Write algorithm for Recursive Backtracking Algorithms pre-cond: I is an instance of the problem. post-cond: optSol is one of the optimal solutions for the instance I, and optCost is its cost.
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Write
pre-cond: I is an instance of the problem.
post-cond: optSol is one of the optimal solutions for the instance I, and optCost is its cost.
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- Recursive filtering techniques are often used to reduce the computational complexity of a repeated operation such as filtering. If an image filter is applied to each location in an image, a (horizontally) recursive formulation of the filtering operation expresses the result at location (x +1, y) in terms of the previously computed result at location (x, y). A box convolution filter, B, which has coefficients equal to one inside a rectangular win- dow, and zero elsewhere is given by: w-1h-1 B(r, y,w, h) = ΣΣΤ+ i,y + ) i=0 j=0 where I(r, y) is the pixel intensity of image I at (x, y). We can speed up the computation of arbitrary sized box filters using recursion as described above. In this problem, you will derive the procedure to do this. (a) The function J at location (x,y) is defined to be the sum of the pixel values above and to the left of (x,y), inclusive: J(r, y) = - ΣΣ14.0 i=0 j=0 Formulate a recursion to compute J(r, y). Assume that I(r, y) = 0 if r <0 or y < 0. Hint: It may be…Given the following recursively defined set S: Basis: 0 € S and 7 € S Recursive rule: if x ES and y = S, then: • x+yЄS x-yes Prove that every element in S is divisible by 7.Given three sequences of length m, n, and p each, you are to design and analyze an algorithm to find the longest common subsequence (LCSS) for the three sequence. Is it possible to use dynamic programming to find the LCSS between the three sequences? If yes, provide recursive solution to the above problem. (Hint: We already designed dynamic programming algorithm for two sequences of length m and n in our class.)
- Boolean Satisfaction Problem Boolean Satisfiability Problem (SAT) (https://en.wikipedia.org/wiki/Boolean_satisfiability_problem) is one of the most important problems in Computer Science. SAT is a problem that has NP-Complete complexity, where the only way to solve the problem is to try all the possibilities and check which one is correct. [LO 1, LO 2, LO 3 & LO 4,] Briefly describe how you used Backtracking to solve the Boolean Satisfiability Problem. Note that your solution must have exponential complexity. [LO 1, LO 2, LO 3 & LO 4,] Briefly explain how you use Strongly Connected Component (SCC) to solve the special case of the Boolean Satisfiability Problem, namely 2-SAT (https://en.wikipedia. org/wiki/2-SAT) . This solution has linear complexity. Solve the Subparts A&B thank u NOTE LO1: Explain fundamental concept of analysis arithms. LO2: Apply algorithm techniques and methods. LO3: Solve a problem using specific algorithm. LO4: Compare several algorithm design…Memoization technique is one of the popular techniques that improve the performance of the recursive algorithms. When applied to a recursive problem how does it affect overall performance? Time complexity decreases and the space complexity increases Time complexity decreases and the space complexity decreases Time complexity increases and the space complexity decreases Time complexity increases and the space complexity increasesGroup scheduling Scheduling tasks to actors (people, CPUs, machines etc) is a problem that one encounters very often in practice. In this small exercise, we practice how to solve such a problem by using recursive problem solving. More specifically, we solve the following problem: We are organizing a course and have n� tutorial groups. To run the groups, we are hiring m� teaching assistants. Due to other responsibilities, an assistant is not necessarily able to teach all possible tutorial groups but has a set of groups that s/he can teach. We call this set of possible groups the preferences of the assistant.Is it possible to assign each tutorial group one assistant in a way that (i) all the assistants' preferences are respected, and (ii) each assistant teaches at most one tutorial group?Needless to say, this a very simplified version of the problem; in real life, some groups need more assistants, some assistants can teach more groups, consecutive group times for an assistant should be…
- Non-recursive loop based approaches are frequently used to tackle recursive problems. Give an example of how a developer decides whether to use a recursive or non-recursive solution in the end product.Algorithm problem w/ recurrence: Frying pancakes: a small pan can only hold two pancakes at a time. Each pancake needs to be fried on both sides. Frying one side takes 1 minute, no matter how many pancakes are on the pan. Consider this recursive algorithm: If n <= 2, fry the pancakes or the two pancakes together on each side. If n > 2, fry any two pancakes together on each side and then apply the same process recursively to the remaining n-2 pancakes. a. Set up and solve the recurrence for the amount of time this algorithm needs to fry n pancakes. b. Explain why this algorithm does not fry the pancakes in the minimum time for all n > 0. c. Give a correct recursive algorithm that executes the task in the minimum amount of time. > I was not sure how to start this. I have had trouble with recurrence in the past. Also from the work that I did do, I didn't know how there could be a better algorithm. Thanks in advanceConsider the following scenario in which recursive binary search could be advantageous. What would you do if you found yourself in such a situation? What is the first requirement that a recursive binary search must satisfy?
- Path: p Words:0 QUESTION 6 Draw the complete memoized recursive function tree for the Fibonacci Sequence using Dynamic Programming when n is 5. Example (where # is the current value of n in a small recursive function tree) f(#) f(#) f(#) TT T 3 (12pt) Arial Words:0 Path: p Save All A Click Save and Submit to save and submit. Click Saue All Answers to sove all ansuers.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.CPE 300 - Optimization Techniques Topic: GA Implementation Scenario: Suppose a genetic algorithm uses chromosomes of the form x = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as: f(x) = (a + b) − (c + d) + (e + f) − (g + h) and let the initial population consist of four individuals with the followingchromosomes: x1 = 6 5 4 1 3 5 3 2x2 = 8 7 1 2 6 6 0 1x3 = 2 3 9 2 1 2 8 5x4 = 4 1 8 5 2 0 9 4 Evaluate the fitness of each individual, showing all your workings, and arrange them in order with the fittest first and the least fit last. Perform the following crossover operations: One–point crossover, Two–point crossover, and uniform crossover.