data structures - Finding the no of leaf nodes -

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an n-ary tree has n sub-nodes each node. if tree has m non-leaf nodes, how find no of leaf nodes?

first of if root level 0, k-th level of tree have n^k nodes. can start incrementing counter level level until m nodes. way find how many levels tree consisting of. , number of leaf nodes number of nodes on last level - n^lastlevel.

here example: n = 3, m = 4.

first level = 3^0 = 1 second level = 3^1 = 3 1 + 3 = 4

so found tree has 2 levels(counting 0). answer 3^2 = 9.

note: can find level number directly, noticing m sum of geometric progression: 1 + 3 + 9 + 27 ... = m

hope clear.


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