(Visualizing Recursion) It’s interesting to watch recursion “in action.” Modify the factorialfunction of Fig. 5.18 to print its local variable and recursive call parameter. For each recursive call,display the outputs on a separate line and add a level of indentation. Do your utmost to make theoutputs clear, interesting and meaningful. Your goal here is to design and implement an output format that helps a person understand recursion better. You may want to add such display capabilitiesto the many other recursion examples and exercises throughout the text.

1)Discuss the pseudo code for recursive function to calculate exponent. 2)Discuss the pseudo code to modify Mod-function.

by using c++. How can I solve this? Kindly, no class, linked list, and pointers shall be used in this program. Kindly use only SELECTION, ITERATION, INPUT, AND OUTPUT, FUNCTION,  ARRAY, AND STRING ONLY.

Task 4: The first problem that you solve recursively is to implement enoughGate() to check if the dogMaze has at least two gates (one for the entrance and one for the exit). This problem must be solved recursively, however there is no limitation on what type of recursion (i.e., direct or indirect recursion) you use . As a reminder, a direct recursion refers to the function that calls itself to solve the given problem. However, by indirect recursion, more than one function involves in solving the problem. It is possible that a non-recursive function solves a small part of the problem and then calls the recursive function to finish the job.   /** * This method returns true if the number of  * gates in dogMaze >= 2.  * @return it returns true, if enough gate exists (at least 2), otherwise false. */ publicboolean enoughGate (){ // insert your code here. Change the return value to fit your purpose.  return true; }

1. Write a recursive function named RecursiveSum that, given a positive number n (n> 0), returns the sum of the numbers from 1 to n. Also, show the process of finding the result using a recursion tree.

Question 10 Code the following in Java using Recursion

2 a) Describe the costs and benefits of defining and using a recursive function.

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?

Iteration versus one-friend recursion. 1. Your job is to accept the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been reversed. You will only take an element off of one end or put an element back on one end because you are being indolent. But you have allies in recursion who can assist you.Please include the recursive code as well as a paragraph with the friend's description of the algorithm. 2. Now imagine that you lack pals but have a stack. (Refer to Chapter 3. Quickly design an incremental programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative algorithm. 3. Trace both of these scripts separately. Compare and contrast their computerised calculations step by step.