Monday, April 23, 2018

A full N-ary tree has M non-leaf nodes, how many leaf nodes does it have

M + (N ^ (n-1)) = (1 - (N ^ n)) / (1 - N)
Here (N ^ (n-1)) is the number of leaf-nodes.
Solving for this leads to the answer
Leaf nodes = M * (N - 1) + 1

Suppose you have a 3-ary tree



So, here M=4 and N=3.

So using the formula above, Leaf nodes = M * (N - 1) + 1 = 4 * (3 - 1) + 1 = 9 

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