You are given an array of n integers, and a target sum S. Give an algorithm that determines if there are two elements in the array (may be the same one) whose sum is S. Your algorithm should have a complexity less than Θ(n^2).

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.

Given an array of integers arr, sort the array by performing a series of pancake flips.   In one pancake flip we do the following steps: Choose an integer k where 1 <= k <= arr.length. Reverse the sub-array arr[0...k-1] (0-indexed). For example, if arr = [3,2,1,4] and we performed a pancake flip choosing k = 3, we reverse the sub-array [3,2,1], so arr = [1,2,3,4] after the pancake flip at k = 3.   Print out the k-values corresponding to a sequence of pancake flips that sort arr.   Example 1: Input: arr = [3,2,4,1] Output: 4, 2, 4, 3 Explanation: We perform 4 pancake flips, with k values 4, 2, 4, and 3. Starting state: arr = [3, 2, 4, 1]. After 1st flip (k = 4): arr = [1, 4, 2, 3] After 2nd flip (k = 2): arr = [4, 1, 2, 3] After 3rd flip (k = 4): arr = [3, 2, 1, 4] After 4th flip (k = 3): arr = [1, 2, 3, 4], which is sorted.   Another potential solution is: Output = 3, 4, 2, 3, 1, 2, 1, 1 with a similar explanation. All potential solutions that solve the problem are…

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