种都需要记录第几条边确定的情况，然后等待输出。

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#define maxn 100000000
int n,m,a[30][30],p,ci;
char tem[5],result[30];
void paixu(int x)
{
	int i,j,k=0,ii;
	int temp;
	int rudu[30],chudu[30];
	int pdian=0,fsure=0,pbian=0;
	int use[30];
	memset(use,0,sizeof(use));
	memset(rudu,0,sizeof(rudu));
	memset(chudu,0,sizeof(chudu));
	for(i=0;i<n;i++)
	{
		for(j=0;j<n;j++)
		{
			if(a[i][j])
			{
				chudu[i]++;
				rudu[j]++;
			}
		}
	}
	do
	{
		temp=0;
		for(ii=0;ii<n;ii++)
		{
			if(rudu[ii]==0&&chudu[ii]>0)
			{
				temp++;
				if(temp==1)
					i=ii;
			}
		}
		if(temp)
		{
			for(j=0;j<n;j++)
			{
				if(a[i][j])
				{
					rudu[j]--;
					pbian++;
				}
			}
			chudu[i]=0;
			pdian++;
			result[k++]=i+'A';
			use[i]=1;
		}
		if(temp>1)
			fsure=1;
	}while(temp!=0);
	if(pbian<x)
	{
		p=1;
		ci=x;
	}
	else
	{
		if(fsure)
			p=0;
		else
		{
			if(pdian==n-1)
			{
				p=2;
				ci=x;
				for(i=0;i<n;i++)
					if(use[i]==0)
						break;
				if(i<n)
					result[k++]=i+'A';
				result[k++]='\0';

			}
			else
				p=0;
		}
	}
}
void print()
{
	int i,j;
	switch(p)
	{
	case 1:printf("Inconsistency found after %d relations.\n",ci);break;
	case 2:printf("Sorted sequence determined after %d relations: ",ci);
		printf("%s.\n",result);break;
	case 0:printf("Sorted sequence cannot be determined.\n");break;
	default:break;
	}
}
int main()
{
	int i,j;
	while(scanf("%d%d",&n,&m)!=EOF&&n)
	{
		p=0;
		memset(a,0,sizeof(a));
		for(i=1;i<=m;i++)
		{
			scanf("%s",tem);
			if(p==0)
			{
				a[tem[0]-'A'][tem[2]-'A']=1;
				paixu(i);
			}
		}
		print();
	}
	return 0;
}