Question

Suppose I am given a undirected tree and I need to find a path(the only path) between two nodes.

What is the best algorithm to do it.I probably could use a Dijkstra’s algorithm but there a probably something better for trees.

C++ example would be helpful but not necessary

Thank you

Answer 1

Supposing you have

struct Node
{
    std::vector<Node *> children;
};

then what could be done is traversing the whole tree starting at root keeping the whole chain during the traversal. If you find e.g. node1 then you save the current chain, if you find node2 then you check for the intersection… in code (UNTESTED):

bool findPath(std::vector<Node *>& current_path, // back() is node being visited
              Node *n1, Node *n2,                // interesting nodes
              std::vector<Node *>& match,        // if not empty back() is n1/n2
              std::vector<Node *>& result)       // where to store the result
{
    if (current_path.back() == n1 || current_path.back() == n2)
    {
        // This is an interesting node...
        if (match.size())
        {
            // Now is easy: current_path/match are paths from root to n1/n2
            ...
            return true;
        }
        else
        {
            // This is the first interesting node found
            match = current_path;
        }
    }
    for (std::vector<Node *>::iterator i=current_path.back().children.begin(),
                                       e=current_path.back().children.end();
         i != e; ++i)
    {
        current_path.push_back(*i);
        if (findPath(current_path, n1, n2, match, result))
          return true;
        current_path.pop_back(); // *i
    }
    return false;
}