Given an array of elements drawn from a totally ordered set. Present an O(n)-time algorithm that either returns an element that appears at least ||n times in the list or reports that no such an element exists. [Hint: Use Algorithm Select]
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- The median value of a set of n numbers is the value that separates the half of higher values from the half of lower values in the set. The median can be found by arranging the values in the set in order and choosing the “middle” value. See the lecture slides for some sorting functions we will talk about tomorrow that will get any list in order. If there are an even number of values in the set, the median is described as the mean of the two middle values. (b) Write a SCHEME function, named list-median, that takes a list of numbers as a parameter and returns the median value in the list.Given two lists sorted in increasing order, create and return a merged list of all the elements in sorted order. You may modify the passed in lists. Ideally, the solution should work in "linear" time, making a single pass through each list.Given an array of 1000 integers: a. In the best-case scenario, what is the fewest possible comparisons needed to find a number using linear search? b. In the worst-case scenario, what is the most number of comparisons needed to find a number using linear search? c. How many comparisons will be done if we attempt to search for a number that does not exist in the list using linear search?
- 1. How many ways can I make a list of length n out of n elements if I allow repeats? (For example, if n=2, if there are no repeats my possible lists are 12 and 21. But if I allow repeats the possible lists are 11, 12, 21, and 22.For each of the algorithms unique 1 and unique2, which solves the element uniqueness problem, perform an experimental study on the same computer to determine: 1) What are these two algorithms doing here? Are they doing the same thing or not? 2) Which algorithm is faster and why? 3) Can you come up with an even faster algorithm? If so, what is it? /** Returns true if there are no duplicate elements in the array.*/ public static boolean uniquel (int[] data) { int n = data.length; for (int j 0; jEvery time I call remove‐from‐end on a dynamic array list it takes O(1) time, except if I’m using half the space or less. In that case, it takes O(n) because it will shrink the array (by making a new smaller array and copying all the elements to the smaller space). Determine and prove the runtime of this algorithm for removal‐from‐end is O(1) amortized. [Note: you may not “prove” it by saying “this is the same as X”, use more formal proof methods.]Write and implement a recursive version of the binary search algorithm. Also, write a version of the sequential search algorithm that can be applied to sorted lists. Add this operation to the class orderedArrayListType for array-based lists. Moreover, write a test program to test your algorithm.Given an array A of random integers and an integer k, find and return the kth largest element in the array. Note: Try to do this question in less than O(N * logN) time.Given a sorted array of positive integers. Your task is to rearrange the array elements alternatively i.e first element should be max value, second should be min value, third should be second max, fourth should be second min and so on.01... ""Implementation of the Misra-Gries algorithm.Given a list of items and a value k, it returns the every item in the listthat appears at least n/k times, where n is the length of the array By default, k is set to 2, solving the majority problem. For the majority problem, this algorithm only guarantees that if there isan element that appears more than n/2 times, it will be outputed. If thereis no such element, any arbitrary element is returned by the algorithm.Therefore, we need to iterate through again at the end. But since we have filtredout the suspects, the memory complexity is significantly lower thanit would be to create counter for every element in the list. For example:Input misras_gries([1,4,4,4,5,4,4])Output {'4':5}Input misras_gries([0,0,0,1,1,1,1])Output {'1':4}Input misras_gries([0,0,0,0,1,1,1,2,2],3)Output {'0':4,'1':3}Input misras_gries([0,0,0,1,1,1]Output None"""..Binary search is performed on a sorted array of n elements. The search key is not in the array and falls between the elements at positions m and m+1 (where 1 ≤ mThat's enough for you! def first_preceded_by_smaller(items, k=1): Find and return the 0irst element of the given list of items that is preceded by at least k smaller elements in the list. These required k smaller elements can be positioned anywhere before the current element, not necessarily consecutively immediately before that element. If no element satisfying this requirement exists in the list, this function should return None. Since the only operation performed for the individual items is their order comparison, and especially no arithmetic occurs at any point during execution, this function should work for lists of any types of elements, as long as those elements are pairwise comparable with each other. items k Expected result [4, 4, 5, 6] 2 5 [42, 99, 16, 55, 7, 32, 17, 18, 73] 3 18 [42, 99, 16, 55, 7, 32, 17, 18, 73] 8 None ['bob', 'carol', 'tina', 'alex', 'jack', 'emmy', 'tammy', 'sam', 'ted']…SEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. 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