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In a complete k-ary, 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)
Correct answer is option 'C'. Can you explain this answer?
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In a complete k-ary, every internal node has exactly k children. The n...
In a complete-k-ary tree. If every internal node has exacity k children then (k - 1) key contains no leaves, if there are n internal nodes, then number of leaves is n(k- 1) + 1.
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In a complete k-ary, every internal node has exactly k children. The n...
In a complete k-ary tree, every internal node has exactly k children. Let's analyze the number of leaves in such a tree with n internal nodes.

To solve this problem, we can use the concept of the number of leaves in a tree and the relationship between internal nodes and leaves in a k-ary tree.

Number of Leaves in a Tree:
In a tree, the number of leaves (L) can be determined by subtracting the number of internal nodes (I) from the total number of nodes (N).

L = N - I

Relationship between Internal Nodes and Leaves in a k-ary Tree:
In a k-ary tree, each internal node has exactly k children. Therefore, the total number of children in a k-ary tree with n internal nodes is n * k.

The total number of nodes (N) in a k-ary tree can be calculated by adding the number of internal nodes (I) and the number of leaves (L).

N = I + L

Substituting the value of L from the first equation, we get:

N = I + (N - I)
N = N

This equation shows that the total number of nodes in a tree is equal to the total number of nodes in a k-ary tree.

Number of Leaves in a k-ary Tree:
Now, let's solve for the number of leaves in a k-ary tree with n internal nodes.

L = N - I
L = (I + L) - I
L = I + L - I
L = L

This equation shows that the number of leaves in a k-ary tree is equal to the number of leaves in any other tree.

Therefore, the number of leaves in a complete k-ary tree with n internal nodes is equal to (n - 1) * k + 1.

Answer:
The correct answer is option 'C': n(k - 1) + 1.
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In a complete k-ary, every internal node has exactly k children. The number of leaves in such a tree with n internal nodes isa)nkb)(n - 1) k + 1c)n(k - 1) + 1d)n(k - 1)Correct answer is option 'C'. Can you explain this answer?
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