Problem 1. Define the internal path length for a ree as ihe sum oi ihe depihs of all iniernal 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 iree with n ini,ernal nodes,is l's inernalxith lengih, eand is 's exienal pxih length, then E-I+2n for n 20