3. A trinary tree is a tree in which each node has between 0 and 3...
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3. A trinary tree is a tree in which each node has between 0 and 3 children (call these the left child, middle child, and right child). Define T(h) for h≥ −1 to be the number of distinct trinary tree structures with height h. We don't care about the contents, just the overall structure. What is T(-1) and why? (b) What is T(0) and why? What is T(1) and why? (d) Prove that for h≥ 1 we have: [5 pts] [5 pts] [5 pts] [20 pts] T(h)=3T(h–1)(T(−1)+T(0)+...+T(h–2))2+3T(h−1)2(T(−1)+T(0)+...+T(h−2))+T(h−1)3 (e) Use this to calculate T(2) for n = 2. [5 pts] 3. A trinary tree is a tree in which each node has between 0 and 3 children (call these the left child, middle child, and right child). Define T(h) for h≥ −1 to be the number of distinct trinary tree structures with height h. We don't care about the contents, just the overall structure. What is T(-1) and why? (b) What is T(0) and why? What is T(1) and why? (d) Prove that for h≥ 1 we have: [5 pts] [5 pts] [5 pts] [20 pts] T(h)=3T(h–1)(T(−1)+T(0)+...+T(h–2))2+3T(h−1)2(T(−1)+T(0)+...+T(h−2))+T(h−1)3 (e) Use this to calculate T(2) for n = 2. [5 pts]
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This question relates to the concept of generating functions and recursive relations in the context of combinatorics and discrete mathematics The ques... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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