topSort

Sorting It All Out（poj1094）

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 30187		Accepted: 10442

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.

题意：

三种情况：  1. 在第x个关系中可以唯一的确定排序，并输出。  

                2. 在第x个关系中发现了有回环（Inconsisitency矛盾）  

                3.全部关系都没有发现上面两种情况，输出第3种.  

要求对于给定的m个关系，一个个的读进去，每读进去一次就要进行一次拓扑排序，如果发现情况1和情况2，那么就不用再考虑后面的那些关系了，但是还要继续读完后面的关系（但不处理）。如果读完了所有关系，还没有出现情况1和情况2，那么就输出情况3.

拓扑排序实现方法一（for循环）：

#include <iostream>
#include <cstring>
#include <string>
#include <fstream>
using namespace std;

int grap[27][27];
int indeg[26],temp[26];
int n,m;
char seq[26];

int topSort()
{
    int flag = 1;
    memcpy(temp,indeg,sizeof(indeg));
    memset(seq, '',sizeof(seq));
    for(int i = 0; i < n; i++)
    {
        int times = 0,loc;
        for(int j = 0; j < n; j++)
        {
            if(temp[j] == 0)     //处理重边的情况，建图时要格外注意！
            {
                times++;
                loc = j;
            }
        }
        if(times > 1) flag = -1;
        if(times == 0) return 0;
        temp[loc]--;
        seq[i] = 'A'+ loc;
        for(int k = 0; k < n; k++)
        {
            if(grap[loc][k])
            {
                temp[k]--;
            }
        }
    }
    return flag;
}

int main()
{
    while(cin >> n >> m)
    {
        if(n == 0 && m == 0)
            break;
            
        memset(grap,0,sizeof(grap));
        memset(indeg,0,sizeof(indeg));
        bool ok = false;

        for(int i = 0; i < m; i++)
        {
            string ss;
            cin >> ss;
            if(ok) continue;
            int row,col;
            row = ss[0] - 65;
            col = ss[2] - 65;
            if(grap[row][col] == 0)
            {
                grap[row][col] = 1;
                indeg[col]++;
            }

            int flag = topSort();
            if(flag==1)
            {
                ok = true;
                cout << "Sorted sequence determined after " << i+1 << " relations: " << seq << "."<<endl;
            }
            else if(flag==0)
            {
                ok = true;
                cout << "Inconsistency found after " << i+1 << " relations." << endl;
            }
        }
        
        if(!ok)
        {
            cout << "Sorted sequence cannot be determined." << endl;
        }
    }

    return 0;
}

拓扑排序实现方法二（借助队列或栈）：

#include <iostream>
#include <cstring>
#include <string>
#include <fstream>
#include <queue>
#include <stack>
using namespace std;

int grap[27][27];
int indeg[26];
int n,m;
char seq[26];

//借助队列实现拓扑排序，改成栈也一样
int topSort()
{
    int in[26];
    memcpy(in,indeg,sizeof(indeg));
    memset(seq, '',sizeof(seq));
    queue<int> s;

    for(int i=0; i<n; i++)
    {
        if(in[i] == 0)
            s.push(i);
    }

    int flag=1;
    int t,j=0;
    while(!s.empty())
    {
        if(s.size()>1)
            flag=-1;      //有多种排序方式，不能唯一确定
        t=s.front();
        s.pop();
        seq[j++] = t + 65;
        for(int i=0; i<n; i++)
        {
            if(grap[t][i])
            {
                if(--in[i]==0)
                    s.push(i);
            }
        }

    }

    if(j != n) return 0;  //存在环
    else return flag;
}

int main()
{
    while(cin >> n >> m)
    {
        if(n == 0 && m == 0)
            break;

        memset(grap,0,sizeof(grap));
        memset(indeg,0,sizeof(indeg));
        bool ok = false;

        for(int i = 0; i < m; i++)
        {
            string ss;
            cin >> ss;
            if(ok) continue;
            int row,col;
            row = ss[0] - 65;
            col = ss[2] - 65;
            if(grap[row][col] == 0)
            {
                grap[row][col] = 1;
                indeg[col]++;
            }

            int flag = topSort();
            if(flag==1)
            {
                ok = true;
                cout << "Sorted sequence determined after " << i+1 << " relations: " << seq << "."<<endl;
            }
            else if(flag==0)
            {
                ok = true;
                cout << "Inconsistency found after " << i+1 << " relations." << endl;
            }
        }

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

    return 0;
}