Q1. GCD-Euclidean Algorithm Execute the Euclidean Algorithm to compute the greatest common divisor of the numbers: 1050 317 Show the steps of the algorithm. For numbers X and Y (X> Y), each step should be in the form Answer: x=qxY+r (0≤r
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- The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5Design an algorithm to find the kth number such that the only prime factors are 3, 5, and 7. Note that 3, 5, and 7 do not have to be factors, but it should not have any other prime factors. For example, the first several multiples would be (in order) 1, 3, 5, 7, 9, 15, 21.Correct answer will be upvoted else downvoted. Computer science. single activity, you should supplant each digit d of the number with the decimal portrayal of integer d+1. For instance, 1912 becomes 21023 in the wake of applying the activity once. You need to find the length of n subsequent to applying m tasks. Since the appropriate response can be exceptionally enormous, print it modulo 109+7. Input The main line contains a solitary integer t (1≤t≤2⋅105) — the number of experiments. The main line of each experiment contains two integers n (1≤n≤109) and m (1≤m≤2⋅105) — the underlying number and the number of activities. Output For each experiment output the length of the subsequent number modulo 109+7.
- Artificial Intelligence - Local Search Starting from a randomly generated state of the 15-puzzle game (https://en.wikipedia.org/wiki/15_puzzle), steepest-ascent hill-climbing (the vanilla version of hill-climbing search) gets stuck 76% of the time, i.e., solving only 24% of problem instances. But it works very quickly, i.e., it takes just 6 steps on average when it succeeds and 5 steps when it gets stuck. In contrast, if sideways moves are allowed, this raises the percentage of problem instances solved by hill-climbing from 24% to 81%, with the success at a cost: the algorithm averages roughly 7 steps for each successful instance and 32 steps for each failure. Now suppose that we are implementing random-restart hill climbing (i.e., if a search fails, it keeps to try, and try, until it gets a success) by the following two versions: one uses vanilla steepest-ascent hill climbing, and the other one uses hill climbing with sideways moves. Can you please tell which version of…Algorithm design with sorting. Each of n users spends some time on a social media site. For each i = 1, . . . , n, user i enters the site at time ai and leaves at time bi ≥ ai. You are interested in the question: how many distinct pairs of users are ever on the site at the same time? (Here, the pair (i, j) is the same as the pair (j, i)).Example: Suppose there are 5 users with the following entering and leaving times: Then, the number of distinct pairs of users who are on the site at the same time is five: these pairs are (1, 2), (1, 3), (2, 3), (4, 6), (5, 6). (Drawing the intervals on a number line may make this easier to see).(a) Given input (a1 , b1),(a2 , b2), . . . ,(an, bn) as above in no particular order (i.e., not sorted in any way), describe a straightforward algorithm that takes Θ(n2)-time to compute the number of pairs of users who are ever on the site at the same time, and explain why it takes Θ(n2)-time. [We are expecting pseudocode and a brief justification for its…Algorithm 6 The greatest common divisor sequential algorithm
- 1. a.An algorithm can be specified in various ways. Identify and explain four ways in which an algorithm can be specified. b. (b). Two algorithms A, B sort the same problem. When you go through each algorithm and break them down into their primitive operations, each can be represented as follows:A = 2n7 + 100n4 + 26n + 50 B = 7n4 + 22n2 + nlogn + 200For very large values of n, which of the algorithms A or B will runin the shortest time to solve the problem and why? (c). Two Computer Science students, Priscilla and Julius, are discussing how to compare two algorithms for solving a given problem. Priscilla suggests that they should use the execution times of the algorithms as criterion; but Julius insists that they should use the number of statements the algorithms execute as criterion. (i). Discuss the reasons why both criteria they are considering are not good for comparing algorithms.(ii). Recommend an ideal solution/criterion that they should rather use for comparing algorithmsPython Algorithm Question (similar to celebrity Python problem). Having trouble implementing the algorithm. Here's the question: Let’s say you’re going to invite some people to a party. You’re considering n friends, but you knowthat they will only have a good time if each of them knows at least k others at the party. (Assume that if A knows B, then B automatically knows A.) Solve your problem by designing an algorithm for finding the largest possible subset of your friends where everyone knows at least k of the others, if such a subset exists. To help you get started I’ve made a graph of “my friends”: G={'Rachel':['Ross','Monica'], 'Ross':['Rachel','Monica'], 'Monica':['Rachel','Ross'], 'Jon Snow':['Daenerys','Sansa','Arya'], 'Daenerys':['Jon Snow','Sansa','Arya','Khal Drogo'], 'Sansa':['Jon Snow','Daenerys','Arya'], 'Arya':['Jon Snow','Daenerys','Sansa'], 'Khal Drogo':['Daenerys'], 'Cersei':['Jaime'], 'Jaime':['Cersei'], 'Bart':['Milhouse'], 'Milhouse':['Bart','Lisa'],…37. Algorithms X and Y each solve the same problem, but X always runs faster. Which assertion applies for the algorithms? A.Algorithm Y is incorrect. B.Algorithm X is more time-efficient than Y. C.Algorithm Y is more time-efficient than X.
- Alice wants to send Bob her account number for his dining dollars. Bob’s account number is 24. Bob wants to encrypt her account number using the RSA algorithm scheme as evil Eve wants to steal her money to buy M&Ms. Bob chooses two prime numbers, 23 and 37, and uses them to compute the number m. Bob then computes the number e and the number d by using things he knows about the number m and its relationship to e. Bob sends the number e and the number m to Alice and she uses them to encrypt her number A and obtains the number C. C is the encrypted version of her code. Alice sends the number C to Bob, and then Bob uses the number d to decrypt Alice’s message. Using this information, encrypt and decrypt the message to show that the RSA algorithm works, then in a few words explain what makes the algorithm secure if the key for encrypting is always public.i. Using the graph below, implement the Breadth First Search algorithm considering the final state is eight(8) and the initial state is five(5) using the python programming language. N.b Kindly add comments to your code ii.. Descriibe in summary how the algorithm was implemented.1. Design an algorithm to find the weighted sum of four test scores (https://en.wikipedia.org/wiki/Weight_function). Assume that the weights have been accurately calculated in advance such that their sum equals one. Your algorithm must-read in the four test scores and four corresponding weights in the following order: score1 weight1 score2 weight2 score3 weight3 score4 weight4 Write your algorithm such that it can be run with any set of data values. However, you can test your algorithm on the following sample data to verify that the result is 70: 90 0.10 80 0.20 70 0.30 60 0.40 2. Write an algorithm that prompts the user for the radius, in inches, and price of a pizza, and then reads in those values. Finally, have the algorithm compute and output the pizza’s cost per square inch. 3. Sports exercise advisor algorithm. In this algorithm you will start out with a temperature value in Celsius, so you do not need to ask the user for it. First, convert the temperature to Fahrenheit.…
