Poj/OpenJudge 1094 Sorting It All Out

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 25547		Accepted: 8861

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 <iostream>
#include <cstring>
#include <cstdio>
#include <cstdlib>

using namespace std;

int n,m;
int map[30][30];
int reg[100];
int in[30],out[30];
char ans[30];
int stack[30];
void fun()
{
int i,j;
for(i='A',j=1;i<='Z';i++,j++)reg[i]=j;
}
void toposort(char *ans)
{
int i,top=0,u,s=0;
for(i=1;i<=n;i++)
if(in[i]==0)stack[top++]=i;
while(top!=0)
{
u=stack[--top];
ans[s++]=u+64;
for(i=1;i<=n;i++)
{
if(map[u][i])
{
in[i]--;
if(!in[i])stack[top++]=i;
}
}
}
ans[s]=0;
}
int main()
{
int i,j,x,y,k,flag1,flag2,flag;
fun();
char ch[5];
while(1)
{
flag1=flag2=0;
memset(map,0,sizeof(map));
scanf("%d%d",&n,&m);
if(n==0&&m==0)break;
for(i=1;i<=m;i++)
{
flag=1;
scanf("%s",ch);
x=reg[ch[0]];
y=reg[ch[2]];
map[x][y]=1;
if(x==y)flag1=i;
memset(in,0,sizeof(in));
memset(out,0,sizeof(out));
if(!flag1&&!flag2)
for(j=1;j<=n;j++)
for(k=1;k<=n;k++)
{
if(j!=x&&k!=y)map[j][k]=map[j][k]||(map[j][x]&&map[y][k]);
if(j==x&&k!=y)map[j][k]=map[j][k]||map[y][k];
if(j!=x&&k==y)map[j][k]=map[j][k]||map[j][x];
if(map[j][k])
{
out[j]++;
in[k]++;
}
}
j=1;
if(!flag1)
for(j=1;j<=n;j++)
{
if(map[j][j])flag1=i;
if(in[j]+out[j]!=n-1)flag=0;
}
if(flag&&!flag2&&j>n){flag2=i;toposort(ans);}
}
if(flag2)
{
printf("Sorted sequence determined after %d relations: %s.\n",flag2,ans);
continue;
}
if(flag1)
{
printf("Inconsistency found after %d relations.\n",flag1);
continue;
}
printf("Sorted sequence cannot be determined.\n");
}
return 0;
}