Beautiful Binary Trees

Computer Science Level 1

The Binary Tree The Binary Tree

A botanist noticed that a certain species of tree satisfies the following properties:

  • From each end point of the branches (except for the last branch) two new branches arise.
  • There is a leaf at the end of each final branch.
  • Every leaf is an equal number of branches away from the trunk.
  • The Tree has an unique trunk and all branches are of equal length.

He has identified a few trees in a forest: They have 14, 15, 16 and 17 leaves respectively.

Which of these trees could possibly be the one that he's looking for?

The one with 16 leaves The one with 17 leaves The one with 14 leaves The one with 15 leaves

Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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1 solution

The given type of organisation is termed dichotomous branching, where every branch gives off two subbranches. It is seen in coralloid roots of gymnosperms and in the phaeophycaea member Dictyota. Clearly leaves represent the ultimate level of branching and given that every leaf is equidistant from a unique trunk and every branch branches dichotomously, the number of leaves will be a value belonging to the 2^n series, where n is the number of branches!😇

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Are there any actual organisms which show this sort of branchings?

Agnishom Chattopadhyay - 4 years, 2 months ago

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Yes Dictyota, it is a brown algae. Also coralloid roots of cycas, which is a symbiotic association of cyanobacteria like anabaena and nostoc and the plant itself. Also the marchantia (a liverwort i.e. hepaticopsida member) thallus, can sometimes show dichotomy. A type of inflorescence called dichasium almost approaches this pattern only you have flowers in the terminal position instead of leaves. Riccia, another liverwort, is also a beautiful example. In fact the picture you used in the question is of Palm trees, which also shows such pattern. :-) Nature, as it turns out, is a pattern lover.

Arkadeep Mukhopadhyay - 4 years, 2 months ago

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Wow, I am going to have to google these.

Agnishom Chattopadhyay - 4 years, 2 months ago

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