compile = truefalse

True means compile the iterator. The default is true.

The OrientedForests command returns an iterator that generates all oriented forests on n-nodes, in decreasing lexicographic order of their level codes.

The iterator output Array contains the parent pointers, in preorder, of the nodes in the forest. If the pointer is zero, the node is the root of a tree. In the following two-tree forest, the representation is [0,1,2,0,4,5,5,4]. For example, the entry at index 8 is 4, which indicates the parent of node 8 is node 4.

$\mathrm{with}\left(\mathrm{Iterator}\right)\:$

$M≔\mathrm{OrientedForests}\left(4\right)\:$

$\mathrm{Print}\left(M\,'\mathrm{showrank}'\right)\:$

1: 0 1 2 3
2: 0 1 2 2
3: 0 1 2 1
4: 0 1 2 0
5: 0 1 1 1
6: 0 1 1 0
7: 0 1 0 3
8: 0 1 0 0
9: 0 0 0 0

$\mathrm{Number}\left(M\right)$

$9$

Knuth, Donald Ervin. The Art of Computer Programming, volume 1, 3rd ed. fundamental algorithms, sec. 2.3, Trees, pp. 308-309.

Knuth, Donald Ervin. The Art of Computer Programming, volume 1, 3rd ed. fundamental algorithms, sec. 2.3.4.4, Enumeration of Trees, pp. 386-394.

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 4; generating all trees, sec. 7.2.1.6, generating all trees, algorithm O, oriented forests, p. 24.

The Iterator[OrientedForests] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.

The Iterator[OrientedForests] command was updated in Maple 2022.

The n parameter was updated in Maple 2022.