Unformatted text preview: (a) A simple path in T is one where all the nodes are distinct and its length is the number of edges on it. The height , h , of T is the length of a longest simple path from the root to a descendant external node (leaf). Let s be the length of a shortest simple path from the root to a descendant external node. Prove that h/s ≤ 2. (b) Let n ′ be the number of internal nodes in T that are at distance less than s from the root (i.e., at most s1 edges away from the root). Derive an expression for n ′ . (c) Use the results in parts (a) and (b) to obtain the desired upper bound of 2log( n + 1) for h . 5. (14 points) Ex. 13.24, p. 314. 6. (16 points) Problem 132, p. 332333....
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 Fall '08
 Sturtivant,C
 Algorithms, Data Structures, Scientific evidence, 14 points

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