Define the internal path length for a tree as the sum of the depths of all internal nodes, while the external path length is the sum of the depths of all leaf nodes in the tree. Prove by induction...

Define the internal path length for a tree as the sum of the depths of all internal nodes, while the external path length is the sum of the depths of all leaf nodes in the tree. Prove by induction that if tree T is a full binary tree with n internal nodes, I is T’s internal path length, and E is T’s external path length, then E = I + 2n for n ≥ 0.