Recursion exercise

Personal project Q5. This question is concerned with the design and analysis of recursive algorithms. You are given a problem statement as shown below. This problem is concerned with performing calculations on a sequence A of real numbers. Whilst this could be done using a conventional loop-based approach, your answer must be developed using a recursive algorithm. No marks will be given if your answer uses loops. FindAverageAndProduct(a1, ...., an) such that n > 1 Input: A sequence of real values A = (a1, ...., an) Output:, A 2-tuple (average, product) containing the average (average) of all the values and the product (product) of all the values of the elements in A. Your recursive algorithm should use a single recursive structure to find the average and product values, and should not use two separate instances of a recursive design. You should not employ any global variables. (a) Produce a pseudo code design for a recursive algorithm to solve this problem. (b) Draw a call-stack…

Investigate both the iterative and the recursive methods of problem resolution, and then compare and contrast the results of your research. When would you use iteration when recursion would be more appropriate, and when would you use recursion when iteration would be more appropriate? Your answer should be justified by giving examples that are different from those that are shown on the slides of the presentation.

Question 5 When writing a recursive method, O you do not need to know ahead of time exactly how many levels of recursion will occur. O you must keep count of how many recursion call levels you have traversed. O you must make sure the method does not take any input parameters.

Computer Science When you are working in an organization, there will be different ways to communicate with your colleagues. based on this give at least 4 methods for team communication (one of the methods must be unique and creative way of communication. Using your own words, specify what type of information can be shared using the suggested method.

Personal project Q5. This question is concerned with the design and analysis of recursive algorithms. You are given a problem statement as shown below. This problem is concerned with performing calculations on a sequence ? of real numbers. Whilst this could be done using a conventional loop-based approach, your answer must be developed using a recursive algorithm. No marks will be given if your answer uses loops. FindAverageAndProduct(a1, ...., an) such that n > 1 Input: A sequence of real values A = (a1, ..., an) Output:, A 2-tuple (average, product) containing the average (average) of all the values and the product (product) of all the values of the elements in A. Your recursive algorithm should use a single recursive structure to find the average and product values, and should not use two separate instances of a recursive design. You should not employ any global variables. (a) Produce a pseudo code design for a recursive algorithm to solve this problem.   (b) Draw a call-stack…

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?

In order to accomplish the task of terminating recursion, you must first describe three distinct types of recursion, a high-level description of each kind, and a specific technique that fits into each category.

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?

Ex. 01 : Recursion About So far, we have learned that we can perform repetitive tasks using loops. However, another way is by creating methods that call themselves. This programming technique is called recursion and, a method that calls itself within it's own body is called a recursive method. One use of recursion is to perform repetitive tasks instead of using loops, since some problems seem to be solved more naturally with recursion than with loops. To solve a problem using recursion, it is broken down into sub-problems. Each sub-problem is similar to the original problem, but smaller in size. You can apply the same approach to each sub-problem to solve it recursively. All recursive methods use conditional tests to either 1. stop or 2. continue the recursion. Each recursive method has the following characteristics: 1. end/terminating case: One or more end cases to stop the recursion. 2. recursive case: reduces the problem in to smaller sub-problems, until it reaches (becomes) the end…

Programming is communication; the programmer “explains” to a computer how to carry out a task, with the explanation being the program. Can you think of any cases where communication directed to people uses direct or indirect recursion? Are there cases where such a use of recursion is indispensable?

In a recursive algorithm, the goal is to solve a problem by breaking it into smaller sub-problems to solve. This is accomplished by constructing an algorithm using two important components. What are these components, what is the purpose of each?

Task 1 Count the number of vowels in a phrase using recursion only. You can think of this problem as "I can count the number of vowels in this phrase by counting the number of vowels in the first character, then counting the number of vowels in the rest of the phrase." We define a vowel as being A, E, I, O or U. This is one of those problems that can just as easily be solved with traditional programming structures such as a loop - but we're asking you to use recursion for the exercise. Consider: what replaces the loop structure? When will we stop recursion? Task 2 The constant e (Euler's number) is approximated by the following sequence: 1₁ n! where the number of terms in the sequence is sufficient to generate the required precision in decimal places. 1+ 2! + ... We say that there is some value epsilon (e) such that, when the change in the approximation from one term to the next is less than said epsilon, we have reached sufficient precision. That is, when the term you're proposing to…

Part C: Function, for and plotting We did a project in the lecture on calculating the free fall speeds and plotting them on a graph. This part is similar to the project. An engineer has derived a relationship between the force applied to a material and the extension in length that the force would cause. The relationship between force f and extension e is given by: You are asked to plot a graph showing the relationship between force and extension. You are asked to complete the following tasks: Task 1 Write a Python function which returns the value of e for a given input f. Do not use literals (e.g. 5.5, 10) in the expressions for e in the function. Instead you should define constants and use them. Note that the relationship between e and f depends on whether f is bigger than 10 or not, this means you need a certain Python construction in your function. If you can't think of that, have a look at Part A of Lab03.

