Suppose that you are asked to select a data structure D that…

Suppose that you are asked to select a data structure D that can support all of the following functions: 1. Search(D, x): Search for x in D, return true if x is present in D and false otherwise. 2. Insert(D, x): Insert x into the data structure D and update the data structure accordingly. 3. Delete(D, x): Delete x from the data structure D, given its address; and update the data structure accordingly. 4. Extract-Max(D): Delete and return the largest element in D; update the data structure accordingly. Assume that the candidate data structures are (i) Binary search tree (BST), (ii) Max-heap (HEAP), and (iii) Red-black tree (RBT). Note that a Max-heap is an array object, hence supports Search and Delete as well. Answer the following questions using the most accurate big-O asymptotic notation. (a11) The worst-case time complexity for Search in a HEAP with n elements is [a11]   (a12) The worst-case time complexity for Search in a BST with n elements is [a12]   (a13) The worst-case time complexity for Search in a RBT with n elements is [a13]     (a21) The worst-case time complexity for Insert in a HEAP with n elements is [a21]   (a22) The worst-case time complexity for Insert in a BST with n elements is [a22]   (a23) The worst-case time complexity for Insert in a RBT with n elements is [a23]   (a31) The worst-case time complexity for Delete in a HEAP with n elements is [a31]   (a32) The worst-case time complexity for Delete in a BST with n elements is [a32]   (a33) The worst-case time complexity for Delete in a RBT with n elements is [a33]   (a41) The worst-case time complexity for Extract-Max in a HEAP with n elements is [a41]   (a42) The worst-case time complexity for Extract-Max in a BST with n elements is [a42]   (a43) The worst-case time complexity for Extract-Max in a RBT with n elements is [a43]

Given an unsorted array A of n distinct integers and an inte…

Given an unsorted array A of n distinct integers and an integer k, you need to return the k smallest integers in the array in sorted order, where k may be any integer between 1 and n. Suppose that you have the following three algorithms to solve this problem. A1: Sort the array in increasing order, then list the first k integers after sorting. A2: Build a min-heap from these n integers, then call Extract-Min k times. A3: Use the linear time selection algorithm to find the k-th smallest integer in the array, then partition the array about that number to obtain the k smallest numbers in the array, and finally sort the k smallest numbers. Assume that you are using mergesort as your sorting algorithm, and use the linear time build-heap algorithm to build the heap. Let T1(n, k) denote the worst-case running time of Algorithm A1. Let T2(n, k) denote the worst-case running time of Algorithm A2. Let T3(n, k) denote the worst-case running time of Algorithm A3. Analyze the worst-case running times of the algorithms. What is the asymptotic notation for T2(n, k)? Use the most accurate big-O notation in your answer. Note that k is between 1 and n. Hence k is nominated by n.

Look at the works-cited or bibliography below. What would th…

Look at the works-cited or bibliography below. What would the in-text citation look like in MLA?   James, Ken and Sue Apple. ( July 2020). ” The Ten Ways to Help Your Coworkers.”  International Today. www.internationaltoday.com/10ways-to-help-your-coworker