POJ 1094, Sorting It All Out

拓扑排序

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

*check loop first, then ambiguous

---

// POJ1094.cpp : Defines the entry point for the console application.
//

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

string TopSort(bool d[26][26], int in[26], int n)
{
    int indegree[26];
    copy (&in[0], &in[n], &indegree[0]);

    int cnt = n;
    string  str;
    bool ambiguous = false;
    while (cnt > 0)
    {
        int zeros = std::count(&indegree[0],&indegree[n], 0);
        if (zeros == 0)
        {
            return "1"; // loop
        }
        else if (zeros > 1)
        {
            ambiguous = true; //ambiguous
        }
        
        int pos = std::distance(&indegree[0],std::find(&indegree[0],&indegree[n], 0));

        for (int i = 0; i < n; ++i)
            if (d[pos][i] == true) --indegree[i];

        --cnt;
        indegree[pos] = -1;
        str += string(1,(char)(pos + 'A'));
    }

    if (ambiguous == true)return "2";
    return str; //OK
}

int main(int argc, char* argv[])
{
    int n,m;
    int in[26];
    bool d[26][26];
    string line;
    while(cin >> n >> m && n != 0 && m != 0)
    {
        memset(in, 0, sizeof(in));
        memset(d, 0, sizeof(d));
        string result = "";
        int step = 0;
        for (int i = 1; i <= m; ++i)
        {
            cin >> line;
            if (d[line[0] - 'A'][line[2] - 'A']==false)
            {
                d[line[0] - 'A'][line[2] - 'A'] = true;
                ++in[line[2] - 'A'];
                if (result == ""||result == "2")
                {
                    result = TopSort(d, in, n); 
                    step = i;
                }
            }
        }
        
        if (result == "1")
        {
            cout << "Inconsistency found after "<<step<<" relations.\n";
        }
        else if (result == "2")
        {
            cout << "Sorted sequence cannot be determined.\n";
        }
        else
        {
            cout << "Sorted sequence determined after "<<step<<" relations: "<<result<<".\n";
        }
    };
    return 0;
}