Question

In a 3-array tree if internal nodes have exactly 3 children,the number of leaf nodes will be  __ ?

Does it vary for binary tree?

What do you mean by internal nodes? Non root node and leaf node?

Comments

Is root node counted as internal node?

Btw what software did you use to draw the graph? Paint?

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@sripo root node is also an internal node unless it is the only node in the tree

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Yes i used paint.

Answer 1

Formula for Leaf Nodes= I(N-1)+1

I---internal nodes

N---n array tree i.e 3

Hence, Leaf Nodes=        3(3-1)+1

                                  =        3×2+1 = 7 nodes

 

Comments

how did u take 3internal nodes?

Answer 2

1. Internal node means non leaf node.

we have for n ary tree

no of leaf node=X(n-1)  +1  [By hand shake degree theorem]

where X =no of internal node 

So for your question n=3 =>no of leaf node=2*X + 1

it will be [X(2-1) +1 =X+1] for binary tree n=2.