Sorting It All Out
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 24591 | Accepted: 8517 |
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.
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.
Source
East Central North America 2001
可以确定关系的 > 矛盾的 > 多解的 所以如果是多解的还要进行判环
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <set> 5 #include <vector> 6 7 using namespace std; 8 9 int n,m,g[30][30],id1[30],id2[30]; 10 bool vis[30],VK; 11 int topo(int nt,int id[30]) 12 { 13 vector<char> v; 14 while(v.size()!=n) 15 { 16 int pos=-1,cnt=0; 17 for(int i=0;i<n;i++) 18 if(id[i]==0) 19 { 20 if(pos==-1) pos=i; 21 cnt++; 22 } 23 if(cnt>1) return 0; 24 else if(cnt==1) 25 { 26 v.push_back(pos+'A'); 27 for(int j=0;j<n;j++) 28 { 29 if(g[pos][j]) 30 { 31 id[j]--; 32 } 33 } 34 id[pos]=-1; 35 } 36 if(pos==-1) 37 { 38 printf("Inconsistency found after %d relations. ",nt); 39 return -1; 40 } 41 } 42 printf("Sorted sequence determined after %d relations: ",nt); 43 for(int i=0;i<n;i++) 44 printf("%c",v[i]); 45 printf(". "); 46 return 1; 47 } 48 49 bool floyd() 50 { 51 int mark[30][30]; 52 memcpy(mark,g,sizeof(mark)); 53 for(int k=0;k<n;k++) 54 for(int i=0;i<n;i++) 55 for(int j=0;j<n;j++) 56 { 57 if(g[i][k]&&g[k][j]) 58 mark[i][j]=1; 59 } 60 for(int i=0;i<n;i++) 61 { 62 for(int j=i+1;j<n;j++) 63 if(mark[i][j]&&mark[j][i]) 64 return true; 65 } 66 return false; 67 } 68 69 int main() 70 { 71 while(scanf("%d%d",&n,&m)!=EOF) 72 { 73 if(n==0&&m==0) break; 74 getchar(); 75 set<char> s; 76 bool cont=false;int num=0; 77 memset(g,0,sizeof(g)); 78 memset(id1,0,sizeof(id1)); 79 for(int i=1;i<=m;i++) 80 { 81 char a[2],b[2]; 82 scanf("%c<%c",&a[0],&b[0]); 83 getchar(); 84 if(cont) continue; 85 g[a[0]-'A'][b[0]-'A']=1; 86 id1[b[0]-'A']++; 87 memcpy(id2,id1,sizeof(id1)); 88 int sin=topo(i,id2); 89 ///youjie 90 if(sin==1||sin==-1) cont=true; 91 if(sin==0) 92 { 93 if( floyd() ) 94 { 95 printf("Inconsistency found after %d relations. ",i); 96 cont=true; 97 } 98 } 99 } 100 if(cont==false) 101 printf("Sorted sequence cannot be determined. "); 102 } 103 return 0; 104 }