In a complete k-ary tree, every internal node has exactly k children. The number of leaves in such a tree with n internal nodes is:
(A)
nk
(B)
(n – 1) k+ 1
(C)
n( k – 1) + 1
(D)
n( k – 1)
Answer: (C)
Explanation:
For an k-ary tree where each node has k children or no children, following relation holds L = (k-1)*n + 1 Where L is the number of leaf nodes and n is the number of internal nodes. Let us see following for example
k = 3
Number of internal nodes n = 4
Number of leaf nodes = (k-1)*n + 1
= (3-1)*4 + 1
= 9
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