Data Structures | Binary Trees | Question 10

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?
(A) 6
(B) 3
(C) 4
(D) 5


Answer: (D)

Explanation: For an n-ary tree where each node has n children or no children, following relation holds

    L = (n-1)*I + 1

Where L is the number of leaf nodes and I is the number of internal nodes.

Let us find out the value of n for the given data.

  L = 41 , I = 10
  41 = 10*(n-1) + 1
  (n-1) = 4
  n = 5


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