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.

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<vector>
 4 using namespace std;
 5 
 6 vector<int>G[27];
 7 int cnt;
 8 char b[27];
 9 int m,n;
10 int c[27];
11 bool mark[27][27];
12 
13 bool dfs(int u)
14 {
15     c[u]=-1;
16     for(int i=0;i<G[u].size();i++)
17     {
18         if(c[G[u][i]]<0)
19             return false;
20         else if(!c[G[u][i]]&&!dfs(G[u][i]))
21             return false;
22     }
23     b[--cnt]=u+'A';
24     c[u]=1;
25     return true;
26 }
27 
28 int toposort()
29 {
30     bool flag;
31     int i,j;
32     for(i=0;i<n;i++)
33     {
34         memset(c,0,sizeof(c));
35         cnt=n;
36         flag=dfs(i);
37         if(!flag)
38             return -1;
39         else
40         {
41             for(j=0;j<n;j++)
42                 if(!c[j])break;
43             if(j!=n)continue;
44             int k;
45             for(k=0;k<n-1;k++)
46             if(!mark[(int)b[k]-'A'][(int)b[k+1]-'A'])
47             break;
48             if(k==n-1)
49             return 1;
50         }
51     }
52     return 0;
53 }
54 
55 int main()
56 {
57    // freopen("in.txt","r",stdin);
58     while(scanf("%d%d",&n,&m),n|m)
59     {
60         memset(mark,0,sizeof(mark));
61         bool key=false;
62         int i;
63         for(i=0;i<n;i++)
64         G[i].clear();
65         for(i=0;i<m;i++)
66         {
67             char u,v;
68             getchar();
69             scanf("%c<%c",&u,&v);
70             if(key)
71                 continue;
72             if(!mark[u-'A'][v-'A'])
73             {
74                 G[(int)u-'A'].push_back((int)v-'A');
75                 mark[u-'A'][v-'A']=1;
76             }
77             int ans=toposort();
78             if(ans==1)
79             {
80                 printf("Sorted sequence determined after %d relations: ",i+1);
81                 for(int j=0;j<n;j++)
82                 printf("%c",b[j]);
83                 printf(".
");
84                 key=true;
85                 continue;
86             }
87             else if(ans==-1)
88             {
89                 printf("Inconsistency found after %d relations.
",i+1);
90                 key=true;
91                 continue;
92             }
93         }
94         if(!key)
95             printf("Sorted sequence cannot be determined.
");
96     }
97     return 0;
98 }