Data Structures | Binary Trees | Question 8

The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:
(A) n/2
(B) (n-1)/3
(C) (n-1)/2
(D) (2n+1)/3


Answer: (D)

Explanation: Let L be the number of leaf nodes and I be the number of internal nodes, then following relation holds for above given tree (For details, please see question 3 of this post)

  L = (3-1)I + 1 = 2I + 1

Total number of nodes(n) is sum of leaf nodes and internal nodes

  n = L + I

After solving above two, we get L = (2n+1)/3

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