nyoj 349 Sorting It All Out

Sorting It All Out

时间限制：3000 ms  |  内存限制：65535 KB

难度：3

描述

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.

输入

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.

输出

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. 

样例输入

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

 

样例输出

Sorted sequence determined after 4 relations: ABCD.

Inconsistency found after 2 relations.

Sorted sequence cannot be determined.

#include<stdio.h>
#include<string.h>
int map[27][27],indegree[27],q[27];//indegree为入度，q存放得到的序列 
int TopoSort(int n) //拓扑排序
{
    int c=0,temp[27],loc,m,flag=1,i,j;  ////flag=1:有序 flag=-1:不确定，m为入度为0的顶点的个数 
    for(i=1;i<=n;i++)
        temp[i]=indegree[i];//复制入度表到temp 
    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
        if(m==0) return 0;  //有环
        if(m>1) flag=-1;  // 无序
        q[c++]=loc;   //入度为零的点入队
        temp[loc]=-1;
        for(j=1;j<=n;j++)
            if(map[loc][j]==1) temp[j]--;
    }
    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))
    {
        if(m==0&&n==0) break;
        memset(map,0,sizeof(map));
        memset(indegree,0,sizeof(indegree));
        sign=0;
        for(i=1;i<=m;i++)
        {
            scanf("%s",str);
            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]++;
            int s=TopoSort(n);
            if(s==0) //有环
            {
                printf("Inconsistency found after %d relations.\n",i);
                sign=1;
            }
            if(s==1) //有序
            {
                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;
}