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Distance measures between trees are useful for comparing trees in a systematic manner and several different distance measures have been proposed. The triplet and quartet distances, for rooted and unrooted trees, are defined as the number of subsets of three or four leaves, respectively, where the topologies of the induced sub-trees differ. These distances can trivially be computed by explicitly enumerating all sets of three or four leaves and testing if the topologies are different, but this leads to time complexities at least of the order n3 or n4 just for enumerating the sets. The different topologies can be counted implicitly, however, and this tqDist computes the triplet distance between rooted trees in O(n log n) time and the quartet distance between unrooted trees in O(dn log n) time, where d degree of the tree with the smallest degree.

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