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COP 5536 Advаnced Dаtа Structures Spring 2024 Exam 1 CLOSED BOOK 8:00 pm – 9:30 pm (60 Minutes + Extra 30 Minutes fоr scanning & submissiоn) PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY Fоr 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) (10) Suppose we perform a sequence of n operations on a data structure in which the i th operation costs i if i is an exact power of 2, and 1 otherwise. Use either the aggregate method or the accounting method to determine the smallest integer amortized cost per operation. (b) (4) State whether the following statements are true or false: (i) The amortized complexity of a task is always equal to the actual task complexity. (ii) In the potential method for amortized analysis, the potential energy should never go negative. Question 2 (12): You are given 6 runs that have 100, 200, 300, 500, 800, 1000 equal-length records to be merged into one, using a loser tree. It takes 2 seconds to read or write one block from/to disk and 1 second of CPU time to merge one block of records. Assume that all input, output, and CPU processing is sequential and there is no waiting time. The block size is 100 records. (a) (6) Give an optimal 4-way merging scheme to merge the 6 runs into 1. (b) (6) What is the total time taken by the optimal scheme? Question 3 (14): (a) (7) Perform a RemoveMin on the interval heap shown below (Figure 1). Show each step. (b) (7) Perform a RemoveMax on the interval heap in Figure 1. Show each step. Question 4 (10): (a) (8) Meld the following min height-biased leftist trees. Describe each step. (b) (2) How many internal nodes can be present in a leftist tree that has 10 external nodes? No proof is needed.