I just need the method they are asking for Write a recursive function that takes a start index, array of integers, and a target sum. Your goal is to find whether a subset of the array of integers adds up to the target sum. The start index is initially 0. A target sum of 0 is true for any array. Examples: subsetSum(0, {2, 4, 8}, 10) -> true   public boolean subsetSum(int start, int[] nums, int target) {   }

The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…

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.

I need the code from start to end with no errors and the explanation for the code ObjectivesJava refresher (including file I/O)Use recursionDescriptionFor this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA7 9# # ###### # #   ## # # #### #     ## ##### ##       ########## RequirementsWrite a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the valid exits found in any order. See the examples below for exact output requirements. Also, record…

Design and implement a program that implements Euclid’s algorithm for finding the greatest common divisor of two positive integers. The greatest common divisor is the largest integer that divides both values without producing a remainder. In a class called DivisorCalc, define a static method called gcd that accepts two integers, num1 and num2. Create a driver to test your implementation. The recursive algorithm is defined as follows:gcd (num1, num2) is num2 if num2 <= num1 and num2evenly divides num1gcd (num1, num2) is gcd(num2, num1) if num1 < num2gcd (num1, num2) is gcd(num2, num1%num2) otherwise

PLZ help with the following: In Java Write a program using recursion to display all valid (i.e. properly open and closed) combinations of n-pairs of parentheses.

write java codes to do the following:  Write a recursive function to check if an integer array is  negative symmetric, for example, an array of 10, 20, 30, 90, -30, -20, -10 is considered as negative symmetric, while an array of 10, 20, 30, 90, 30, 20, 10 is not  considered as negative symmetric.   public static boolean checkArraySym(int [ ] A, int first, int last) that receives an array A, first index, last index and checks if the array is negative symmetric

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In c++, Thanks!!! Write the simplest program that will demonstrate iteration vs recursion using the following guidelines -  Write two primary helper functions - one iterative (IsArrayPrimeIter) and one recursive (IsArrayPrimeRecur) - each of which Take an array and its size as input params and return a bool such that 'true' ==> array and all elements are prime, 'false' ==> at least one element in array is not prime, so array is not prime.  Print out a message "Entering <function_name>" as the first statement of each function. Perform the code to test whether every element of the array is a Prime number. Print out a message "Leaving <function_name>" as the last statement before returning from the function. Remember - there will be nested loops for the iterative function and there can be no loops at all in the recursive function. You will need to define one other helper function (IsPrimeRecur) for the recursion which should also not contain any loops to make it a…