Suppose you are given two sets A and B, each containing n positive integers. Let a; be the i th element of set A, and let b; be the i th element of set B. You would like to receive maximum payoff [I=1a;". bi Give an algorithm that will maximize your payoff. Explain that how/why your algorithm maximizes the payoff, and analyze the running time.
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- Indicate whether each of the following statements is true (T) or false (F): 1. (∀x)(A(x)&D(x)→B(x)) is equivalent to (∀x) (¬B(x)→( ¬D(x)→A(x))) 2. ¬(∀x)(A(x)→(B(x) V C(x))) is equivalent to (∃x)(A(x)& ¬B(x)& ¬C(x)) 3. ¬(∃x)(A(x)→(B(x)&C(x))) is equivalent to (∀x)(A(x)&(B(x)→ ¬C(x)))Imagine you have a strip of highway connecting n towns in a line. Each town is being evaluated as a possible location for building a cellular phone tower. Each cell tower will provide coverage to the town it’s built in, but no other towns. However, due to the way that cell towers interfere with one another, it’s not possible to build cell phone towers in two adjacent towns.Describe an algorithm that, given the populations of each of the towns, reports the maximum number of people you can provide cell phone coverage to, subject to the restriction that no two adjacent towns can each have cell towers in them. Use dynamic programming to dramatically speed up your solution over a na ̈ıve recursive algorithm.my mobile number is 741367590
- You are given +ve integers a and b, let assume that numerator and denominator a/b is special if and only if it's like m/(m+1) where m is any +ve integer. Suppose you are given an integer X. Find the number of pairs of integers i, j such that 1< i, jResearchers are trying to use machine learning algorithms to make redistricting more equitable and efficient. For a sample of six zones (labelled Z1-Z6), each zone can be described by at least one letter (A-F), which is a qualitative measure of that zone. One part of the algorithm is to output a potential district layout, which can only happen if each zone can be matched to exactly one letter.Consider the following descriptions for one sample of six zones: Z1 matches B or D; Z2 matches C, E, or F; Z3 matches A or F; Z4 matches B or D; Z5 matches C or F; and Z6 matches D.(a) Draw the bipartite graph that models the zones (Z1-Z6) and the letters they match (A-F).(b) Use Hall’s theorem to determine if algorithm will be able to successfully create a district layout.Let Ax = {a,b,...,z,—}, |Ax| = 27, denote alpahabet of letters in English text where - represents the space character between words. Let Px = {P₁, P2,..., P27} denote the probability of letters. 1) Estimate pi, by parsing the text "All Systems Red' by Martha Wells. To do this you have to parse the letters in the book and form a character vector x = = [1, 2,..., TN] where N is the number of letters in the book. (Turn all uppercase letters into lowercases and ignore the characters that are not in Ax). You may use Matlab or Python. Then you can estimate p; by its frequency in the text #(x₁ = ai) N where #(i = a;) denotes the number of times ï¿ = a¿ in x. Pi = (1)You solve a non-singular system of 10,000 linear equations with 10,000 unknowns using the Gauss-Jordan algorithm without pivoting with single precision numbers and arithmetics on a computer that natively can do single precision operations very fast, but can operate in double and half precision as well. Your solution has a residual infinity-norm that is unacceptably large. In which order should you apply the following strategies to lower the residual norm? If a strategy is not / no longer helpful, do not list it as an option. a) use half precision numbers and arithmetics instead of single precision; b) use double precision numbers and arithmetics instead of single precision; c) use partial pivoting; d) use pivoting when encountering a zero in the pivot position.Josefine and her friends has invented a new game called Pillar Jumpers. In this game, a sequence of N pillars of non decreasing heights are placed next to each other. The player starts on the first pillar, and the target is to reach the la pillar in at most J jumps. The player has a certain jump strength S that determines how far he can jump. Let h; be t height of the i'th pillar for i e [1...N). The player can jump from pillar i to j iff. iProblem1Given a value `value`, if we want to make change for `value` cents, and we have infinitesupply of each of coins = {S1, S2, .. , Sm} valued `coins`, how many ways can we make the change?The order of `coins` doesn't matter.For example, for `value` = 4 and `coins` = [1, 2, 3], there are four solutions:[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3].So output should be 4. For `value` = 10 and `coins` = [2, 5, 3, 6], there are five solutions: [2, 2, 2, 2, 2], [2, 2, 3, 3], [2, 2, 6], [2, 3, 5] and [5, 5].So the output should be 5. Time complexity: O(n * m) where n is the `value` and m is the number of `coins`Space complexity: O(n)""" def count(coins, value): """ Find number of combination of `coins` that adds upp to `value` Keyword arguments: coins -- int[] value -- int """ # initialize dp array and set base case as 1 dp_array = [1] + [0] * value.. (+.Given a rod of length n inches and an array of prices that contains prices of all pieces of size smaller than n. Determine the maximum value obtainable by cutting up the rod and selling the pieces. For example, if length of the rod is 8 and the values of different pieces are given as following, then the maximum obtainable value is 22 (by cutting in two pieces of lengths 2 and 6) length 1 2 3 4 5 6 7 8 price | 1 5 8 9 10 17 17 20 And if the prices are as following, then the maximum obtainable value is 24 (by cutting in eight pieces of length 1 Please provide the solution in the assembly programming language and please use both recursion and dynamic programing method to solve the problem.Write a program to find the solution to Maxone problem (You want to maximize the number of ones) using agenetic algorithm where the population size is 2000 and each chromosome is 20 genes long. Use a mutationprobability of 0.02 and a cross-over probability of 0.5. Make separate functions for different components of thegenetic algorithm.Given is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).SEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. 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