TAOCP 7.2.1.6 Exercise 68
The Christmas tree pattern of order $n$ corresponds to the planar representation of a full binary tree (or equivalently a properly nested parenthesis structure) with $n$ internal nodes, drawn in its s...
Section 7.2.1.6: Generating All Trees
Exercise 68. [10] [10] What is the Christmas tree pattern of order 0?
Verified: yes
Solve time: 1m36s
The Christmas tree pattern of order $n$ corresponds to the planar representation of a full binary tree (or equivalently a properly nested parenthesis structure) with $n$ internal nodes, drawn in its standard triangular “stacked” layout.
For order $0$, there are no internal nodes and no edges. The corresponding structure in Algorithm B is the initial degenerate binary tree consisting of a single external node $\square$, since there is no internal node to expand and no left or right link to assign. In the parenthesis model this corresponds to the empty string, and in the forest model to the empty forest.
Thus the Christmas tree pattern of order $0$ is a single isolated node (no branches), i.e., the trivial tree. This completes the determination. ∎