Efficient enumeration of ordered trees with k leaves

Authors:
Katsuhisa Yamanaka;Yota Otachi;Shin-Ichi Nakano
Affiliations:
Graduate School of Information Systems, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan;Graduate School of Information Sciences, Tohoku University, 6-3 Aramaki Aza Aoba, Aoba, Sendai, Miyagi 980-8579, Japan;Department of Computer Science, Gunma University, 1-5-1 Tenjincho, Kiryu, Gunma 376-8515, Japan
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

This paper presents a simple algorithm to generate all ordered trees with exactly n vertices including exactly k leaves. The best known algorithm generates such trees in O(n-k) time per tree, whereas our algorithm generates such trees in O(1) time per tree in the worst case.