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Isn't it possible to classify the tree structure into two types, one in which all the nodes have values and one in which only the leaves have values?
To be more precise, the handling of knots and leaves is different from the same.
The former is like a heap and the latter is like a directory.
In general, isn't there something like naming or calling each one?
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Answer # 1
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As far as I know, I don't think there is a fixed name that distinguishes the two.
By the way, "value" here is generally called "label".
If there is a need to distinguish between the two, I would say something like "tree with labeled clause" and "tree with unlabeled clause".
Although I answered this time, I think you should refrain from such questions because it is not directly related to programming.
If questions regarding the tree structure are allowed at this site because "something is handled by programming", especially in image processing and sound processing, it uses a lot of mathematical knowledge such as matrix and Fourier transform. Because math questions are OK.