Totally Ordered Trees
Definition: A binary tree B is totally ordered iff:
- There is a total order relation < defined for the vertices of B;
and
- For any vertex v of B and any decendant u of
v.left_child, u <= v.
- 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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