POJ1094 Sorting It All Out【拓扑排序】

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 
  
Sample Output
 
  
Sorted sequence determined after 4 relations: ABCD.
Inconsistency found after 2 relations.
Sorted sequence cannot be determined.
 
  
解题思路
 
  
题目大意：用小于号"<"来定义两元素之间的关系，并于一个没有重复元素的有序上升序列 从小到大地排列这些元素。比如说，序列A,B,C,D意味着A 
  
思路：
 
  
 
   
先判断是否有环（一旦发现找不到入度为0的结点，立即return）
 
   
再判断是否严格有序（当每一步能且只能找到一个度为0的结点，则输出）
 
   
最后才能判断是否能得出结果（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）。
 
   
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，则必须遍历完整个图才能知道是否有环。
 
  
 
  
#include
#include
#include
using namespace std;

int n, m;
char s[10];
int indegree[30];
int map[30][30];
vector ans;

int topologicalSort()
{
	int tmp[30];
	int flag = 1;
	ans.clear();
	for (int i = 1; i <= n; i++)
		tmp[i] = indegree[i];
	for (int i = 1; i <= n; i++)
	{
		int cnt, node;
 
		cnt = 0;
		for (int j = 1; j <= n; j++)
			if (tmp[j] == 0)
			{
				cnt++;
				node = j;
			}
		if (!cnt)
			return 0;
		if (cnt > 1) flag = -1;
		ans.push_back(node);
		tmp[node] = -1;
		for (int i = 1; i <= n; i++)
			if (map[node][i])
				tmp[i]--;
	}
	return flag;
}

int main()
{
	while (scanf("%d%d", &n, &m))
	{
		if (n == 0 && m == 0)
			break;
		memset(indegree, 0, sizeof(indegree));
		memset(map, 0, sizeof(map));
		int fin = 0;
		for (int i = 1; i <= m; i++) 
		{
			scanf("%s", s);
			if (fin)continue;
			int u = s[0] - 'A' + 1;
			int v = s[2] - 'A' + 1;
			map[u][v] = 1;
			indegree[v]++;
			int flag = topologicalSort();
			if (flag == 0)
			{
				printf("Inconsistency found after %d relations.\n",i);//注意标点符号
				fin = 1;
			}
			else if (flag == 1)
			{
				printf("Sorted sequence determined after %d relations: ",i);
				for(int j=0;j