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.
题意是给出一些比较关系,求给出这些关系的过程中1 )能否有一个确定的排序,有的话给出关系的个数并求出这个排序的序列;2)是否成环;3)不能确定
只有一个确定排序的拓扑序列的性质应该是,只有一个入度为0的节点,去掉此节点后,剩下的还是只有一个入度为0的点。按照这个性质模拟就行了。
#include
#include
#include
#include
#include
#include
#include
#include
#include
#define INF 0x3f3f3f3f
#define MAXN 105
#define Mod 10001
using namespace std;
int n,m,c;
int map[30][30],temp[30],indegree[30],q[30];
int topsort(int n)
{
int m,pos,flag=1;
c=0;
for(int i=1; i<=n; ++i)
temp[i]=indegree[i];
for(int i=1; i<=n; ++i)
{
m=0;
for(int j=1; j<=n; ++j)
if(temp[j]==0) //选择一个入度为0的点,即可能为起点
{
m++;
pos=j;
}
if(m==0)
return 0; //有环
if(m>1)
flag=-1; //还不确定
q[c++]=pos; //该起点入栈
temp[pos]=-1;
for(int j=1;j<=n;++j)
if(map[pos][j]) //把起点去掉后,相连的点要有处理
temp[j]--;
}
return flag;
}
int main()
{
char op[10];
while(~scanf("%d%d",&n,&m))
{
getchar();
if(n==0&&m==0)
break;
memset(indegree,0,sizeof(indegree));
memset(map,0,sizeof(map));
int s=-1,flag=0;
for(int i=1; i<=m; ++i)
{
gets(op);
if(s==0||s==1)
continue;
int x=op[0]-'A'+1;
int y=op[2]-'A'+1;
map[x][y]=1;
indegree[y]++;
s=topsort(n);
if(s==0)
{
printf("Inconsistency found after %d relations.\n",i);
flag=1;
}
if(s==1)
{
printf("Sorted sequence determined after %d relations: ",i);
for(int j=0;jprintf("%c",q[j]+'A'-1);
printf(".\n");
flag=1;
}
}
if(!flag)
printf("Sorted sequence cannot be determined.\n");
}
return 0;
}