poj 1094 拓扑排序(判断严格小于关系&判断是否有环)

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 24933		Accepted: 8662

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

这道题目考察了拓扑排序的基本思想：每一步寻找一个入度为0的结点，然后删除之。将这个结点指向的结点入度减1。删除从这个结点出发的所有边

同时考察了对于一个有向图是否有环、是否严格有序的判断。（当发现多个结点的度为0时，则不是严格有序。当发现没有结点入度为0时，则有环）

需要注意的是逻辑上的关系。“Sorted sequence cannot be determined.”这个判断，要放在最后，即只有发现了所有的点都没有环，且并没有发现严格有序性质的时候，才可以判为“Sorted sequence cannot be determined."

逻辑上的判决一定要注意优先级。

这个问题中优先级最高的是判断有环。一旦发现找不到度为0的结点，则立即return。

第二优先级是是否严格有序的判断。当每一步能且只能找到一个度为0的结点，则return。

第三优先级是无法确定。(当发现无法确定时，并不能立即return，因为还需要判断是否有环）

思维方式:问问自己，当条件x成立时，另外的条件y，z是否一定不成立。如果一定不成立，则可以断言return。否则必须继续判断下去。

提交记录：

1.样例未过！ 由于拓扑排序算法中，处理过程中入度减1的同时，并没有将对应的边删掉。

2.样例未过！ 由于在子函数judge中，对graph图进行了修改，导致后面处理失败。增加了memcpy解决。

3.segmentation fault! 当判断为1或者2的时候，不能立即break。因为后面还有输入，需要读入。修改为continue解决。

4.wrong answer！ 在judge函数中，当出现多个结点度为0的时候，还需要继续判冲突，而不能直接return.

5.AC！ 代码如下：