poj 1094 Sorting It All Out(拓扑排序)

题目链接：http://poj.org/problem?id=1094

思路分析：此题目涉及到图论拓扑排序的多个知识点：

1.判断给定的图是否可以拓扑排序；

2.判断给定的图能否产生一个唯一的拓扑排序，即全序；

 

代码如下：

#include <iostream>
#include <fstream>
#include <queue>
using namespace std;

const int MAX_N = 30;
int graph[MAX_N][MAX_N];
int set[MAX_N];
int topoSort[MAX_N];
int symbolNum;
int result;

void TopologicalSorting(int vertexNum, int j, int inDegree[])
{
    queue<int> Q;
    int count = 0;
    int flag = 0;

    for (int i = 0; i < vertexNum; ++ i)
    {
        if (set[i] == 1 && inDegree[i] == 0)
            Q.push(i);
    }
    
    if (flag == 0 && Q.size() >= 2)
        flag = 1;

    while (!Q.empty())
    {
        int num = 0;
        int vertex;
       
        vertex = Q.front(); Q.pop();
        topoSort[count] = vertex;
        for (int i = 0; i < vertexNum; ++i)
        {
            if (graph[vertex][i] != 0 && --inDegree[i] == 0)
            {
                Q.push(i);
                ++num;
            }
        }
        ++count;
        if (flag == 0 && num >= 2)
            flag = 1;
    }

    if (count != symbolNum)
        result = 1;
    else
    if (count == vertexNum && j == 0 && flag == 1)
        result = 2;
    else
    if (count == vertexNum && flag == 0)
        result = 3;
}

int main()
{
    int i, j, relations;
    char a, b, tmp;
    int flagOutput = 0;
    int inDegree[MAX_N];
    int inDegreeCopy[MAX_N];
    
    while ((cin >> i >> j) && (i != 0) && (j != 0) )
    {
        
        memset(graph, 0, sizeof(graph));
        memset(inDegree, 0, sizeof(inDegree));
        memset(set, 0, sizeof(set));
        memset(topoSort, 0, sizeof(topoSort));
        memset(inDegreeCopy, 0, sizeof(inDegreeCopy));
        symbolNum = result = relations = flagOutput = 0;

        if (j < i-1)
        {
            flagOutput = 1;
            result = 2;
            cout << "Sorted sequence cannot be determined.
";
        }

        while(j--)
        {
            cin >> a >> tmp >> b;

            ++relations;
            /* 统计出现的元素个数 */
            if (set[a-'A'] != 1)
                set[a-'A'] = 1, ++symbolNum;
            if (set[b-'A'] != 1)
                set[b-'A'] = 1, ++symbolNum;
            ++inDegree[b - 'A'];
            graph[a - 'A'][b - 'A'] = 1;

            if (flagOutput == 0)
            {
                for (int k = 0; k < i; ++k)
                    inDegreeCopy[k] = inDegree[k];
                TopologicalSorting(i, j, inDegreeCopy);
            }

            if (flagOutput == 0 && result == 1)
            {
                flagOutput = 1;
                cout << "Inconsistency found after " << relations << " relations.
";
            }
            
            if (flagOutput == 0 && symbolNum == i && result == 3)
            {
                char vertex;
                flagOutput = 1;
                cout << "Sorted sequence determined after "
                << relations << " relations: ";
                for (int j = 0; j < i; ++j)
                {
                    vertex = topoSort[j] + 'A';
                    cout << vertex;
                }
                cout << ".
";
            }

            if (flagOutput == 0 && result == 2)
            {
                flagOutput = 1;
                cout << "Sorted sequence cannot be determined.
";
            }
        }
        if (flagOutput == 0 && symbolNum < i)
        {
            flagOutput = 1;
            cout << "Sorted sequence cannot be determined.
";
        }
    }

    return 0;
}