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Data Structures | Binary Trees | Question 15
• Difficulty Level : Medium
• Last Updated : 14 Apr, 2020

In a complete k-ary tree, every internal node has exactly k children or no child. 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.
since its a complete k tree, so every internal node will have K child
Let us see following for example

```               o
/      |      \
o        o        o
/ | \    / | \    / | \
o  o  o  o  o  o  o  o  o

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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