Question: Define the internal path length, I(T), of a tree T to be the sum of the depths of all the internal positions in T. Likewise,

Define the internal path length, I(T), of a tree T to be the sum of the depths of all the internal positions in T. Likewise, define the external path length, E(T), of a tree T to be the sum of the depths of all the external positions in T. Show that if T is a proper binary tree with n positions, then E(T) = I(T)+n−1.

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