POJ训练计划1094_Sorting It All Out(拓扑排序)

Sorting It All Out

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 26348 Accepted: 9120

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 6A<BA<CB<CC<DB<DA<B3 2A<BB<A26 1A<Z0 0

Sample Output

Sorted sequence determined after 4 relations: ABCD.Inconsistency found after 2 relations.Sorted sequence cannot be determined.

Source

解题报告

题意很难理解，我是看一本书才做这题的，表示没看英语。

在Discuss里看到这样解释的

Sorted sequence determined after 4 relations: ABCD.  输入前4个关系后，决定出了一个序列（关系总数可能大于4）Inconsistency found after 2 relations.输入前2个关系后，冲突出现了（环，关系总数可能大于2）Sorted sequence cannot be determined.所有关系输入后，序列和冲突均无出现

#include <iostream>#include <cstdio>#include <cstring>using namespace std;int n,m,head[30],cnt,d[30];char tops[1000];struct node{    int v,next;}edge[100100];void add(int u,int v){    edge[cnt].v=v;    edge[cnt].next=head[u];    head[u]=cnt++;}int topsort(int s){    int dd[30],i,j,u,c=0,f=1,k=0;    for(i=0;i<n;i++)        dd[i]=d[i];    while(s--)    {        c=0;        for(i=0;i<n;i++)        {            if(dd[i]==0)            {                c++;                u=i;            }        }        if(c>=1)        {            if(c>1)f=0;            for(i=head[u];i!=-1;i=edge[i].next)            {                dd[edge[i].v]--;            }            dd[u]--;            tops[k++]=u+'A';            tops[k]=0;        }        else return -1;    }    if(f)    return k;    else return 0;}int main(){    int i,j,k,hash[30],dt=0,c=0;    char str[4];    while(cin>>n>>m)    {        cnt=0;        c=0;        dt=0;        if(!n&&!m)        break;        memset(hash,0,sizeof(hash));        memset(edge,0,sizeof(edge));        memset(head,-1,sizeof(head));        memset(d,0,sizeof(d));        for(i=0;i<m;i++)        {            cin>>str;            int u=str[0]-'A';            int v=str[2]-'A';            add(u,v);            d[v]++;            if(!hash[u])            {                c++;                hash[u]=1;            }            if(!hash[v])            {                c++;                hash[v]=1;            }            if(dt==0)            {                int t=topsort(c);                if(t==-1)                {                    dt=-1;                    k=i+1;                }                else if(t==n)                {                    dt=1;                    k=i+1;                }            }        }        if(dt==1)        printf("Sorted sequence determined after %d relations: %s.\n",k,tops);        else if(dt==-1)        printf("Inconsistency found after %d relations.\n",k);        else cout<<"Sorted sequence cannot be determined."<<endl;    }    return 0;}