COP 5536 Advanced Data Structures Fall 2024 Makeup Exam 2 CL…
COP 5536 Advanced Data Structures Fall 2024 Makeup Exam 2 CLOSED BOOK 8:30 pm – 10:00 pm (60 Minutes + Extra 30 Minutes for scanning & submission) PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY For all problems, use only the algorithms discussed in class. Write your answers directly on your own white blank paper. You may use extra scratch paper for calculation, but these are not to be submitted. All answers will be graded on correctness, efficiency, clarity, elegance, and other normal criteria that determine quality. Late submission will not be accepted. Only submissions made using Honorlock will be graded. You will be monitored through Honorlock. In the response sheet please enter your name and UFID. Note. All answers will be graded on correctness, efficiency, clarity, elegance and other normal criteria that determine quality. The points assigned to each question are provided in parentheses. Last Name: _____________ First Name: _______________ UFID: _______________ Q. 1 (14) Q. 2 (12) Q. 3 (14) Q. 4 (10) Total (50) Question 1 (14): (a) (7) Drawn below is a min Fibonacci heap (The ChildCut field is shown in parentheses): Perform a DecreaseKey operation by changing 17 to 4. (b) (7) For the following min Fibonnaci heap , assume that the ChildCut field of each node is True. Perform DeleteMin operation on the Fibonacci heap, clearly labeling the ChildCut value of each node. Show each step. Question 2 (12): (a) (8) Insert the keys 1,2,7,8,4,5,6, and 3 into an initially empty red-black tree in the order given. Show the red-black tree following each insertion. (b) (4) Prove that the height h of a red-black tree satisfies h ≤ 2∗ log2(n+1) where n is the number of nodes in the tree. Question 3 (14): (a) (8) Given the following 5-way B+ -tree, insert 55 and 95 in the given order. Show each step and the resulting tree. (b) (6) Delete the key 11 from this 3-way B+ tree. Question 4 (10): (a) (8) Insert the following keys into an initially empty splay tree: 25, 20, 37, 27, 23, 21. Assume that this is a bottom-up splay tree. Show all steps. (b) (2) What is the actual and amortized complexity of join and split in splay trees? No proof needed.
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