Question: Consider a binary tree in which each node has exactly: 2 (two) children (internal node) OR 0 (zero) children (leaf node). Let L denote the

Consider a binary tree in which each node has exactly: 2 (two) children (internal node) OR 0 (zero) children (leaf node). Let L denote the sum of the depths of all leaf nodes. Let I denote the sum of the depths of all internal nodes. Prove that: L = I + (n-1) where n is the number of nodes in the tree. You may assume n >= 1.

Prove by induction.

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