7. (s) have a randomized algorithm that finds a solution to a problem with probability .01 every time I run it. (I can verify solutions easily, so if it fails, I can re-run). On average, how many times do I need to run the algorithm before I find a solution?
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- Artificial Intelligence - Adversarial Search 1. Consider the following three variants of minimax search: the simple version, alpha-beta search, anddepth-limited search, and consider the games of tic-tac-toe and chess. For the chess game, supposethat the Threefold Repetition Rule and the Fifty-Move Rule, and the similar rules if any, are notconsidered, i.e., the game will not terminate if the same position occurs multiple times. For eachcombination of minimax variant and game, answer the following question: can that minimax variantpossibly never terminate, in computing the best next move? Justify your answer.Find the maximum value of the following function F(x)=2x3 , using the genetic algorithm, performing two iterations.5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ S
- (b) Let n be an integer. Show that n if the sum of the digits of n is a multiple of 3,then n is a multiple of 3. You must do so by a direct proof. For this problem youmay assume that ∀a, b ∈ Z, ∀m ∈ Z+, (a ≡ x (mod m) ∧ b ≡ y (mod m)) ⇒ ab ≡ xymod m. *Solve by direct proof*I have a hand of five cards, n of which are aces. An observation is: I shuffle the cards, pick one at random, and show it to you. You are estimating n by counting the total number of aces (let's denote it k) in m observations, and then computing 5k m You may assume that 1Python answer only. Correct answer will upvoted else downvoted. It is the ideal opportunity for your very first race in the game against Ronnie. To make the race intriguing, you have wagered a dollars and Ronnie has wagered b dollars. Yet, the fans appear to be frustrated. The fervor of the fans is given by gcd(a,b), where gcd(x,y) means the best normal divisor (GCD) of integers x and y. To make the race seriously invigorating, you can perform two kinds of activities: Increment both an and b by 1. Diminishing both an and b by 1. This activity must be performed if both an and b are more noteworthy than 0. In one action, you can play out any of these activities. You can perform self-assertive (potentially zero) number of moves. Decide the greatest energy the fans can get and the base number of moves needed to accomplish it. Note that gcd(x,0)=x for any x≥0. Input The principal line of input contains a solitary integer t (1≤t≤5⋅103) — the number of experiments.…
- SUCCESSIVE-OVER-RELAXATION Method TROUBLESHOOTING: Fix the errors in the code below and run the script with your modified code and screenshot your output and codes with answer function [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % Solves Ax = b by Gauss-Seidel method with relaxation. % USAGE: [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % INPUT: % func = handle of function that returns improved x using % x = starting solution vector % maxIter = allowable number of iterations (default is 500) % epsilon = error tolerance (default is 1.0e-9) % OUTPUT: % x = solution vector % numIter = number of iterations carried out % omega = computed relaxation factor if nargin < 4; epsilon = 1.0e-9; end if nargin < 3; maxIter = 500; end k = 10; p = 1; omega = 1; for numIter = 1:maxIter xOld = x; x = feval(func,x,omega); dx = sqrt(dot(x - xOld,x - xOld)); if dx < epsilon; return; end if numIter == k; dx1 = dx; end if numIter == k + p omega = 2/(1 + sqrt(1 -…Correct answer will be upvoted else downvoted. Computer science. There is an exhibit a1,a2,… ,an of n positive integers. You should isolate it into a negligible number of ceaseless portions, to such an extent that in each section there are no two numbers (on various positions), whose item is an ideal square. Also, it is permitted to do all things considered k such activities before the division: pick a number in the exhibit and change its worth to any certain integer. However, in this form k=0, so it isn't significant. What is the base number of consistent fragments you should utilize in the event that you will make changes ideally? Input The primary line contains a solitary integer t (1≤t≤1000) — the number of experiments. The principal line of each experiment contains two integers n, k (1≤n≤2⋅105, k=0). The second line of each experiment contains n integers a1,a2,… ,an (1≤ai≤107). It's surefire that the amount of n over all experiments doesn't surpass 2⋅105.…1(a). For an M/M/1 queuing system, write your own function in R to compute andoutput the:1. long-run probability po,p1,…,pn of there being 0,..,n people in the system.2. the values L, Lq, W, Wq, and Wse. The function should return elements with the names probs (vector of po,…,pn), L, Lq, W,Wq, and Wse (does not have to be in this order) The function should take as inputs, lambda (arrival rate), mu (service rate), and n (thenumber of people to compute probabilities for 0,…,n) Note: you are to code the computations for the above on your own, so none of the functionsin the queueing package are to be used. 1(b). Using your function from 1(a), find the values (b)-(f) in the Queuing Theory(M_M_1).
- An n x n matrix is called a positive Markov matrix if eachelement is positive and the sum of the elements in each column is 1. Write thefollowing method to check whether a matrix is a Markov matrix:public static boolean isMarkovMatrix(double[][] m) Write a test program that prompts the user to enter a 3 x 3 matrix of doublevalues and tests whether it is a Markov matrix. Here are sample runs: Enter a 3−by−3 matrix row by row:0.15 0.875 0.375 ↵Enter0.55 0.005 0.225 ↵Enter0.30 0.12 0.4 ↵EnterIt is a Markov matrix Enter a 3−by−3 matrix row by row:0.95 −0.875 0.375 ↵Enter0.65 0.005 0.225 ↵Enter0.30 0.22 −0.4 ↵EnterIt is not a Markov matrixIn R-Studio Problem 2. Find a large set of integers (with at least 10000 observations) representing a sample drawn from real life (i.e., do not generate the numbers using some random number generator). First, explain what the integers correspond to in real life. Then, investigate the distribution of the integers, and also the first and last digits of the integers in this sample (For example, if the data has [34 65], plot the distribution of these numbers and also distribution of [3,6] and [4 ,5] separately). Does any of these digits follow a uniform distribution? Is this expected? If one of them does not follow a uniform distribution, what distribution does it follow? Can you explain why? [You can analyze the image age dataset provided by IMDB Wiki, which contains the ages of actors and actresses whose photos are present in the IMDB database. The data contains 459868 age values in years, ranging from 1 to 99 years.]Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux. a) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do? (b) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory. In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.] (c) Gradient ascent search is prone to local optima just like hill climbing.…