POJ 1094 拓扑排序

最新推荐文章于 2020-03-04 17:49:32 发布

tanmlh

最新推荐文章于 2020-03-04 17:49:32 发布

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本文介绍了一个关于拓扑排序的问题，通过一系列输入确定元素间的排序关系。讨论了如何通过每组输入快速判断是否能确定最终排序或是存在矛盾的情况，并分享了作者在实现过程中的思考与经验。

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Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 27010		Accepted: 9336

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

拓扑排序的一个水题，虽说是水题，但是写起来要保证逻辑清晰倒是挺难，曾经写过两遍这个题，但是第二遍时还是调试了半天。

分析其原因，一个是代码能力还不强，总是有很多手误，再一个是做题时盲目追求速度，导致逻辑不够清晰。

思路（可能很啰嗦，是为了理清我的逻辑）：

首先，题目要求如果能在前几个输入结束后就确定结果（即发现矛盾或者得到正确唯一的顺序），就不在进行后面的处理（只要读入即可），所以必须要每读入一次数据就要处理一次。

其次，进行操作的过程中，可能需要对每个元素的入度进行处理，所以就需要有一个拷贝数组储存入度值，保证下一次读入数据时入度值没有因为操作而改变。

再次，需要一个标记数组记录每个元素是否被访问，如果被访问，获取下一个入度为0的节点时就不能考虑这个节点。

如果处理过程中发现环，就可以做出标记，后面就只读入数据不进行处理，同时应该记录当前一共读入了几个数据，以便输出。

同样，如果处理过程中发现每次去入度为0的点的这个操作都只有唯一的取法，并成功处理n个点退出，做出标记，记录当前读入了几个数据，同时还要记录方案。

大概就是这么多，希望能吸取教训，做题时不贪快，保证逻辑的清晰。