POJ 1094 Sorting It All Out(拓扑排序)

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.

该题题意明确，就是给定一组字母的大小关系判断他们是否能组成唯一的拓扑序列。是典型的拓扑排序，但输出格式上确有三种形式：

1.该字母序列有序，并依次输出；

2.该序列不能判断是否有序；

3.该序列字母次序之间有矛盾，即有环存在。

而这三种形式的判断是有顺序的：先判断是否有环（3），再判断是否有序（1），最后才能判断是否能得出结果（2）。注意：对于（2）必须遍历完整个图，而（1）和（3）一旦得出结果，对后面的输入就不用做处理了。

#include<stdio.h>#include<string.h>int map[27][27],indegree[27],q[27]; //map代表有向图，map[i][j]=1代表字母i<j。//indegree[i]代表结点i的入度，即直接小于i的个数int TopoSort(int n) //拓扑排序，n指共有多少字母如abcd=4，abccd=4{    int c=0,temp[27],loc,m,flag=1,i,j;  ////flag=1:有序 flag=-1:不确定    //m:入度为零的顶点个数    for(i=1;i<=n;i++)        temp[i]=indegree[i];//temp=indegree=入度数，是为了在后面的主函数的循环中不改变indegree的值    for(i=1;i<=n;i++)    {        m=0;        for(j=1;j<=n;j++)            if(temp[j]==0) { m++; loc=j; }  //查找入度为零的顶点个数，设置为m        if(m==0) return 0;  //有环        if(m>1) flag=-1;  // 无序，m大于1，则出现一个以上没有入度的，证明无序        q[c++]=loc;   //入度为零的点入队        temp[loc]=-1;  //标记，将入度为0的点删除，并将两个出度取消        for(j=1;j<=n;j++)             if(map[loc][j]==1) temp[j]--;  //如果j含有入度，则入度--    }    return flag;}int main(){    int m,n,i,sign;  //当sign=1时，已得出结果    char str[5];    while(scanf("%d%d",&n,&m)) //n代表字母个数，m代表要输入的关系的行数    {        if(m==0&&n==0) break;//都等于0时，结束输入        memset(map,0,sizeof(map));        memset(indegree,0,sizeof(indegree));        sign=0;        for(i=1;i<=m;i++)        {            scanf("%s",str); //str[0]=字母，str[1]=空格，str[2]=字母            if(sign) continue; //一旦得出结果，对后续的输入不做处理            int x=str[0]-'A'+1;            int y=str[2]-'A'+1;            map[x][y]=1;            indegree[y]++;  //y的入度+1            int s=TopoSort(n);            if(s==0) //有环,即x<y && y<x的情况            {                printf("Inconsistency found after %d relations.\n",i);//表示在输入了第几个之后出的结果，后面的就不作处理了。                sign=1;            }            if(s==1) //有序,正常情况            {                printf("Sorted sequence determined after %d relations: ",i);                for(int j=0;j<n;j++)                    printf("%c",q[j]+'A'-1);                printf(".\n");                sign=1;            }        }        if(!sign) //不确定            printf("Sorted sequence cannot be determined.\n");    }    return 0;}