Poj/OpenJudge 1094 Sorting It All Out

1.链接地址：

http://poj.org/problem?id=1094

http://bailian.openjudge.cn/practice/1094

2.题目：

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 25547		Accepted: 8861

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

3.思路：

 

4.代码：

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdio>

 4 #include <cstdlib>

 5 

 6 using namespace std;

 7 

 8 int n,m;

 9 int map[30][30];

10 int reg[100];

11 int in[30],out[30];

12 char ans[30];

13 int stack[30];

14 void fun()

15 {

16      int i,j;

17      for(i='A',j=1;i<='Z';i++,j++)reg[i]=j;

18 }

19 void toposort(char *ans)

20 {

21     int i,top=0,u,s=0;

22     for(i=1;i<=n;i++)

23      if(in[i]==0)stack[top++]=i;

24     while(top!=0)

25     {

26        u=stack[--top];

27        ans[s++]=u+64;

28        for(i=1;i<=n;i++)

29        {

30          if(map[u][i])

31          {

32             in[i]--;

33             if(!in[i])stack[top++]=i;

34          }

35        }

36     }

37     ans[s]=0;

38 }

39 int main()

40 {

41     int i,j,x,y,k,flag1,flag2,flag;

42     fun();

43     char ch[5];

44     while(1)

45     {

46       flag1=flag2=0;

47       memset(map,0,sizeof(map));

48       scanf("%d%d",&n,&m);

49       if(n==0&&m==0)break;

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

51       {

52          flag=1;

53          scanf("%s",ch);

54          x=reg[ch[0]];

55          y=reg[ch[2]];

56          map[x][y]=1;

57          if(x==y)flag1=i;

58          memset(in,0,sizeof(in));

59          memset(out,0,sizeof(out));

60          if(!flag1&&!flag2)

61          for(j=1;j<=n;j++)

62           for(k=1;k<=n;k++)

63           {

64              if(j!=x&&k!=y)map[j][k]=map[j][k]||(map[j][x]&&map[y][k]);

65              if(j==x&&k!=y)map[j][k]=map[j][k]||map[y][k];

66              if(j!=x&&k==y)map[j][k]=map[j][k]||map[j][x];

67              if(map[j][k])

68              {

69                out[j]++;

70                in[k]++;

71              }

72           }

73          j=1;

74          if(!flag1)

75          for(j=1;j<=n;j++)

76          {

77            if(map[j][j])flag1=i;

78            if(in[j]+out[j]!=n-1)flag=0;

79          }

80          if(flag&&!flag2&&j>n){flag2=i;toposort(ans);}

81       }

82       if(flag2)

83       {

84          printf("Sorted sequence determined after %d relations: %s.\n",flag2,ans);

85          continue;

86       }

87       if(flag1)

88       {

89          printf("Inconsistency found after %d relations.\n",flag1);

90          continue;

91       }

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

93     }

94     return 0;

95 }