Try to compute gcd or lcm ( gcd(9, 6) or lcm(9,6) ) by the following algorithm, support it with a programming code

The code shows an implementation of the Rabin-Karp algorithm in Python. What is the best and worst case of this algorithm? Explain with an example for each case, without going into mathematical details

The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S = [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Let S be a sequence with ten distinct integers. Prove by Contradiction that there must exist an increasing subsequence of length 4 (or more) or a decreasing subsequence of length 4 (or more). Hint: for each integer k in the sequence you found in the first part, define the ordered pair (x(k), y(k)), where x(k)…

A piece of code implementing a recursive algorithm has been produced, and a student has analysed the recurrences. They have produced the recurrence equations as shown below: T(n) = T(n − 2) + 2(n − 2) + C₁ T(2) = C₂ So the recursive algorithm features a base case when the size of the problem is n = 2. The values of c₁ and c₂ are constants. You should assume the initial value of n (the size of the problem) is divisible by 2. Determine the running time complexity of this recursive algorithm. your analysis should be as complete as possible. To get an idea of how to perform a complete analysis, refer to the example recursive algorithm analysis on Canvas. You can verify your analysis by modelling the recurrence equations in a program like Excel or MATLAB. Your answer must include: (a) Evidence of at least two cycles of substitutions to establish the running time function T(n). (b) A clear statement of the generalisation of that pattern to k iterations of the recursive step. (c) A statement…

suppose that n is not 2i for any integer i. How would we change the algorithm so that it handles the case when n is odd? I have two solutions: one that modifies the recursive algorithm directly, and one that combines the iterative algorithm and the recursive algorithm. You only need to do one of the two (as long as it works and does not increase the BigOh of the running time.)

Consider a divide-and-conquer algorithm that calculates the sum of all elements in a set of n numbers by dividing the set into two sets of n/2 numbers each, finding the sum of each of the two subsets recursively, and then adding the result. What is the recurrence relation for the number of operations required for this algorithm?   Answer is f(n) = 2 f(n/2) + 1. Please show why this is the case.

A graph is a collection of vertices and edges G(V, E). A weighted graph has weights (numbers, etc.) on every edge. A multigraph can have more than one edges between any vertices. Explain why a person should use a weighted graph instead of a multigraph. Give examples.   An adjacency matrix might be a better choice for speeding up a program, however, it consumes huge memory for large graphs. How this situation can be improved? What programming constructs better suit graph representation? Explain with example

Please do not give solution in image format thanku Implement the following recursively using sudo code:   Suppose an elevator which is on a floor on n. For this elevator to go from the nth floor to the base(ground) floor, it should go to every floor under the nth floor.   Let's consider an elevator on the 4th floor.   This elevator 1st comes on the third(3rd) floor.   4th-> 3rd then   3rd-> 2nd then   2->1 and   next 1->0(ground floor)   The recursive equation defined is F(n)=1+F(n-1)

Calculate the result of f(n) using recursion. Depict the recursive tree and demonstrate the result calculation for the following recursive functions. i) f(n)= n * f(n-1 ), where f(0) = 1 calculate the result for N = 8. ii) f(n) = f(n-1)+ f(n-2) , where f(0) = 1, f(1)=1. Calculate the result for N = 6.