Consider an n x n array ARR stored in memory consisting of 0’s and 1’s such that, in a row of ARR, all 0’s comes before any of 1’s in the row. Write an algorithm having complexity O(n), if exists, that finds the row that contains the most 0’s. Step by step explain r algorithm with an illustrative example. 6

## Format Requirement Algorithms in pseudo code **MUST** be placed in code blocks/fences, and use highlighter. Algorithms should follow the pseudo code standard described in *Pseudocode Handout*. срр as the syntax Do NOT change the template except the answer portion. Formulas and equations should be in math mode using Latex math symbols. - Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmat h.pdf Two ways to enter math mode: Insert a pair of dollar signs: \$your equations go here\$. This is the inline math mode. *Notice that there is no space between the \$ and the letter*. Insert a pair of double-dollar signs: \$\ $ your equations go here \$\,ドル which produces a standalone equation/formula set.

Determine the big-O notation of the following algorithm: // A is an array with index from 0 to N-1Algorithm C(A, x, a, b); if (b<a) return a m = (b + a)/2 if (A[m] x) return C(A, x, a, m-1) else return C(A, x, m+ 1,b) Please answer max in 15-20 minutes thank u

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

Considering the following algorithm, analyze its best case, worst case and average case time complexity in terms of a polynomial of n and the asymptotic notation of ɵ. You need to show the steps of your analysis.

Question 1. The input is an array a[1],. ,..., a[n] of size n containing natural numbers between 1 and n. Describe an O(n) algorithm that determines if the array contains 2 consecutive integers.

Given A[1...n] which is an increasingly sorted array of distinct positive integers, and t which is an integer; provide an O(n) algorithm deciding whether A contains two distinct elements x and y such that x + y = t.

Let A[1, ., n] be a sorted array of distinct integers. Write an efficient algorithm with proper pseudocode for finding whether an element exists such that: A[i] i, for 1 <= i <= n. (i.e., an element whose index and value are both equal to 'i'). ==

Given an unsorted array. The array has this property that every element in the array is at most k distance from its position in sorted array where k is a positive integer smaller than the size of the array. Which sorting algorithm can be easily modified for sorting this array and what is the obtainable time complexity? (A) Insertion Sort with time complexity O(kn) (B) Heap Sort with time complexity O(nLogk) (C) Quick Sort with time complexity O(kLogk) (D) Merge Sort with time complexity O(kLogk)

given an array with repeating elements each element repeats thrice except one.find that one in O(1) space and O(n) time complexity in machine independent language.

Given an unsorted array of integers, write a function in Python to find the length of the longest increasing subsequence (LIS) in the array. For example, given the array [10, 9, 2, 5, 3, 7, 101, 18], the LIS is [2, 3, 7, 101], which has a length of 4. Your solution should have a time complexity of O(n log n), where n is the length of the input array. Here's some code to get you started: def longest increasing_subsequence(arr): # TODO: implement function pass # example usage arr = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(arr)) # should print 4

Problem 2. Suppose we have an array A[1 : n] which consists of numbers {1,...,n} written in some arbitrary order (this means that A is a permutation of the set {1,...,n}). Our goal in this problem is to design a very fast randomized algorithm that can find an index i in this array such that A[i] mod 8 € {1,2}, i.e., the reminder of dividing A[i] by 8 is either 1 or 2. For simplicity, in the following, we assume that n itself is a multiple of 8 and is at least 8 (so a correct answer always exist). For instance, if n = 8 and the array is A = [8,7, 2,5, 4, 6,3, 1], we want to output either of indices 3 or 8. (a) Suppose we sample an index i from {1,...,n} uniformly at random. What is the probability that i is a correct answer, i.e., A[i] mod 8 E {1,2}? (b) Suppose we sample m indices from {1,...,n} uniformly at random and with repetition. What is the probability that none of these indices is a correct answer? Now, consider the following simple algorithm for this problem: Find-Index-1(A[1:...