Poj 1094 Sorting It All Out

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 31190		Accepted: 10839

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
思路：简单的拓扑排序，但是要注意这里的排序是根据每一次的输入的，也就是每一个输入，如果能够得出成环 或者已经能够确定拓扑序列，那么接下来输入的东西应该忽略，直到最后输入结束还不能确定关系的话 答案就是 不能确定
AC代码如下：

#include <iostream>
#include <cstring>
#include <map>
using namespace std;
int n,m;
const int maxn=30;
int mm[maxn][maxn];
int dis[maxn];
int ans[maxn];
int tmp[maxn];

int toposort(){

    int flag=1;
    for(int i=1;i<=n;i++){
           // cout<<dis[i]<<" ";
        tmp[i]=dis[i];
    }
    //cout<<endl;

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

        int m=0,lol;
        for(int j=1;j<=n;j++){
            if(tmp[j]==0){
                lol=j,m++;
            }
        }
       // cout<<"m"<<m<<endl;
        if(m==0) return 0;
        if(m>1) flag=-1;
        ans[sign++]=lol;
        tmp[lol]--;
        for(int j=1;j<=n;j++)
            if(mm[lol][j])
                tmp[j]--;
    }
    return flag;

}

int main(){

    map<char,int> mp;
    for(int i=0;i<26;i++) mp[(char)(i+'A')]=i+1;
    while(cin>>n>>m &&n &&m){

        memset(mm,0,sizeof(mm));
        memset(dis,0,sizeof(dis));
        int sign=0;
        for(int i=1;i<=m;i++){
            char a,b,c;
            cin>>a>>b>>c;
            if(sign) continue;
            mm[mp[a]][mp[c]]=1;
            dis[mp[c]]++;
            int ttmp=toposort();
            if(ttmp==0){
                cout<<"Inconsistency found after "<<i<<" relations."<<endl;
                sign=1;
            }
            if(ttmp==1){
                cout<<"Sorted sequence determined after "<<i<<" relations: ";
                for(int i=0;i<n;i++)
                    cout<<(char)(ans[i]+'A'-1);
                    cout<<"."<<endl;
                    sign=1;
            }

        }

       if(!sign) cout<<"Sorted sequence cannot be determined."<<endl;
    }

    return 0;
}

总结：这道题目是很不错、很经典的拓扑排序的题目，增加对拓扑排序过程的了解，加油。