POJ1094 Sorting It All Out（拓扑排序）

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 30110		Accepted: 10411

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：这题题意好蛋疼啊！！！一个一个给边，一个一个的判断，先判断是否有环。然后再判断是否确定序列。最后前两者都不满足，则此序列不确定。
收获：1.知道只有有环时才k<n。2.入度为0的点不唯一，则此序列不确定。3.入度很重要。
下面是能AC代码，但是 0 0会有问题，不知道为什么?还请各位指教。

#include <cstdio>
#include <iostream>
//#include <cstdlib>
#include <algorithm>
#include <ctime>
#include <cmath>
#include <string>
#include <cstring>
#include <stack>
#include <queue>
#include <list>
#include <vector>
#include <map>
#include <set>
using namespace std;

const int INF=0x3f3f3f3f;
const double eps=1e-10;
const double PI=acos(-1.0);

const int maxn=5000;
struct Edge
{
    int u, v, next;
};
Edge edge[maxn];
int head[maxn];
int num, n,m;
void init_edge()
{
    num = 0;
    memset(head, -1, sizeof(head));
}
void addedge(int u, int v)
{
    edge[num].u = u;
    edge[num].v = v;
    edge[num].next = head[u];
    head[u] = num++;
}
int ans;
int topo[maxn];
int in[maxn];
int topsort()
{
    queue<int> q;
    int indeg[26];
    for(int i = 65; i < 65+n; i++)
    {
        indeg[i] = in[i];
        if(indeg[i] == 0) q.push(i);
    }
    int k = 0;
    int flag=0;
    while(!q.empty())
    {
        if(q.size()>1)
            flag = 1;
        int u = q.front();
        q.pop();
        topo[k++] = u;
        for(int i = head[u]; i != -1; i = edge[i].next)
        {
            int v = edge[i].v;
            indeg[v]--;
            if(indeg[v]==0)
                q.push(v);
        }
    }
    if(k < n)
        return 0;
    if(flag)
        return -1;
    else
    return 1;
}
char s[5];
int main()
{
    while(~scanf("%d%d", &n, &m))
    {
        if(n==0 && m==0)
           break;
        init_edge();
        memset(in, 0, sizeof(in));
        int flag2 = 0;
        int flag3 = 0;
        for(int j = 1; j <= m; j++)
        {
            scanf("%s",s);
            if(!flag2&&!flag3)
            {
                in[s[2]]++;
                addedge(s[0],s[2]);
                int res = topsort();
                if(res == 0)
                {
                    printf("Inconsistency found after %d relations.
", j);
                    flag2 = 1;
                }
                if(res == 1)
                {
                    printf("Sorted sequence determined after %d relations: ", j);
                    for(int i=0; i < n; i++)
                        printf("%c", topo[i]);
                    printf(".
");
                    flag3 = 1;
                }
            }
        }
        if(!flag2&&!flag3)
            puts("Sorted sequence cannot be determined.");

    //puts("QAQ");
    }
    return 0;
}