Suppose arrays A and B are both sorted in increasing order and both contain n elements. What is the time complexity to find the median of A U B, i.e., the set of elements in A or B?

Suppose that we use insertion sort on a randomly ordered array where elementshave only one of three values. Is the running time linear, quadratic, or something inbetween?

An array is called a winner if it has two entries which together add up to a third entry, i.e. if A[i] + A[j] = A[k]for some i,j,k, where i≠j≠k. a)Write an algorithm (pseudocode preferred) to determine if a given array A is a winner. Your algorithm should not use any additional data structures. b)Analyze the running time of your algorithm using Big-O notation.

Describe an algorithm for finding the 10 largest elements in an array of size n. What is the running time of your algorithm?

Give an efficient sorting algorithm for an array C[1,...,n] whose elements are taken from the set {1,2,3,4,5,6,7}

During each iteration of Quick Sort algorithm, the first element of array is selected as a pivot. The algorithm for Quick Sort is given below. Modify it in such a way that last element of array should be selected as a pivot at each iteration. Also explain the advantages.

Algorthim of how to find the largest element missing in an unsorted array of n positive integers and the running time of the algorthim is in O(n). Example of this is that the n=6 array C= [5,90,8,6,26,9] The largest element missing in the array is 7

Suppose you have to compute AG sum(C)(r) as well as A,B Gsum(C)(r). Describe how to compute these together using a single sorting of r.

Given a Sorted Array of integers containing duplicates. Find the frequency of every unique element present in the array. Frequency is defined as the number of occurrence of any element in the array. Solve in Java

Question A: Mapping. The two-sum problem is a popular algorithm problem. Given an array of integers and an integer target, return indices of the two numbers such that they add up to the target. You may assume that each input would have exactly one solution, and you may not use the same element twice. For example, suppose we have an array arr = [1,10,100]. If the target is 11, you should return [0,1] because arr[0] + arr[1] = 1+ 10 = 11. If the target is 101, you should return [0,2] because arr[0] + arr[2] = 1+ 100 = 101. Complete this problem in O(n). Hint: using a hash table.

Use the Transform-and-Conquer algorithm design technique with Instance Simplification variant to design an O(nlogn) algorithm for the problem below. Show the pseudocode. Given a set S of n integers and another integer x, determine whether or not there exist two elements in S whose sum is exactly x.

We apply the binary search on a 17-element ordered array. Assume that a givenkey appears in the array, and it is between the 5th element and the 13th element(inclusive). How many comparisons do we need for the average-case efficiency?

Let M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2.