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1. The path length of a tree T is the sum of the depths of all positions in T. Describe a…

1. The path length of a tree T is the sum of the depths of all positions in T. Describe a…

1. The path length of a tree T is the sum of the depths of all positions in T. Describe a linear-time method for computing the path length of a tree T.2. 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.