Exercise 8.10.1: Recursively computing sums of cubes. About (a) Give a recursive algorithm to compute the sum of the cubes of the first n positive integers. The input to the algorithm is a positive integer n. The output is 1 j3. The algorithm should be recursive, it should not compute the sum using a closed form expression or a loop.
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- CodeW For fun X C Solved https://codeworkou... 臺亂 CodeWorkout X272: Recursion Programming Exercise: Is Reverse For function isReverse, write the two missing base case conditions. Given two strings, this function returns true if the two strings are identical, but are in reverse order. Otherwise it returns false. For example, if the inputs are "tac" and "cat", then the function should return true. Examples: isReverse("tac", "cat") -> true Your Answer: 1 public boolean isReverse(String s1, String s2) { 2. if > 3. 4. else if > return true; return false; 5. 6. else { String s1first = String s2last return s1first.equals (s2last) && 51. substring(0, 1); s2, substring(s2.length() 1); 7. 8. 6. isReverse(s1.substring(1), s2.substring(0, s2.length() 1)); { 12} 1:11AM 50°F Clear 12/4/20211. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…CS211 Non-recursive solution for Towers of Hanoi Using the algorithm discussed in class, write an iterative program to solve the Towers of Hanoi problem. The problem: You are given three towers a, b, and c. We start with n rings on tower a and we need to transfer them to tower b subject to the following restrictions: 1. We can only move one ring at a time, and 2. We may never put a larger numbered ring on top of a smaller numbered one. There are always 3 towers. Your program will prompt the user for the number of rings. Here is the algorithm. Definition: A ring is "available" if it is on the top of one of the towers. Definition: The "candidate" is the smallest available ring that has not been moved on the most recent move. The first candidate is ring 1. The Algorithm: 1. Find the candidate. 2. Move the candidate (right or left, depending if the number of rings is odd or even) to the closest tower on which it can be placed. Move "around the circle" if necessary. 3. If not done, go back…
- Use the recursion to solve the following problems 1. Calculate the sum of an array of n integers. 2. Compute Powers, p(x,n)=xn 3. Revers an array of n integers 4. Calculate the length of string (number of characters) 5. Implement the tail recursion for problems 1 and 2. Please test the program by using 2 different input sets!Part 1) Write pseudocode for an iterative algorithm which finds the maximum value of a list of integers. Use a loop invariant to prove your algorithm is correct. (Presumably you have already witten a program like this over the course of your studies! The interesting part here is the proof.) Part 2) Prove by induction the recursive program Foo is correct: Foo determines if there are two indices i and j, p4. CodeW. X b For fun X Solved x b Answer x+ Ohttps://codeworko... CodeWorkout X264: Recursion Programming Exercise: Multiply For function multiply,write the missing base case condition and action. This function will multiply two numbers x and y.You can assume that both x and y are positive. Examples: multiply(2, 3) -> 6 Your Answer: 1 public int multiply(int x, int y) { 2. if > { > } else { return multiply(x 1, y) + y; 3. 5. { 7. 1:08 AM 50°F Clear 日Artificial Intelligence (Part - 1) ==================== The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (1) Propose a state representation for the problem?T/F 7. The recursive procedure for solving the Towers of Hanoi can only be used if the number of discs parameter is 7 or less.One-friend recursion vs iteration. 1. Your objective is to receive the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been inverted. You will only take an element off of one end or put an element back on one end because you are being lazy. But you have friends in recursion who can assist you.Please provide the recursive code as well as a paragraph with the friend's description of the algorithm.2. Now imagine that you lack friends but have a stack. Quickly design an iterative programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative method.3. Trace both of these scripts separately. On a computer, step by step compare and contrast their calculations.Artificial Intelligence (Part - 2) ==================== The Towers of Hanoi is a famous problem for studying recursion incomputer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (2) What is the size of the state space?Use the recursion to solve the following problems using Java Programming Language 1. Calculate the sum of an array of n integers. 2. Compute Powers, p(x,n)=xn 3. Revers an array of n integers 4. Calculate the length of string (number of characters) 5. Implement the tail recursion for problems 1 and 2. Please test the program by using 2 different input sets!# Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):SEE MORE QUESTIONS