Show that if C₁ and C₂ are conditions that elements of the satisfy, relation R n-ary may then SC, ^ C₂ (R) = SC₁ (SC₂ (R).
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- 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.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…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…
- Correct answer will be upvoted else Multiple Downvoted. Computer science. You need to change this grouping so all components in it are equivalent (I. e. it contains a few events of a similar component). To accomplish this, you pick some integer x that happens to some extent once in a, and afterward play out the accompanying activity quite a few times (perhaps zero): pick some portion [l,r] of the arrangement and eliminate it. Yet, there is one special case: you are not permitted to pick a fragment that contains x. All the more officially, you pick some adjoining aftereffect [al,al+1,… ,ar] to such an extent that ai≠x if l≤i≤r, and eliminate it. After expulsion, the numbering of components to one side of the eliminated portion changes: the component that was the (r+1)- th is presently l-th, the component that was (r+2)- th is currently (l+1)- th, etc (I. e. the leftover arrangement simply falls). Note that you can not change x after you picked it. For instance, assume n=6,…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…please. use matlab.
- Code in C++ only. Correct answer will upvoted else downvoted. framework of size n×m, with the end goal that every cell of it contains either 0 or 1, is considered lovely if the total in each adjoining submatrix of size 2×2 is actually 2, i. e. each "square" of size 2×2 contains precisely two 1's and precisely two 0's. You are given a network of size n×m. At first every cell of this network is unfilled. How about we indicate the cell on the crossing point of the x-th line and the y-th segment as (x,y). You need to handle the inquiries of three sorts: x y −1 — clear the cell (x,y), in case there was a number in it; x y 0 — compose the number 0 in the cell (x,y), overwriting the number that was there already (assuming any); x y 1 — compose the number 1 in the cell (x,y), overwriting the number that was there beforehand (assuming any). After each question, print the number of ways of filling the unfilled cells of the grid so the subsequent network is delightful. Since the appropriate…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.need in C++...asap
- Problem 4 We can use lists of numbers like l to represent a mathematical vector. Recall from math classes that a vector is an object with a magnitude and direction. The magnitude is the sqrt of the sum of the squares (for a vector (x,y) it's the Pythagorean theorem for the magnitude (x^2 + y^2)**(1/2)). For a vector of any other length, the formula generalizes to (l[0]^2 + l[1]^2 + l[2]^2 + ... )**(1/2). For this problem use l from Problem 1 and a for loop to compute the magnitude of l with the result stored in l_mag. For l above, its magnitude is 12.96. Python gives you the ** exponentiation operator to raise a number to a power. You could also import math and use math.sqrt(). l = [1, 2, 3, 4, 5, 7, 8] Please give proper explanation and typed answer only.Question 5: A 2D matrix can be represented as a list and a column count value in Python. For example, the 3x3 matrix 1 2 3 45 6 7 8 9 can be row-wise represented as ([1,2,3,4,5,6,7,8,9], 3), where the number 3 represents the number of columns in the matrix. Similarly, 135 2 4 6 becomes ([1,3,5,2,4,6], 3). A submatrix can be defined as an (1,r,t,b) tuple, where 1 and r are left and right column indices, andt and b are top and bottom row indices (all inclusive). Write representing a matrix, and the column count of the matrix, along with another tuple representing a specific submatrix, and returns the list representation of the submatrix along with its column count as a tuple. For example, given function that takes a tuple containing the list submatrix(([1,2,3,4,5,6,7,8,9,10,11,12], 4), (1,2,0,1)) returns: ([2,3,6,7], 2) because, ([1,2,3,4,5,6,7,8,9,10,11,12], 4) represents: 1 2 3 4 5 6 7 8 9 10 11 12 and (1,2,0,1) represents the submatrix between column indices 1 and 2 (both inclusive),…