POJ1094 Sorting It All Out —

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 35468		Accepted: 12458

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.

题解：

1.由于要输出当关系确定时是第几步，所以每一步都需要进行拓扑排序。（假如读完所有数据再进行拓扑排序，则无法确定关系确定时是第几步）。

2.在进行拓扑排序时（flag为状态类型，1表示冲突； 2表示不能确定； 3表示关系确定。 flag初始化为3）：

(1) 如果入度为0的点的个数为0，则成环，可直接得出结果：冲突。直接return 1。

(2) 如果入度为0的点的个数为1，继续。

(3) 如果入度为0的点的个数大于1，则表明最小的那个不能确定。这时把flag改为2，然后继续。（为什么还要继续，不是可以直接return 2，表明关系还不能确定了吗？虽然如此，但是继续拓扑排序下去，可能会发现环，即冲突。）

代码如下：

#include<stdio.h>//poj 1094

#include<string.h>

#include<stdlib.h>

int deg[27], sub_deg[27],edge[27][27],n,m;

char a,b,c,ans[27];

int TopoSort()

{

    int flag = 3;

    memcpy(sub_deg,deg,sizeof(deg));

    for(int i = 0; i<n; i++)

    {

        int k, cnt = 0;

        for(int j = 0; j<n; j++)

            if(sub_deg[j]==0) cnt++, k = j;

        if(cnt==0) return 1;    //成环

        if(cnt>1) flag = 2;     //最小的不能确定。但不能直接退出，因为接下来可能会出现环。

        sub_deg[k] = -1;

        ans[i] = k+65;

        for(int j = 0; j<n; j++)

            if(edge[k][j]) sub_deg[j]--;

    }

    return flag;

}

int main()

{

    int flag,step;

    while(scanf("%d%d",&n,&m) && (n||m))

    {

        int finished = 0, flag, step;

        memset(deg,0,sizeof(deg));

        memset(edge,0,sizeof(edge));

        for(int i = 1; i<=m; i++)

        {

            getchar();

            scanf("%c%c%c",&a,&c,&b);

            if(finished) continue;

            deg[b-65]++;

            edge[a-65][b-65] = 1;

            ans[n] = 0;

            flag = TopoSort();

            if(flag==1 || flag==3) { step = i; finished = 1; }

        }

        if(flag==1)

            printf("Inconsistency found after %d relations.\n",step);

        else if(flag==2)

            printf("Sorted sequence cannot be determined.\n");

        else

            printf("Sorted sequence determined after %d relations: %s.\n",step,ans);

    }

    return 0;

}

巴特西

POJ1094 Sorting It All Out —— 拓扑排序

最新文章

热门文章