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COP 5536 Advаnced Dаtа Structures Spring 2024 Makeup Exam 1 CLOSED BOOK 8:30 pm – 10:00 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. The points assigned to each question are provided in parentheses. Late submission will not be accepted. Only submission made using Honorlock will be graded. You will be monitored through Honorlock. In the response sheet please enter your name and UFID. Q. 1 (12) Q. 2 (16) Q. 3 (10) Q. 4 (12) Total (50) Question 1 (12): Consider a data structure with the operations: put(x), find(x), and remove(x). Put(x) inserts an element x into the structure, find(x) searches for x, and remove(x) removes x from the structure. A find(x) and a remove(x) operation take 1 unit of time each and a put(x) operation takes 1 unit of time except when the number of elements in the structure prior to the put(x) operation equals the capacity n of the structure. In this case, put(x) takes (2n+1) time units to double the capacity and then put x into the data structure. Assume that the structure is initially empty, and its initial capacity is 1. Use the accounting method to show that the amortized complexity of put(x), find(x), and remove(x) are respectively, 5, 1, and 1. Question 2 (16): You are given n=900 records to be sorted on a computer with a memory capacity of S=100 records. Assume that the entire S-record capacity may be used for input/output buffers, i.e., you have extra memory for a k-way loser tree. The input is on disk and consists of m runs. Assume that phase 2 of an external merge sort is done using a k-way merge with k buffers for input and 1 for output and that the buffer or the block size may be selected by the user. Each time a disk access is made, the seek time is t_s=6ms and the latency time is t_l=4ms. The transmission time is t_t=0.2ms per record transmitted. Assume that input, output, and CPU processing cannot be overlapped.(a)(9) What is the buffer size, b, and the total input time for phase two of external sorting, merging, when a k-way merge scheme is used? What is the better k with respect to the total input time for phase two? Consider only k=3 and 6.(b)(5) Assume that it takes 0.2ms to merge 10 records. Compute the total time for phase two of external sorting, when k=6, i.e. compute the total time taken for input, merging, and output. (c)(2) Is the run time expected to increase or decrease if a winner tree is used instead of a loser tree? Why? Question 3 (10): Given the interval heap shown below, show the final interval heap produced by the following sequence of operations: insert(23), deleteMin(). (Use the algorithms discussed in class and show steps) Question 4 (12): (a)(10) Consider a min binomial heap with the following elements: 8, 11, 9, 7, 21, 27, 20, 40, 14, 19, 10, 25 Each element defines a min tree of the binomial heap. Perform a DeleteMin operation and show the resulting min trees. Show all the steps. (b)(2) What are the actual and amortized complexities of RemoveMin in min binomial heaps? No proof is needed.
Which оf the fоllоwing best describes why clients need to sign estimаtes?