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poj 1094

2024-07-13 10:04:57   225人阅读

Sorting It All Out
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 26911 Accepted: 9285

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

AC代码：

#include<iostream>
#include<vector>
#include<stack>
#include<algorithm>
#include<cstring>
#include<stdio.h>
using namespace std;
int n,m;
int in[30],tmp_in[30];
int f1,f2;
int str[30];
vector <int> G[30];
void top_sort(){                //拓扑排序
    f1=0;             //没有环
    f2=1;             //唯一排序
    for(int i=0;i<n;i++)
        tmp_in[i]=in[i];
    stack <int> s;
    while(!s.empty())
        s.pop();
    for(int i=0;i<n;i++)
        if(tmp_in[i]==0)
            s.push(i);
    int counter=0;
    while(!s.empty()){
        if(s.size()>=2){
            f2=0;
        }
        int tmp=s.top();
        s.pop();
        str[counter++]=tmp;
        for(int i=0;i<G[tmp].size();i++){
            tmp_in[G[tmp][i]]--;
            if(!tmp_in[G[tmp][i]])
                s.push(G[tmp][i]);
        }
    }
    if(counter<n)
        f1=1;
}
int main(){
    while(cin>>n>>m&&(n!=0||m!=0)){
        memset(in,0,sizeof(in));
        int i;
        for(i=0;i<n;i++)
            if(!G[i].empty())
                G[i].clear();

        for(i=0;i<m;i++){
            char ch[5]; cin>>ch;
            G[ch[0]-'A'].push_back(ch[2]-'A');
            in[ch[2]-'A']++;
            top_sort();
            if(f1){
                cout<<"Inconsistency found after "<<i+1<<" relations."<<endl;
                for(int j=i+1;j<m;j++)    //注意这里要输入剩下的信息才能退出
                    cin>>ch;
                break;
            }
            else if(f2){
                cout<<"Sorted sequence determined after "<<i+1<<" relations: ";
                for(int j=0;j<n;j++)
                    cout<<char (str[j]+'A');
                cout<<'.'<<endl;
                for(int j=i+1;j<m;j++)      //注意这里要输入剩下的信息才能退出
                    cin>>ch;
                break;
            }
        }
        if(i>=m)
            cout<<"Sorted sequence cannot be determined."<<endl;
    }
    return 0;
}



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