Generating Regular k-ary Trees Efficiently

A recursive algorithm GenWordsR and a non-recursive algorithm GenWordsNR are presented in this paper to generate sequences for regular k-ary trees efficiently. They are compared with some of the previous recursive and non-recursive algorithms for this problem that were found in the literature. When the average number of recursive calls is used as a measure of the time complexity of recursive algorithms for generating k-ary trees, O(k) calls for a k-ary tree is the bestresult in the previous recursive algorithms, while O(1/k) calls for a k-ary tree is needed by GenWordsR. When the average number of comparisons is used as a measure of the time complexity of non-recursive algorithms for generating k-ary trees, GenWordsNR outperforms the previous non-recursive algorithms. As k increases, the number (and the average number) of comparisons performed by GenWordsNR tends to 66% that of the best previous non-recursive algorithms.