EFFICIENT GENERATION OF K-ARY TREES IN NATURAL ORDER

A k-ary tree with n nodes can be encoded as a k-inorder-preorder sequence of length (k - 1) n by labelling the tree from 1 to (k - 1) n in generalised inorder and then reading off the labelled integers in generalised preorder. The natural ordering of a set of k-ary trees with n nodes is shown to be preserved in the lexicographic ordering of a set of k-inorder-preorder sequences of length (k - 1) n. An efficient algorithm for generating a set of k-inorder-preorder sequences in lexicographic order is presented. This set of k-inorder-preorder sequences can subsequently be converted to the corresponding set of k-ary trees in natural order.