poj——1094——Sorting It All Out(拓扑排序)

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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 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.

#include <iostream>#include <cstring>#include <cstdio>#include <algorithm>using namespace std;#define MAXN 28bool 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;}


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