Give an O(n)-time algorithm for computing the depths of all positions of a tree T, where n is the number of nodes of T.
2. The balance factor of an internal position p of a proper binary tree is the difference between the heights of the right and left subtrees of p. Show how to specialize the Euler tour traversal of Section 8.4.6 to print the balance factors of all the internal nodes of a proper binary tree.
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