Multi-way trees, also known as rose trees.

Ternary trees on n nodes (synonym for regularNaryTrees 3)

regularNaryTrees d n returns the list of (rooted) trees on n nodes where each node has exactly d children. Note that the leaves do not count in n. Naive algorithm.

All trees on n nodes where the number of children of all nodes is in element of the given set. Example:

autoTabulate RowMajor (Right 5) $ map asciiTreeVertical 
                                $ map labelNChildrenTree_ 
                                $ semiRegularTrees [2,3] 2

[ length $ semiRegularTrees [2,3] n | n<-[0..] ] == [1,2,10,66,498,4066,34970,312066,2862562,26824386,...]

The latter sequence is A027307 in OEIS: https://oeis.org/A027307

Remark: clearly, we have

semiRegularTrees [d] n == regularNaryTrees d n

# = \frac {1} {(2n+1} \binom {3n} {n}

We have

length (regularNaryTrees d n) == countRegularNaryTrees d n == \frac {1} {(d-1)n+1} \binom {dn} {n} 

Computes the set of equivalence classes of rooted trees (in the sense that the leaves of a node are unordered) with n = length ks leaves where the set of heights of the leaves matches the given set of numbers. The height is defined as the number of edges from the leaf to the root.

TODO: better name?

Vertical ASCII drawing of a tree, without labels. Example:

autoTabulate RowMajor (Right 5) $ map asciiTreeVertical_ $ regularNaryTrees 2 4 

Nodes are denoted by @, leaves by *.

Prints all labels. Example:

asciiTreeVertical $ addUniqueLabelsTree_ $ (regularNaryTrees 3 9) !! 666

Nodes are denoted by (label), leaves by label.

Prints the labels for the leaves, but not for the nodes.

Generates graphviz .dot file from a tree. The first argument is the name of the graph.

Generates graphviz .dot file from a forest. The first argument tells whether to make the individual trees clustered subgraphs; the second is the name of the graph.

Left is leaf, Right is node

The leftmost spine (the second element of the pair is the leaf node)

The leftmost spine without the leaf node

The length (number of edges) on the left spine

leftSpineLength tree == length (leftSpine_ tree)

Adds unique labels to the nodes (including leaves) of a Tree.

Adds unique labels to the nodes (including leaves) of a Forest

Attaches the depth to each node. The depth of the root is 0.

Attaches the number of children to each node.