POJ 1094 Sorting It All Out(拓扑排序)

Sorting It All Out

 

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.

#include<cstdio>
#include<cstring>
#include<vector>
using namespace std;

vector<int>G[27];
int cnt;
char b[27];
int m,n;
int c[27];
bool mark[27][27];

bool dfs(int u)
{
    c[u]=-1;
    for(int i=0;i<G[u].size();i++)
    {
        if(c[G[u][i]]<0)
            return false;
        else if(!c[G[u][i]]&&!dfs(G[u][i]))
            return false;
    }
    b[--cnt]=u+'A';
    c[u]=1;
    return true;
}

int toposort()
{
    bool flag;
    int i,j;
    for(i=0;i<n;i++)
    {
        memset(c,0,sizeof(c));
        cnt=n;
        flag=dfs(i);
        if(!flag)
            return -1;
        else
        {
            for(j=0;j<n;j++)
                if(!c[j])break;
            if(j!=n)continue;
            int k;
            for(k=0;k<n-1;k++)
            if(!mark[(int)b[k]-'A'][(int)b[k+1]-'A'])
            break;
            if(k==n-1)
            return 1;
        }
    }
    return 0;
}

int main()
{
   // freopen("in.txt","r",stdin);
    while(scanf("%d%d",&n,&m),n|m)
    {
        memset(mark,0,sizeof(mark));
        bool key=false;
        int i;
        for(i=0;i<n;i++)
        G[i].clear();
        for(i=0;i<m;i++)
        {
            char u,v;
            getchar();
            scanf("%c<%c",&u,&v);
            if(key)
                continue;
            if(!mark[u-'A'][v-'A'])
            {
                G[(int)u-'A'].push_back((int)v-'A');
                mark[u-'A'][v-'A']=1;
            }
            int ans=toposort();
            if(ans==1)
            {
                printf("Sorted sequence determined after %d relations: ",i+1);
                for(int j=0;j<n;j++)
                printf("%c",b[j]);
                printf(".
");
                key=true;
                continue;
            }
            else if(ans==-1)
            {
                printf("Inconsistency found after %d relations.
",i+1);
                key=true;
                continue;
            }
        }
        if(!key)
            printf("Sorted sequence cannot be determined.
");
    }
    return 0;
}