Given an array of real numbers A[1..n], the maximum sum of contiguous subarray is 3 OPT: max ΣA[k]. 1<

Problem 2: Finding an element.(i) Let n be an even positive integer. Let A be an array containing n not necessarydifferent integers. Elements in A are not necessary sorted. Describe an algorithmwhich in time O(n) tests whether there exists an element x in A that appears in Aat least n/2 times.(ii) Let S be a set containing n integers. An element x ∈ S is an approximate median ofS, if|{y ∈ S | y < x}| ≥ n/4and |{y ∈ S | y > x}| ≥ n/4Given an array A containing n different integers, not necessary sorted, describe analgorithm which in time O(n) finds all approximate medians of the set {A[i] | i =1, 2, . . . , n}.

A robber is planning to rob the houses along a street. The constraint is, that he cannot rob adjacent houses. If done, it will alert the police. For the below-given algorithm and input, your task is to draw a DP matrix AND return the maximum earnings in a single night: nums = [4,3,6,2,7,10,5] Algorithm: def rob(self, nums: List[int]) -> int: dp = [0]*len(nums) // Initialize dp array n = len(dp) if len(nums) == 1: return nums[0] elif len(nums) == 2: return max(nums[0],nums[1]) dp[0]=nums[0] dp[1]=max(nums[1],nums[0]) for i in range(2,len(nums)): dp[i] = max(nums[i]+dp[i-2],dp[i-1]) return dp[n-1]