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.
#include <iostream>
#include <algorithm>
#include <string>
#include <string.h>
#include <set>
#include <queue>
const int maxn=30;
using namespace std;
char ww[26];
int a[26];
int n;
int ip;
int head[maxn],indegree[maxn],seq[maxn];
struct note
{
int v,next;
} edge[maxn*maxn];
void init()
{
memset(head,-1,sizeof(head));
//memset(seq,'\0',sizeof(seq));
ip=0;
}
void addedge(int u,int v)
{
edge[ip].v=v,edge[ip].next=head[u],head[u]=ip++;
}
int topo()///拓扑,可做模板
{
queue<int>q;
int indeg[maxn];
for(int i=0; i<n; i++)
{
indeg[i]=indegree[i];
if(indeg[i]==0)
q.push(i);
}
int k=0;
int res=0;
int v;
while(!q.empty())
{
if(q.size()!=1) {
res=1;
}
int u=q.front();
q.pop();
seq[k++]=u;
for(int i=head[u]; i!=-1; i=edge[i].next)
{
v=edge[i].v;
indeg[v]--;
if(indeg[v]==0)
q.push(v);
}
}
int sum=0;
for(int i=0;i<26;i++)
if(a[i])
sum++;
if(k<sum)return -1;///存在有向环,总之不能进行拓扑排序
if(res)return 0;///可以进行拓扑排序,并且只有唯一一种方式,seq数组即是排序完好的序列
return 1;///可以进行拓扑排序,有多种情况,seq数组是其中一种序列
}
int main(){
int m;
while(scanf("%d %d",&n,&m)!=EOF){
char c1,c2,c3;
if (!n && !m)
break;
memset(a,0,sizeof(a));
init();
memset(indegree,0,sizeof(indegree));
int err = -1,ans = -1;
for(int i=0;i<m;i++){
getchar();
scanf("%c%c%c",&c1,&c3,&c2);
if (err != -1 || ans != -1) continue;
a[c1-'A']=1;
a[c2-'A']=1;
indegree[c2-'A']++;
addedge(c1-'A',c2-'A');
int res = topo();
if (res == 1) ans = i + 1;
else if (res == -1) err = i + 1;
}
if (ans != -1)
{
printf("Sorted sequence determined after %d relations: ", ans);
for (int i = 0; i < n; ++i) putchar('A' + seq[i]);
printf(".\n");
}
else if (err != -1)
{
printf("Inconsistency found after %d relations.\n", err);
}
else
{
printf("Sorted sequence cannot be determined.\n");
}
}
}