What is the maximum possible height of a decision tree?

Question

BlackTom AI · Accepted Answer

The provided data for this question is incomplete: there are no answer options listed to evaluate, only an answer field stating 'The number of attributes'.

In a typical discussion of decision trees, the maximum height (in the worst case, with no pruning and using one attribute per level) is bounded by the number of attributes available for splitting, since each level can potentially reveal information from a new attribute choice. Therefore, if we consider the standard setup where each split tests a single attribute and there are n attributes in total, the height can grow up to n in the worst case.

However, without the actual set of answer choices to compare against, it is not possible to definitively determine which option is correct for this specific question instance. If the answer choices included 'The number of attributes' as the correct option, that would be consistent with the common theoretical upper bound. If alternatives suggested a different bound or involved different assumptions (such as pruning, continuous attributes, or multiway splits), those could change the interpretation. In short, the missing options prevent a complete option-by-option analysis, but the rationale for the bound aligns with the idea that the maximum height is tied to the number of attributes available for splitting.

COMP90049_2025_SM1 Lecture 5 Decision Tree Practice Quiz

What is the maximum possible height of a decision tree?

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