poj——1094——Sorting It All Out（拓扑排序）

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. 

Sample Input

4 6
A

Sample Output

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

#include 
#include 
#include 
#include 

using namespace std;
#define MAXN 28

bool adj[MAXN][MAXN];
int in_degree[MAXN];
char str[MAXN];
int n,m;

int topo_sort()
{
    int i,j,k;
    bool flag=true;
    memset(in_degree,0,sizeof(in_degree));
    memset(str,'\0',sizeof(str));
    for(i=1; i<=n; i++)
    {
        for(j=1; j<=n; j++)
            if(adj[i][j])
                in_degree[j]++; //入度加一
    }
    for(i=1; i<=n; i++)  //每次产生一个字符
    {
        k=0;
        for(j=1; j<=n; j++)
        {
            if(in_degree[j]==0)
            {
                if(k==0) 
				k=j;
                else 
				flag=false;  //还有入度为零的节点
            }
        }
        if(k==0)
		 return 0; //没有入度为零的节点，即存在环
        in_degree[k]=-1;
        str[i-1]=k+'A'-1;
        for(j=1; j<=n; j++)  //k指向的节点入度都减一，即去掉A及它相关的边
        {
            if(adj[k][j])
                in_degree[j]--;
        }
    }
    if(flag) return 1;  //没有入度为零的点，完成排序
    else return 2;     //排序没有完成
}

int main()
{
    int i,a,b,result;
    char s[4];
  //  freopen("acm.txt","r",stdin);
    while(scanf("%d%d",&n,&m),m+n)
    {
        memset(adj,false,sizeof(adj));
        bool h=false;
        for(i=1; i<=m; i++)
        {
            scanf("%s",s);
            a=s[0]-'A'+1; 
			b=s[2]-'A'+1;
            adj[a][b]=true;
            if(h) 
			continue;   //必须有，因为还要继续把剩下的数据都读完
            result=topo_sort();
            if(result==1)
            {
                printf("Sorted sequence determined after %d relations: %s.\n",i,str);
                h=true;
            }
            if(result==0)
            {
                printf("Inconsistency found after %d relations.\n",i);   //有换存在
                h=true;
            }
        }
        if(!h) printf("Sorted sequence cannot be determined.\n");
    }
    return 0;
}