write a computer program that produces the desired output from the given input. Input: Elements in a finite set SOutput: Elements in ℘(S)Algorithm: Use recursion.

Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.

Given a list of integers, we want to know whether it is possible to choose a subset of some of the integers, such that the integers in the subset adds up to the given sum recursively. We also want that if an integer is chosen to be in the sum, the integer next to it in the list must be skipped and not chosen to be in the sum. Do not use any loops or regular expressions. Test cases: skipSum([2, 5, 10, 6], 12) true skipSum([2, 5, 10, 6], 7) false skipSum([2, 5, 10, 6], 16) false Given code: public static boolean skipSum (List list, int sum) { // call your recursive helper method return skipSumHelper (list, e, sum); 1. 2. 3. 4.

Solve the recursion by substitution: T(n) = 3T(n/2)+ 5n where T(1)=1