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poj 1094 Sorting It All Out

2024-07-06 10:59:12   226人阅读

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.

这是一道有点复杂的拓扑排序的题目
由于一开始只是考虑第一次有没有多个点入站，所以WA了几次，后来才知道是每次都应该考虑一下，于是才AC的
#include<map>
#include<set>
#include<stack>
#include<queue>
#include<cmath>
#include<vector>
#include<cstdio>
#include<string>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define  inf 0x0f0f0f0f

using namespace std;

int group[27][27],indegree[27],in[27],list[27],n,m;
vector<int>G[27];

int top_sort()
{
    int flag=0;
    for (int i=0;i<n;i++) in[i]=indegree[i];
    stack<int>S;
    for (int i=0;i<n;i++)
    {
        if (in[i]==0) S.push(i);
    }
    if (S.size()>1) flag=1;
    int cut=0;
    while(!S.empty())
    {
        if (S.size()>1) flag=1;
        int u=S.top();
        S.pop();
        list[cut++]=u;
        for (int i=0;i<G[u].size();i++)
        {
            int v=G[u][i];
            in[v]--;
            if (in[v]==0) S.push(v);
        }
    }
    if (cut<n) return 1;//maodun
    if (flag==1) return 2;//don‘t sure
    return 0;//ok
}

int main()
{
    int error,ok,x,y;
    char str[5];
    while(scanf("%d%d",&n,&m)!=EOF && n && m)
    {
        memset(group,0,sizeof(group));
        memset(indegree,0,sizeof(indegree));
        for (int i=0;i<=n;i++) G[i].clear();
        error=0; ok=0;
        for (int i=1;i<=m;i++)
        {
            scanf("%s",str);
            x=str[0]-‘A‘;
            y=str[2]-‘A‘;
            if (error==0 && ok==0)
            {
                if (group[y][x]==1)
                {
                    error=1;
                    printf("Inconsistency found after %d relations.\n",i);
                    continue;
                }
                if (group[y][x]==0)
                {
                    if (group[x][y]==0){
                        group[x][y]=1;
                        G[x].push_back(y);
                        indegree[y]++;
                    }
                    int temp=top_sort();
                    if (temp==1)
                    {
                        error=1;
                        printf("Inconsistency found after %d relations.\n",i);
                    }
                    if (temp==0)
                    {
                        ok=1;
                        printf("Sorted sequence determined after %d relations: ",i);
                        for (int j=0;j<n;j++) printf("%c",list[j]+‘A‘);
                        printf(".\n");
                    }
                    if (temp==2) continue;
                }
            }
        }
        if (error==0 && ok==0)
        printf("Sorted sequence cannot be determined.\n");
    }
    return 0;
}

作者 chensunrise


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