Partial subtree-matching algorithm

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借酒劲吻你
借酒劲吻你 2021-02-10 17:28

I searched the forums but I couldn\'t figure it out if the other similar questions are necessarily related to this one.

What I\'m trying to do is match a subtree to a t

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  • 2021-02-10 18:14

    It appears that what I was looking for was an algorithm to solve the "tree inclusion problem". I have found some useful documents:

    Fast Algorithms for Finding Nearest Common Ancestors

    The Tree Inclusion Problem: In Optimal Space and Faster

    Tree Isomorphism And Related Problems

    I translated one of the algorithms from the last paper into C# (returns the number of pairs in a largest matching between first-level subtrees of a and b).

    public static int Match(Node a, Node b, NodeSimilarityComparer comp) {
      if (!comp.Equals(a, b))
        return 0;
      int m = a.SubtreeCount;
      int n = b.SubtreeCount;
      var matrix = new int[m + 1, n + 1];
    
      for (int i = 0; i <= m; ++i)
        matrix[i, 0] = 0;
    
      for (int j = 0; j <= n; ++j)
        matrix[0, j] = 0;
    
      for (int i = 1; i <= m; ++i)
        for (int j = 1; j <= n; ++j) {
          var ai = a.GetSubtree(i - 1);
          var bj = b.GetSubtree(j - 1);
          var match = Match(ai, bj, comp);
          matrix[i, j] = Math.Max(Math.Max(matrix[i, j - 1], matrix[i - 1, j]), matrix[i - 1, j - 1] + match);
        }
      return matrix[m, n] + 1;
    }
    

    Hope this helps others too.

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  • 2021-02-10 18:24

    Here are a few references that may help you:

    Aho's Efficient Tree Pattern Matching: an Aid to Code Generation

    Stanford's Tree pattern matching programs

    From IMECS 2011: Tree Pattern Matching Algorithm Using a Succinct Data Structure

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