poj1094

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 32966		Accepted: 11458

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.

题目大意：给你n个大写字母，和m组字母相互之间的大小关系，让你判断在哪一次能够将所有字母
排好序，又或者在哪一次给出的关系与前面矛盾，即构成环了，否则就不能判断

思路：利用拓扑排序，如果能够排序，那么入度为0的点只可能有一个，否则就不知道选择哪一个在前
如果所有的点不能全部进行出栈排序，说明一定形成环了
注意：在拓扑排序时一定要注意判断顺序，就因为这个WA了好多次

代码如下：

 1 #include <iostream>
 2 #include<cstdio>
 3 #include<stack>
 4 #include<cstring>
 5 using namespace std;
 6 int n,m;
 7 char str[4];
 8 int degree[27],A[27][27];//入度，以及邻接矩阵
 9 char letter[27];//存储排序好的字母
10 int topSort()
11 {
12     //如果能够排序，那么肯定入度为0的点只有一个,有多个则不能确定选择哪一个
13     stack<int> st;
14     int temp[27],flag=0;
15     memcpy(temp,degree,sizeof(degree));
16     for(int i=1;i<=n;i++)
17         if(temp[i]==0)
18             st.push(i);//找到入度为0的点
19     int index=0,cur;
20     while(!st.empty())
21     {
22         if(st.size()>1)//入度为0点有多个，不能唯一排序
23             flag=1;
24         cur = st.top();
25         st.pop();
26         letter[index++]=cur+'A'-1;
27         for(int i=1;i<=n;i++)
28             if(A[cur][i]==1)
29             {
30                 temp[i]--;
31                 if(temp[i]==0)
32                     st.push(i);//找到入度为0的点
33             }
34     }
35     if(index<n)
36         return 0;//有环
37     if(flag)
38         return -1;
39     return 1;//排序成功
40 
41 }
42 int main()
43 {
44     freopen("in1.txt","r",stdin);
45     while(scanf("%d%d",&n,&m)!=EOF&&n)
46     {
47         bool sucess=false;
48         int flag=-1,time=0;
49         memset(degree,0,sizeof(degree));
50         memset(A,0,sizeof(A));
51         memset(letter,0,sizeof(letter));
52         if(m==0&&n==1)
53         {
54             printf("Sorted sequence determined after 0 relations: A.\n");
55             continue;
56         }
57         for(int i=1;i<=m;i++)
58         {
59             scanf("%s",str);
60             if(sucess)
61                 continue;
62             int x = str[0]-'A'+1;
63             int y = str[2]-'A'+1;
64             degree[y]++;//入度加1
65             A[x][y]=1;//表示x邻接y
66             int flag1 = topSort();
67             if(flag1==0)
68             {
69                 flag=0;time=i;
70                 sucess=true;
71             }
72             if(flag1==1)
73             {
74                 flag=1;time=i;
75                 sucess=true;
76             }
77 
78         }
79         if(flag==-1)
80             printf("Sorted sequence cannot be determined.\n");
81         else if(flag==0)
82             printf("Inconsistency found after %d relations.\n",time);
83         else
84         {
85              printf("Sorted sequence determined after %d relations: ",time);
86              for(int j=0;j<n;j++)
87                 printf("%c",letter[j]);
88              printf(".\n");
89         }
90     }
91     return 0;
92 }

posted on 2016-08-08 20:29 wastonl 阅读(159) 评论(0) 编辑收藏举报