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Totally Ordered Trees

Definition: A binary tree B is totally ordered iff:

  1. There is a total order relation < defined for the vertices of B; and
  2. For any vertex v of B and any decendant u of v.left_child, u <= v.
  3. For any vertex v of B and any decendant w of v.right_child, v <= w.

Consequences:

  • The smallest element in a totally ordered tree (TOT) is the "left-most" node
  • The largest element in a TOT is the "right-most" node
  • Inorder traversal of a TOT encounters nodes in increasing order

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