Use the Transform-and-Conquer algorithm design technique with Instance Simplification variant to design an O(nlogn) algorithm for the problem below. Show the pseudocode. Given a set S of n integers and another integer x, determine whether or not there exist two elements in S whose sum is exactly x.

Exercise 3D Write a function sundaram which implements this algorithm. You should check the results by comparing the final list to that produced by the sieve of Eratosthenes, and for the avoidance of doubt, the output of sundaram (5) should be [ 3,5,7,11].

= Trace the Winnow algorithm with 3: 1 for the following input. Suppose the domain is vectors of length n = 6 over {V1, V2, V3, V4, V5, V6} and the actual labels are with respect to formula v₁/v3/v6; for example, the true label of (1, 0, 1, 0, 1, 1) is '1' and that of 1, 1, 1, 1, 1,0 is '0'. The input vectors are: x1 = (1, 0, 1, 1, 0, 1) x2 = (1,0,1,1,0,0) x3 = x4= X5 x6 x7 x8 = = = = x9 = (0, 1, 0, 1, 0, 1) 1, 1, 1, 0, 0, 1) (1, (0, 1, 1, 1, 1,0) (1, 1, 1, 1, 1, 1) (0, 1, 0, 1, 1, 1) (1, 1, 0, 1, 1, 1) (1, 0, 1, 0, 0, 1) You need to follow the same assumptions as in the example in Slide 4 of Module 11. Show your work and specify whether it is possible that the algorithm makes more mistakes after processing the above vectors; justify your answer.

Let A be an array of n integers: (a) Write a pseudo code for a divide-and-conquer algorithm that computes the MAX and MIN values in array A . (b) Write the recurrence for this algorithm. (c) Solve the recurrence using the substitution method.