All Possible Full Binary Trees

Given an integer \(n\), generate all the unique full binary trees that can be formed using exactly \(n\) nodes. A full binary tree is a binary tree in which every node has either 0 or 2 children. In mathematical terms, a full binary tree exists only when \(n\) is odd, i.e. \(n = 2k+1\) for some integer \(k\). Each tree should be represented by a list showing its level-order traversal. In this representation, every missing (null) child is shown as None. If no full binary tree can be constructed, output an empty list.

inputFormat

The input consists of a single integer \(n\) (for example, 0 \(\leq n \leq\) 19) provided via standard input.

outputFormat

Output the list of all possible full binary trees in Python list format. Each tree is represented as a list showing its level-order traversal, with missing nodes shown as None. The output should be printed on standard output.

1

[[0]]