For the following algorithms given in pseudocode, describe what each algorithm does.
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- Write an algorithm in pseudocode that finds the average of (n) numbers. For example) (numbers are [4,5,14,20,3,6] ?Design a type of sieve algorithm that would (1) Create a list of consecutive integers from 1 to n. (2) Initially, let k=2. (3) Consider each of the multiples of k less than or equal to n and either place or remove a mark on it as follows: - If you encounter an unmarked multiple, mark it with a zero. - If you encounter a multiple that has already been marked, remove the mark by restoring to its original value. (4) Increase k by one. (5) Repeat steps (3) and (4) as long as k <= n.Develop Pseudo-code (English-like) for: In the Find Largest pseudo-code algorithm of Figure 2.14, listed below, if the numbers in our list were not unique and therefore the largest number could occur more than once. Modify the algorithm below to find all the occurrences of the largest number and their position in the list.
- You have an array containing the heights of n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, height[i]). Your task is to find the maximum volume of liquid that can hold by these lines. Program Specification: Language: Java Time Complexity: O(n) Space Complexity: 0(1)Consider an array of N integers. Describe an algorithm with an 0(N) runtime that processes the array so that: All of the negative numbers are removed. All of the remaining numbers maintain their relative order. All the null elements are at the end. Note: This is not language specific, but you can assume that the array can have null elements. Examples: (a) Input: [0, 2, 8, 1, 0, 2] Output: [0, 2, 8, 1, 0, 2] (b) Input: [9, -1, 0, 4, -8, 0, 2] Output: [9, 0, 4, 0, 2, null, null] (c) Input: [-2, null, 8, -2, -1, -4, null] Output: [8, null, null, null, null, null, null]Let A and B be two arrays of length n, each containing a random permutation of the numbers from 1 to n. An inversion between the two permutations A and B is a pair of values (x, y) where the index of x is less than the index of y in array A, but the index of x is more than the index of y in array B. Design an algorithm which counts the total number of inversions between A and B that runs in O(n log n) time.
- Please do not give solution in image format thanku Implement the following recursively using sudo code: Suppose an elevator which is on a floor on n. For this elevator to go from the nth floor to the base(ground) floor, it should go to every floor under the nth floor. Let's consider an elevator on the 4th floor. This elevator 1st comes on the third(3rd) floor. 4th-> 3rd then 3rd-> 2nd then 2->1 and next 1->0(ground floor) The recursive equation defined is F(n)=1+F(n-1)A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k – 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 26? For each integer n 2 1, let s, -1 be the number of operations the algorithm executes when it is run with an input of size n. Then s, = and s = for each integer k 2 1. Therefore, So, S1, S21 -Select--- with constant Select--- |, which is So, for every integer n 2 0, s, It follows that for an input of size 26, the number of ... is operations executed by the algorithm is s which equals ---Select--- vFind the intersection of two sets of numbers. Your algorithm's time complexity should be 0(n log n) or better. Prove your algorithm's time complexity. Algorithm FindIntersection(A[0 .. n – 1], B[0..m– 1]) // Input: Arrays A[1..n] and B[1..n] whose elements are unique ( A and B are sets). //0utput:Arrayу С
- A certain computer algorithm executes twice as many operations when it is run with an input of size k as when it is run with an input of size k - 1 (where k is an integer that is greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. How many operations does it execute when it is run with an input of size 24? For each integernz 1, let s,-1 be the number of operations the algorithm executes when it is run with an input of size n. Then for each integer 2 1. Therefore, So, S3. Sz. is -Select- and s,= with constant Select- ,which is . So, for every integer n 2 0, s, = It follows that for an input of size 24, the number of operations executed by the algorithm is s -Select-v which equals Need Heln? DesdEuclid’s algorithm (or the Euclidean algorithm) is an algorithm that computes thegreatest common divisor, denoted by gcd, of two integers. Below are the original versions ofEuclid’s algorithm that uses repeated subtraction and another one that uses the remainder.int gcd_sub(int a, int b){ if (!a) return b; while (b) if (a > b) a = a – b; else b = b – a; return a;}int gcd_rem(int a, int b){ int t; while (b) { t = b; b = a % b; a = t; } return a;}1. Trace each of the above algorithm using specific values for a and b.2. Compare both algorithms.Given an unsorted array of integers, A, its size n, and two numbers x and y both elements of A. write an algorithm that returns the distance between x and y. The distance between the two numbers of an array is the number of elements that lie between them in the sorted order. Achieve the asymtotically fastest time for this problem