Given an array A = <1, 1, 1, 1, 1>, if we run Hoare-Quicksort(A, 1, 5), how many key comparisons will be made? if we run Lomuto-Quicksort(A, 1, 5), how many key comparisons will be madel
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A: We саn асhieve О(nLоgn) wоrst саse. The ideа is bаsed оn the fасt thаt the mediаn…
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A: Given :- Apply quicksort to sort the sequence {45, 29, 71, 90, 12, 31, 10}.
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A:
Q: Recall the problem of finding the median of an array of an unsorted list. How fast can one complete…
A: Solution: Recurrence relation: Let the problem be: finding the Kth largest element in an…
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A: Lets discuss the solution in the next steps
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A: SUMMARY: -Hence we discussed all the points.
Q: Apply mergesort to sort the list [14, 13, 11, 12, 16, 12, 18, 15, 19, 17] in increasing order.
A: The solution for the above given question is given below:
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- Given an array A = [10, 7, 4, 2, 1], and target = 7, return the index of the target if found, else return -1. 1. Can this problem be solved in O(logN)? 2. If so, write the implementation. Mention time and space complexity 3. If this problem cannot be solved using O(logN), what is the solution that you suggest - write the code and also mention time and space complexity.can you solve this please ? Given an array of unsorted integers, you are requested to investigate whether there exist a pair of numbers in this array that has a sum equal to a given key or not. For example, if the arr = [8, 7, 2, 5, 3] and the key = 12, the answer will be "Yes" as the array has a pair (7 and 5) where their sum = 12 = key, otherwise "No" is returned. To solve this problem, the following idea can be used: i. Consider every pair in the given array and check if their sum = key. ii. Sort the array first, keeping two pointers to on the minimum and maximum of the array and then move from both directions toward the center of the array while checking whether the sum = key or not. Answer the following questions: a) Transform each of the above ideas (i) & (ii) into algorithm (pseudocode) and compute their complexities b) Critic these two ideas: [Which is better? Why?] c) Design a better solution with less complexity. [note: your idea should be…A hash table is an efficient data structure to store and access data via keys. In this problem, you need to find the longest subarray of distinct elements. For example, given an array A = <milk, water, 6724, water, soda, beer, apple, grape, wine>, the longest subarray is <milk, water, 6724, soda, beer, apple, grape, wine> Hint: you need to keep track and update the positions of the elements. a) Explain how many unique subarrays are there from a given array b) Describe your ideas on how to solve the problem, especially how hash tables can be used to keep track of the important information c) Write the most efficient algorithm (pseudo code) to solve this problem with complexity analysis. You can assume that a good hash function is given.
- You are given an array of positive integers S[1, . . . , n]. You are initially positioned at the array’s first index 1, and each element S[i] represents your maximum length of jump at position i. For example, you can jump from position i to any position among i + 1, . . . , i + S[i]. Return true if you can reach the last index, or false otherwise. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.Let A be an array with n = 2k − 1 elements, where k is some positive integer. Determine a formula (in terms of n) for the minimum possible number of total comparisons required by Quicksort, as well as a formula for the maximum possible number of total comparisons required by Quicksort. Use your formulas to show that the running time of Quicksort is O(nlogn) in the best case and O(n2) in the worst case.Given an array of integers, return the largest gap between the sorted elements of the array. For example, consider the array: [9, 4, 26, 26, 0, 0, 5, 20, 6, 25, 5] ... in which, after sorting, the array becomes: [0, 0, 4, 5, 5, 6, 9, 20, 25, 26, 26] so that we now see that the largest gap in the array is between 9 and 20 which is *** 11. Examples largestGap ([9, 4, 26, 26, 0, 0, 5, 20, 6, 25, 5]) → 11 // After sorting: [0, 0, 4, 5, 5, 6, 9, 20, 25, 26, 26] // Largest gap between 9 and 20 is 11
- 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 ≤ mModify the ArrayDeque implementation so that it does not require the modulus (%) operator. The modulus operator is "expensive" on some systems. Instead, the implementation should make use of the fact that if a.length is a power of 2, then k % a.length = k & (a.length - 1). Here, & is the bitwise and operator. (p 61) Open Data Structures in Java, section 2.7You are running radix sort (base 10) on values 123, 322, 311, 332, 312, 132, 213, 321, 323. Unfortunately, the counting-sort implementation that your radix-sort calls is "anti-stable", that is, in case of a tie, it always reverses the order of two keys. What is the final order you get? Show the array after each pass.Given an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1. Code please.A matrix is an array of numbers of size m by n (i.e., m x n). When we multiply 2 matrices, we multiply the matching numbers, then sum them up. Multiplying a matrix of size m x n with another matrix of size n x q will result in a matrix of size m x q. An example is shown in Figure 1: [ ? ? ? ? ? ? ] x [ ? ? ? ? ] = [ ?? +?? ?? + ?? ?? + ?? ?? + ?? ?? + ?? ?? + ?? ] Matrix 3 x 2 Matrix 2 x 2 Matrix 3 x 2 Figure 1: Multiplication of Matrix 3 x 2 and 2 x 2 Write a C++ program that multiplies 2 matrices and return the sum of the transposed matrix. Your program shall include the following: a) Define two 2 dimensional arrays, M and N that each represents a matrix of size 3 x 2 and a matrix of size 2 x 2. Request the user to enter the values for the 2 arrays using advanced pointer notations (refer to your slides for the list of array pointer notations). b) Create a function named multMatrix() that passes as arguments, the values of array M and N, multiplies them and store the results in a new…You are given an unsorted array A[1, ..., n].We know that the maximum (or minimum) element in the array can be found in (n-1) comparisons.Write an algorithm that finds both the maximum and the minimum element in the array in ~(3n/2) comparisons, i.e., (3n/2) + THETA(1) comparisons.SEE MORE QUESTIONS