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.

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

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.

You are given a 0-indexed array nums of size n consisting of non-negative integers. You need to apply n - 1 operations to this array where, in the ith operation (0-indexed), you will apply the following on the ith element of nums: • If nums[i] == nums [1 + 1], then multiply nums [1] by 2 and set nums [i+1] to 0. Otherwise, you skip this operation. After performing all the operations, shift all the 0's to the end of the array. • For example, the array [1,0,2,0,0,1] after shifting all its 0's to the end, is [1,2,1,0,0,0]. Return the resulting array. Note that the operations are applied sequentially, not all at once. Example 1: Input: nums = [1,2,2,1,1,0] Output: [1,4,2,0,0,0]

Consider a hallway in a building, with N equally sized rooms, numbered 1,..., N. Several meetings are planned, which require different numbers of adjacent rooms. You are given a list of meeting requests with the number of rooms need for each. The requests are represented by the array r[1, ..., k]. For example, meeting j requires r[j] adjacent rooms. You are offered a programmatic tool, which requires n steps to partition a set of n rooms, to accommodate two meeting requests of sizes s1 and s2, where s1+s2 = N. Describe an algorithm that receives a set of meeting requests s1, s2, ..., etc., and calculates the rooms allocations in the least number of steps. Formally prove that the algorithm is correct and that the solution it provides requires the lowest cost (in computational steps). Explain your solution with a concrete example. There was a similar question, but I did not understand the answer the expert gave. It had almost no details, and I could not follow it.

Help only for b and c, not question a

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

it's not a programming question.

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.

Now let's examine a Dynamic Program algorithm to solve this problem. 3.3 Let's say we have an array of length X+1. How would we define array[x]? or What is array[x] defined for?

Can someone help me with this algorithm? No coding needed

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.

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.