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In: Advanced Math

20. The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems...


20. The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf.
(a) Find the best-case height of a binary tree with five nodes.
(b) Find the worst-case height of a binary tree with five nodes.
(c) Find the average-case height of a binary tree with five nodes. For this problem, you will have to list all possible binary trees with five nodes. Assume that each of these is equally likely to occur.
(d) Find the worst-case height of a binary tree with n nodes. (e) Approximate the best-case height of a binary tree with n nodes.

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Colby Messinger answered 1 year ago
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