Sorting It All Out
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 29182 | Accepted: 10109 |
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.
Source
East Central North America 2001
#include<stdio.h>
const int N = 30;
int mapt[N][N],in[N],n,m;
int tope(int tm)
{
int path[N],k=0,l=0,uncertain=0;
for(int i=0;i<n;i++)
if(in[i]==0)
path[k++]=i,in[i]=-1;
while(l<k)
{
int s=path[l++];
if(k-l!=0)
uncertain=1;
for(int j=0;j<n;j++)
if(in[j]>0&&mapt[s][j])
{
in[j]--;
if(in[j]==0)
path[k++]=j,in[j]=-1;
}
}
int flag=0;
if(k!=n)//说明有环，矛盾
printf("Inconsistency found after %d relations.\n",tm),flag=1;
else if(uncertain==0)
{
printf("Sorted sequence determined after %d relations: ",tm);
for(int i=0;i<k;i++)
printf("%c",path[i]+'A');
printf(".\n");
flag=1;
}
else if(tm==m)//最后一次加入一个关系判断，可能的输出
printf("Sorted sequence cannot be determined.\n"),flag=1;
return flag;
}
int main()
{
int in_t[N];
char st[10];
while(scanf("%d%d",&n,&m)>0&&n+m!=0)
{
for(int i=0;i<n;i++)
{
in_t[i]=0;
for(int j=0;j<n;j++)
mapt[i][j]=0;
}
int flag=0;
for(int i=1;i<=m;i++)
{
scanf("%s",st);
if(flag)
continue;
int a=st[0]-'A';
int b=st[2]-'A';
if(mapt[a][b]==0)
{
mapt[a][b]=1; in_t[b]++;
for(int j=0;j<n;j++)
in[j]=in_t[j];
flag=tope(i);
}
}
}
}