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# hw04 - HW04 CSE 331 Section 1 Due Friday 8 Feb noon 1 Feb...

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HW04 CSE 331 Section 1 Due Friday 8 Feb noon 1 Feb version Remember to appropriately justify answers/reasoning. Also remember that this is individual work. 1) Problem 4.5 of the text: use mathematical induction to do the proof. Show that the maximum number of nodes in a binary tree of height h is 1 2 ) 1 ( - + h . 2) Relate this to problem 4.5 of the text. a) Compute the average depth of a node in a perfect binary tree of height h and n = 1 2 ) 1 ( - + h nodes (give a formula). (Give an exact answer for h = 4 .) b) What is the average case effort for a successful search in this tree? c) What is the worst case effort of a failed search in the tree? d) What is the average case effort of a failed search in this tree? Be more precise than Big Oh: Derive formulas in terms of h and n that are simple and also accurate to within 0.5 of the exact answer. In doing this, assume that the cost of finding the root key is 1, the cost of finding a key in the root’s children is 2, and the cost of finding a leaf node is h+1. Also, the cost of not finding a key in a leaf node is h+1.

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hw04 - HW04 CSE 331 Section 1 Due Friday 8 Feb noon 1 Feb...

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