Provide justification that a strictly binary tree regular bi

Provide justification that a strictly binary tree (regular binary tree) with n leaves contains 2n-1 nodes.

Solution

Any complete binary tree can be seen as a structure of single elimination tournment with n teams, corresponding to leaves. Each non leaf(internal node) is a game in which one goes home and the winner goes to nest round(upper level). There will be on champion in the highest level(root). So their must be n-1 non leaf nodes since every other team losses exactly once.

Hence n+n-1=2n-1