A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?radio_button_unchecked6radio_button_unchecked3radio_button_unchecked4radio_button_unchecked5
Question
A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?radio_button_unchecked6radio_button_unchecked3radio_button_unchecked4radio_button_unchecked5
Solution
In a complete n-ary tree, the relationship between the number of internal nodes (I) and the number of leaves (L) is given by the formula:
I = (L-1)/ (n-1)
Given that L = 41 and I = 10, we can substitute these values into the formula and solve for n:
10 = (41-1) / (n-1)
This simplifies to:
10 = 40 / (n-1)
Multiplying both sides by (n-1) gives:
10(n-1) = 40
Solving for n gives:
n = 40/10 + 1 = 4 + 1 = 5
So, the value of n is 5.
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