1. The entrance room (or the starting of the maze) is considered as level 1. Now, answer these following questions: (a). Write an algorithm to figure out how many maximum levels the maze can go up to. (b). Figure out the complexity of your algorithm. To create a maze some rooms of a building is connected. Starting room is called Entrance room. From the entrance room other rooms are there connected from it. However, some rooms of that maze- building have connected room from it, and some rooms do not have any connected room. Each of the room can have at most or up to two rooms connected from it. The starting room is the entrance room of the maze or building. Fore example: It can be any one like the followings: Exemple -: Room1 Roono Room Entrance Room Raom Room2 Room? Roo Roomo Here, maxinum level =7 Example -2; Entrace Room D- Room5 Room 2 Room 4 Maxximum level=3

Do not use static variables to implement recursive methods.  USING JAVA 1.  Using Big Oh notation, indicate the time requirement for each of the following tasks in the worst case. Describe which operations are assumed to take constant time to. After arriving at a party, you shake hands with each person there. n is the number of persons in the party. Each person in a room shakes hands with everyone else in the room. n is the number of persons in the room. You climb a flight of stairs. n is the number of stairs After entering an elevator, you press a button to choose a floor. n is the number of floors You ride the elevator from the ground floor up to the nth floor. You read a book twice. n is the number of pages in the book Using Big Oh notation, indicate the time requirement of each of the following tasks in the worst case. Display all the integers in an array of integers. Display all the integers in a chain of linked nodes. Display the nth integer in an array of integers. Compute…

Recursion is the best and the fastest way to solve any problem.True or False

Backtracking normally uses ______ to find out all solutions to a computational problem. (recursion, iteration).

DISCRETE STRUCTURE   A game is played by moving a marker ahead either 2 or 3 steps on a linear path. Let cn be the number of different ways a path of length n can be covered. Given, Cn =Cn-2 + Cn-3, Ci=0, c2=1, c3=1 Write a recursive algorithm to compute Cn.

Design and implement a recursive program that solves the Nonattacking Queens problem. That is, write a program to determine how eight queens can be positioned on an eight-by-eight chessboard so that none of them is in the same row, column, or diagonal as any other queen. There are no other chess pieces on the board. Design and implement a recursive program that solves the Nonattacking Queens problem. That is, write a program to determine how eight queens can be positioned on an eight-by-eight chessboard so that none of them is in the same row, column, or diagonal as any other queen. There are no other chess pieces on the board. Design and implement a recursive program that solves the Nonattacking Queens problem. That is, write a program to determine how eight queens can be positioned on an eight-by-eight chessboard so that none of them is in the same row, column, or diagonal as any other queen. There are no other chess pieces on the board.

write a recursive method to schedule compatible activities that result in the maximum usage of the room.

When recursion is used to solve a problem, why must the recursive method call itself to solve a smaller version of the original problem?

Compare and contrast between iterative and recursive solutions. When would you preferiteration over recursion and vice-versa? Justify your answer by giving different examples than the ones which are provided in the lecture slides    java code

Pascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2,  pascal(1, 2) -> 0   public int pascal(int row, int column) {   }

What are the basic components required to create a recursive method? How can you avoid creating an infinitely recursive method? In your post, also provide an example of how recursion can be used in a specific example.

Question-1 Friend's Party Circle: There are a few friends living in the same area. They have a party every weekend and the place of party change each week. It is always a lifficult task to select a place which is nearest for everyone. They advantage of Computer Science to solve this problem. all decided to take Names of friends are Ahmed, Rehman, Careem, Basit, Dawood, Ghani, and Farid. Ahmed lives at 5 minutes' walk from rehman and at 10 minutes' walk from Careem. Careem lives at 3 minutes' walk from Dawood. Rehman lives at 4 minutes' walk from Basit and 2 minutes' walk from Dawood. Dawood lives at two minutes' walk from Farid. Ghani lives at 2 minutes' walk from Basit. a. If we represent a graph G = V (V, E) in which set of vertices are home of each Friend and an edge represents a path between two homes. Provide the adjacency matrix of directed graph of the graph G. b. In above directed graph G. You are required to devise an algorithm to find all possible paths.

When an algorithm that normally recursively calls itself will no longer do so, what are the conditions that must be met?

For each of the following recursive methods, identify the base case, the general case, and the constraints on the argument values, and explain what the method does. (images below)

Only correct answer will be appreciated else downvoted.

Please draw the working of this semaphore. If you don't know please skip it:

Logic Desgin Take your time in answering the questions. I want to solve questions ( f ) correctly please.

Any simple task may be aided by the Spiral Model.