Questions: 1. For the set of {1, 4, 5, 16, 17, 21} of keys, draw binary search trees of heights 2, 3, 4, 5, and 6.
2. Use the Binary Search Tree class to Write the TREE-PREDECESSOR procedure.
3. Show that there are at most [n/2h+1] nodes of height h in any n-element heap.
4. Use the Principle of Mathematical Induction to verify that, for n any positive integer, 6n-1 is divisible by 5
5. Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures.
(a) f(n) + g(n) = Θ(min(f(n), g(n)).
(b) f(n) + O(f(n)) = Θ(f(n)).
6. Use the following tree to answer the questions:
(a) Write the a pseudocode to find key 36 successor.
(b) Write the pseudocode to find the minimum key in the previous tree.
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Attachment:- DS.rar