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COMPUTER SCIENCE Verified answer COMPUTER SCIENCE Verified answer COMPUTER SCIENCE This problem examines three algorithms for searching for a value x in an unsorted array A consisting of n elements. Consider the following randomized strategy: pick a random index i into A. If A[i] = x, then we terminate; otherwise, we continue the search by picking a new random index into A. We continue picking random indices into A until we find an index j such that A[j] = x or until we have checked every element of A. Note that we pick from the whole set of indices each time, so that we may examine a given element more than once. a. Write pseudocode for a procedure RANDOM-SEARCH to implement the strategy above. Be sure that your algorithm terminates when all indices into A have been picked. b. Suppose that there is exactly one index i such that A[i] = x. What is the expected number of indices into A that we must pick before we find x and RANDOM-SEARCH terminates? c. Generalizing your solution to part (b), suppose that there are k ≥ 1 indices i such that A[i] = x. What is the expected number of indices into A that we must pick before we find x and RANDOM-SEARCH terminates? Your answer should be a function of n and k. d. Suppose that there are no indices i such that A[i] = x. What is the expected number of indices into A that we must pick before we have checked all elements of A and RANDOM-SEARCH terminates? Now consider a deterministic linear search algorithm, which we refer to as DETERMINISTIC-SEARCH. Specifically, the algorithm searches A for x in order, considering A[1], A[2], A[3], ...,A[n] until either it finds A[i] = x or it reaches the end of the array. Assume that all possible permutations of the input array are equally likely. e. Suppose that there is exactly one index i such that A[i] = x. What is the average-case running time of DETERMINISTIC-SEARCH? What is the worst case running time of DETERMINISTIC-SEARCH? f. Generalizing your solution to part (e), suppose that there are k ≥ 1 indices i such that A[1] = x. What is the average-case running time of DETERMINISTIC SEARCH? What is the worst-case running time of DETERMINISTIC-SEARCH? Your answer should be a function of n and k. g. Suppose that there are no indices i such that A[i] = x. What is the average-case running time of DETERMINISTIC-SEARCH? What is the worst-case running time of DETERMINISTIC-SEARCH? Finally, consider a randomized algorithm SCRAMBLE-SEARCH that works by first randomly permuting the input array and then running the deterministic linear search given above on the resulting permuted array. h. Letting k be the number of indices i such that A[i] = x, give the worst-case and expected running times of SCRAMBLE-SEARCH for the cases in which k = 0 and k = 1. Generalize your solution to handle the case in which k ≥ 1. i. Which of the three searching algorithms would you use? Explain your answer. Verified answer
COMPUTER SCIENCE Verified answer Other Quizlet setsRelated questionsWhat type of analytics seeks to determine what is likely to happen in the future?Predictive analytics aims to determine what is likely to happen in the future.
Which analytics are about understanding the future?Predictive analytics has its roots in the ability to “predict” what might happen. These analytics are about understanding the future. Predictive analytics provides companies with actionable insights based on data.
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What type of data analytics should be used when you are trying to predict a future outcome based on historical data quizlet?
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