25. The banker's algorithm is being run in a system with m resource classes and n proc- esses. In the limit of large m and n, the number of operations that must be performed to check a state for safety is proportional to manb. What are the values of a and b?
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- Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.A certain cat shelter has devised a novel way of making prospective adopters choose their new pet. To remove pet owners’ biases regarding breed, age, or looks, they are led blindfolded into a room containing all the cats up for adoption and must bring home whichever they pick up. Suppose you are trying to adopt two cats, and the shelter contains a total of N cats in one of only two colors: black or orange. is it still possible to pick up two black cats with probability ½, given that there is an even number of orange cats in the room? If so, how many cats should be in the room? How many black, how many orange?The Harvard robotics club has organized a Robothon. n robots are placed alongthe edge of a circular area at the middle of the OAT(open air theatre). Each robot will move along arbitrary tracksinside the circle while leaving behind a heat signature along its trail. However, they have beenprogrammed not to cross their own trail or the trail of another robot, neither will they ever moveout of the circle. In case a pair of robots i and j meet at any point, they are removed from the sceneand the club will pay a reward sum of M[i, j] to the owners of these robots. Note that some robotscan keep moving infinitely without ever meeting another one. Given the reward matrix M whereM[i, j] = M[j, i], design a polynomial time algorithm that determines the maximum money theclub might potentially end up spending. For this particular problem, give a very brief justificationof the recurrence. Give pseudo-code for a dynamic program which solves the recurrence efficiently Youdo not need to prove…
- Correct answer will be upvoted else downvoted. Computer science. You are given a grid a comprising of positive integers. It has n lines and m segments. Develop a framework b comprising of positive integers. It ought to have a similar size as a, and the accompanying conditions ought to be met: 1≤bi,j≤106; bi,j is a various of ai,j; the outright worth of the contrast between numbers in any nearby pair of cells (two cells that share a similar side) in b is equivalent to k4 for some integer k≥1 (k isn't really something similar for all sets, it is own for each pair). We can show that the appropriate response consistently exists. Input The primary line contains two integers n and m (2≤n,m≤500). Every one of the accompanying n lines contains m integers. The j-th integer in the I-th line is ai,j (1≤ai,j≤16). Output The output ought to contain n lines each containing m integers. The j-th integer in the I-th line ought to be bi,j.Correct answer will be upvoted else downvoted. Computer science. You are given three positive (more prominent than nothing) integers c, d and x. You need to track down the number of sets of positive integers (a,b) with the end goal that balance c⋅lcm(a,b)−d⋅gcd(a,b)=x holds. Where lcm(a,b) is the most un-normal various of an and b and gcd(a,b) is the best normal divisor of an and b. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Each experiment comprises of one line containing three integer c, d and x (1≤c,d,x≤107). Output For each experiment, print one integer — the number of sets (a,b) to such an extent that the above uniformity holds.Correct answer will be upvoted else downvoted. Computer science. You are given two integers n and k. You ought to make a variety of n positive integers a1,a2,… ,a to such an extent that the total (a1+a2+⋯+an) is distinguishable by k and greatest component in an is least conceivable. What is the base conceivable most extreme component in a? Input The primary line contains a solitary integer t (1≤t≤1000) — the number of experiments. The solitary line of each experiment contains two integers n and k (1≤n≤109; 1≤k≤109). Output For each experiment, print one integer — the base conceivable most extreme component in cluster a to such an extent that the aggregate (a1+⋯+an) is distinct by k.
- A hungry mouse wants to eat all four fruits in a maze such as the one below, in as few moves as possible.. At each turn the mouse can move any number of squares in one of the directions up, down, left or right, but it is not allowed to enter (or jump over) any walls (i.e., the black squares). Thus, the mouse moves just like a rook in chess. To eat a fruit, the mouse has to stop at that square. Assume that the maze has 4 fruits, and the size of b xh squares. 1. Give a suitable representatión of the states in this searching problem. 2. How many possible actions can the mouse perform at each move? (1.e., what is the branching factor?)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.…In a prison, there is a door b/w any pair of adjacent cells and one exit guarded by a guard G. One prisoner is a maniac M which kills anybody he can see when he enters a cell. If M returns to the cell with his victim, then he loses consciousness and stops. In the evening all inmates and the guard went to sleep in their cells. In the morning, maniac M is gone and all other prisoners with the guard were found dead in their cells. Show the route of the maniac.
- Correct answer will be upvoted else downvoted. Computer science. Assume you are living with two felines: An and B. There are n resting where the two felines normally rest. Your felines like to rest and furthermore like this load of spots, so they change snoozing spot every hour consistently: Feline A progressions its snoozing place all together: n,n−1,n−2,… ,3,2,1,n,n−1,… at the end of the day, at the main hour it's on the spot n and afterward goes in diminishing request consistently; Feline B changes its resting place all together: 1,2,3,… ,n−1,n,1,2,… all in all, at the primary hour it's on the spot 1 and afterward goes in expanding request consistently. The feline B is a lot more youthful, so they have a severe pecking order: An and B don't lie together. All in all, on the off chance that both cats'd prefer to go in spot x, the A has this spot and B moves to the following submit in its request (assuming x<n, to x+1, however on the off chance that x=n, to 1). Feline…Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BFive philosophers are sitting at a round table. In the center of the table is a bowl of rice. Between each pair of philosophers is a single chopstick. A philosopher is in one of the three states: thinking, hungry or eating. At various times, a thinking philosopher gets hungry. A hungry philosopher attempts to pick one of the adjacent chopsticks, then the other (not both at the same time). If the philosopher is able to obtain the pair of chopsticks (they are not already in use), then the philosopher eats for a period of time. After eating, the philosopher puts the chopsticks down and returns to thinking. Write a monitor for the dining philosopher’s problem.