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What is the minimum number of nodes a full d-ary tree must have to determine its height?

a) d
b) 2d
c) d+1
d) 2d+1

User Evaldas B
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1 Answer

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Final answer:

The minimum number of nodes required to determine the height of a full d-ary tree is d+1.

Step-by-step explanation:

A full d-ary tree is a tree in which each node has up to d children. To determine the height of a full d-ary tree, we consider the number of nodes it must have. The height of a full d-ary tree can be found by following this formula: height = log base d (N+1), where N is the number of nodes.

The minimum number of nodes required to determine the height of a full d-ary tree is d+1. This is because for a height of h, there must be at least (d+1)^h nodes in the tree. Any number of nodes less than (d+1)^h would result in a height less than h.

Therefore, the correct answer is c) d+1.

User Dan Billings
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