c++ - Floyd-Warshall 算法的路径重建不适用于某些值

Question

我像那里一样实现算法 http://en.algoritmy.net/article/45708/Floyd-Warshall-algorithm .

 void Graph::floydWarshal()
{
 for (int k = 0; k < weight_matrix.size(); k++)
 {
     for (int i = 0; i < weight_matrix.size(); i++)
     {
         for (int j = 0; j < weight_matrix.size(); j++)
         {
             if (weight_matrix[i][k] != infinity && weight_matrix[k][j] != infinity)
             {
                 int temp = weight_matrix[i][k] + weight_matrix[k][j];
                 if (weight_matrix[i][j] > temp)
                 {
                     weight_matrix[i][j] = temp;
                     predecessors[i][j] = predecessors[k][j];
                 }
             }
         }
     }
 }
}

 void Graph::getPath(int start, int finish, std::vector<int> &path)
 {
  if (start == finish)
  {
      path.push_back(start);
  }
  else if (predecessors[start][finish] == 0)
  {
      path.clear();
      return;
  }
  else
  {
      getPath(start, this->predecessors[start][finish], path);
      path.push_back(finish);
  }
 }

在构造函数中初始化前辈

for (int i = 0; i < weight_matrix.size(); i++)
  {
     for (int j = 0; j < weight_matrix[i].size(); j++)
    {
        if (weight_matrix[i][j] != 0 && weight_matrix[i][j] != infinity)
        {
            predecessors[i][j] = i;
        }
        else
        {
            predecessors[i][j] = -1;
        }
    }
 }  

这是长度矩阵

0   2 1  4   inf inf
2   0 7  3   inf inf
1   i 0  5   10  4
4   7 5  0   inf 5
inf 3 10 inf 0  4 
inf inf 4 5  4  0

它仅适用于某些值，例如从顶点 5 到顶点 0 构建的路径(返回 5 2 0)。但从 0 到 5 不构建(返回 5)。长度矩阵正确构建

Answer 1

我认为问题出在这一行(寻找一条不可能的路径):

else if (predecessors[start][finish] == 0)

你的节点是从零开始索引的，所以前导可以合法地等于 0。当路由涉及节点零时，您将错误地清除路径。

试试用这个代替:

else if (predecessors[start][finish] == -1)