Given an unsorted array A of integers of any size, n ≥ 3, and an integer value x, write an algorithm as a pseudo code (not a program!) that would find out if there exist EXACTLY 3 occurrences in the array with value x. What is the time complexity of your algorithm, in terms of Big-O? What is the space complexity of your algorithm, in terms of Big-O? What if , the given array A is sorted. Will time complexity change from the case that A was unsorted? • If yes; give a new algorithm that achieves this better complexity (indicate the time complexity as of that algorithm). • If no, explain why such new constraints/conditions cannot lead to a better time complexity.

Consider the problem of finding the distance between the two closest numbers in an array of n and y is computed as x - y.) numbers. (The distance between two numbers x Design a presorting-based algorithm in pseudo code for solving this problem and determine its efficiency class. Answer: // your algorithm goes here Provide the the algorithm efficiency analysis here:

The following is a pseudocode representation of an algorithm that takes an array of integers and sorts them in ascending order. What is the order of this algorithm in the worst case? Explain your answer in detail. What is the order of the algorithm if anArray is already sorted? Justify your answer. +sort (in anArray[]: integer)n: integer = length of anArray temp: integer = 0; for (i: integer = 0; i < n - 1; i++) { for (j: integer = 0; j < n – i - 1; j++) { if (anArray[j] > anArray[j + 1]) { temp = anArray[j] anArray[j] = anArray[j + 1] anArray[j + 1] = temp } } }

Using Java, Write an algorithm that finds both the smallest and largest numbers in a list of n numbers. Try to find a method that does at most 1.5n comparisons of array items. Also, provide every-case and worst-case- time complexity

Write an efficient algorithm for the following problem, and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem: Binary Array Core Input: Two integers p and q and a binary array A[1...n], i.e., each entry contains either a 0 or 1. Output: Print Yes - if there exists a subarray A[i...k], where 1<= i < k <= n, with exactly p zeros in A[1...i-1] (there may be 1s) and exactly q ones in A[k+1...n] (there may be 0s). Print No - otherwise. Outputs with examples Input: A = [0,1,1,0,1], p = 2, q =1, Output: No. Input: A = [0, 1,1,0, 0,1,0,1], p = 1, q =1, Output: Yes because we can have A[1...i-1] = [0] and A[k+1 ... n] = [0,1,0,1]

Give an example of an algorithm that is O(1), an algorithm that is O(n) and an algorithm that is O(n2). Discuss the difference between them.

Given an array of integers, in which each elements repeats twice except one. Your task is to find that element in O(n) Time complexity and O(1) Space Complexity.

Call a sequence X[1 · · n] of numbers oscillating if X[i] < X[i + 1] for all even i, and X[i] > X[i + 1] for all odd i. Describe an efficient algorithm to compute the length of the longest oscillating subsequence of an arbitrary array A of integers.

You are given a two-dimensional array A with n rows and n columns such that every element is either 1 or 0, and for every row, the 1s are placed ahead of 0s. Find the quickest algorithm to find a row with the most significant number of 1s. Analyze the time complexity of your algorithm.

for question 1, please use java language for coding

You are given an array A[1, ., n] in which the elements A[2] to A[n] are already sorted, i.e., A[2, .., n] is a sorted array. Write down an efficient algorithm with proper pseudocode for moving A[1] in the correct place, so that the full array A[1, ..., n] is sorted.

algorithms are solely theoretical for a and b. please number the steps of the algorithm, thank you

Let A be an array of size n >= 6 containing integers from 1 to n-5, inclusive, with exactly five repeated. Describe an efficient algorithm for finding the five integers in A that are repeated. Provide pseudocode for the algorithm. Provide the correctness proof. State and justify time and space complexity.