Sorting It All Out


Time Limit: 1000MS

 

Memory Limit: 10000K

Total Submissions: 33756

 

Accepted: 11806


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：输入n和m，n是有n个点，m是有m条边，然后输入m行，如果这n个顶点可以构成有向无环路（拓扑），则输出第一种形式，如果有环就输出第二种形式，否则输出第三种形式。

题解：判断是否是拓扑排序，而且要每输入一行就要去进行判断。


#include <iostream>
#include <string.h>
#include <stdio.h>
using namespace std;

int n, m;
int flag;
int Map[50][50];//用来储存链接矩阵
int in[50];//记录入度
int rein[50];//临时记录入度
char a[50];//记录排序
int k;

void topu()
{
    int i, j, pos;
    for(i = 1; i <= n; i++)//临时入度
    {
        rein[i] = in[i];
    }

    for(i = 1; i <= n; i++)
    {
        int s = 0;
        for(j = 1; j <= n; j++)//寻找入度为0的顶点并记录加和
        {
            if(rein[j] == 0)
            {
                s++;
                pos = j;
            }
        }

        if(s == 0)//说明没有找到入度为0的顶点，表示有环
        {
            flag = 1;
            return ;
        }
        else if(s > 1)//第三种情况，例如多起点或无法比较两点的大小
        {
            flag = -1;
        }

        a[k++] = pos + 'A' - 1;//储存
        a[k] = '\0';

        rein[pos] = -1;

        for(j = 1; j <= n; j++)//将与pos这个位置相连的所有的点的入度减一
        {
            if(Map[pos][j])
            {
                rein[j]--;
            }
        }

    }
}

int main()
{
    char str[4], i;
    while(cin>>n>>m && n && m)
    {
        memset(Map, 0, sizeof(Map));
        memset(in, 0, sizeof(in));
        memset(a, 0, sizeof(a));

        int sign = 0;

        for(i = 1; i <= m; i++)
        {
            k = 0;
            flag = 0;

            cin>>str;
            Map[str[0] - 'A' + 1][str[2] - 'A' + 1] = 1;
            in[str[2] - 'A' + 1] ++;
            if(sign == 1)//已经满足了其中一种情况，不在进行操作
                continue;
            topu();

            if(flag == 1)
            {
                printf("Inconsistency found after %d relations.\n",i);
                sign=1;
            }
            if(flag == 0)
            {
                printf("Sorted sequence determined after %d relations: %s.\n",i,a);
                sign=1;
            }
        }
        if(flag == -1)
        {
            printf("Sorted sequence cannot be determined.\n");
        }
    }
    return 0;
}