in python One chose to visit his relatives. There are s animals and n animal pens on the him. For utility reason, creature pens are built in one line. Uncle let Theofanis know that a ranch is fortunate on the off chance that you can disseminate all animals in all pens so that there are no unfilled pens and there is something like one ceaseless section of pens that has precisely k animals altogether. In addition, a ranch is great in case it's fortunat

in python One chose to visit his relatives. There are s animals and n animal pens on the him. For utility reason, creature pens are built in one line. Uncle let Theofanis know that a ranch is fortunate on the off chance that you can disseminate all animals in all pens so that there are no unfilled pens and there is something like one ceaseless section of pens that has precisely k animals altogether. In addition, a ranch is great in case it's fortunat

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 5P

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When Bobby’s friends visit her on the farm, she likes to show them around. Thefarm consists of n fields numbered 1, 2, . . . , n, the first of which contains her house and the n-th of whichcontains the big barn. A total of m directed paths connect the fields. The i-th path is from field ui to fieldvi, and has a nonzero length wi.1 Suppose there are k friends coming today. To show off the farm in the best way, Bobby designs a tourfor each friend that starts at her house, potentially travels through some fields, and ends at the barn.Bobby wants the total length of the k tours to be as short as possible, where the length of a tour is thetotal length of paths in the tour. However, she doesn’t want any two friends to share any path. That is,for any two friends, their tours should not have any common paths (but they can travel through the samefields). Write an LP that can calculate the shortest total length of k tours that satisfies Bobby. You canassume that at least one feasible…
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.…
Show that it is undecidable, given the source code of a program Q, to tell whether ornot any of the following is true:(i) Q halts on input 0.(ii) Q is total – that is, Q(y) halts for all y.(iii) Q(y) = true for all y.(iv) The set of y on which Q halts is finite.(v) There is a y such that Q(y) = y.(vi) Given a second program R, Q is equivalent to R. That is, even though Q and Rhave different source codes, they compute the same partial function – for all y,either Q(y) and R(y) both halt and return the same answer, or neither halts.Prove each of these by reducing Halting to them. That is, show to how convert aninstance (P, x) of Halting to an instance of the problem above. For instance, you canmodify P’s source code, or write a new program that calls P as a subroutine. Eachof these is asking for a Turing reduction; your reduction does not necessarily have tomap yes-instances to yes-instances and no-instances to no-instances – all that mattersis that if you could solve the problem, then…
Write a python program based on the discussion we had on the last day of class, to train a network with two hidden layers each with 5 neurons. Finish the gradient computation we did in class, and implement a steepest decent search for a network which minimizes the cost function. Once you believe that your network is trained, compute the value of n(1, 1) and see what you get. Bonus: If you easily get this to work, then try to generalize to K neurons in each of the two hidden layers. Does the training work better with more neurons?
Suppose you’re consulting for a bank that’s concerned about fraud detection, and they come to youwith the following problem. They have a collection of n bank cards that they’ve confiscated, suspectingthem of being used in fraud. Each bank card is a small plastic object, containing a magnetic stripe withsome encrypted data, and it corresponds to a unique account in the bank. Each account can have manybank cards corresponding to it, and we’ll say that two bank cards are equivalent if they correspond to thesame account.It’s very difficult to read the account number off a bank card directly, but the bank has a high-tech “equivalence tester” that takes two bank cards and, after performing some computations, determines whether theyare equivalent.Their question is the following: among the collection of n cards, is there a set of more than n/2 of themthat are all equivalent to one another? Assume that the only feasible operations you can do with the cardsare to pick two of them and plug them…
Problem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Prove that the coin changing problem exhibits optimal substructure. Design a recursive backtracking (brute-force) algorithm that returns the minimum number of coins needed to make change for n cents for any set of k different coin denominations. Write down the pseudocode and prove that your algorithm is correct.
We have been working extensively with the predicate "eventually greater than" defined on pairs of functions f of g. Which of the following is equivalent to f(x) is not eventually greater than g(x)? (Select all that apply) Group of answer choices ¬((∃x0)(∀x)(x>x0→f(x)>g(x))) ((∃x0)(∀x)(x>x0→f(x)≤g(x))) (∀x)(∃x0)(x0>x→f(x0)≤g(x0)) (∀x)(∃x0)(x0>x→f(x0)≤g(x0))
PLEASE HELP ME. kindly show all your work 1. Prove that∀k ∈ N, 1k + 2k + · · · + nk ∈ Θ(nk+1). 2. Suppose that the functions f1, f2, g1, g2 : N → R≥0 are such that f1 ∈ Θ(g1) and f2 ∈ Θ(g2).Prove that (f1 + f2) ∈ Θ(max{g1, g2}). Here (f1 + f2)(n) = f1(n) + f2(n) and max{g1, g2}(n) = max{g1(n), g2(n)}. 3. Let n ∈ N \ {0}. Describe the largest set of values n for which you think 2n < n!. Use induction toprove that your description is correct.Here m! stands for m factorial, the product of first m positive integers. 4. Prove that log2 n! ∈ O(n log2 n). Thank you. But please show all work and all steps
We consider certain strings of length 6 over the alphabet S = {A,B,C}. We require that the string contains exactly two As, and exactly two B's, and exactly two C's. How many such strings are there? That is, how many strings of length 6 over the alphabet {A,B,C} contains exactly two A's, two B's and two C's?