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Q) Propose a simple
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- Weighted Intervals Problem EXAMPLE:Suppose we have the following weighted intervals. start finish weight 11 14 4 10 13 5 9 11 5 11 14 3 8 9 2 To solve the problem, we start out by sorting the intervals by finish time. This gives us the following. start finish weight 8 9 2 9 11 5 10 13 5 11 14 4 11 14 3 Next we calculate the p-values. P(j) = k where interval k is the last interval prior to interval j in the list below which does not conflict with interval j, or P(j) = 0 if all intervals prior to interval j conflict with it. # start finish weight P 1 8 9 2 0 2 9 11 5 1 3 10 13 5 1 4 11 14 3 2 5 11 14 4 2 Finally, we use the formula OPT(j) = max{OPT(j-1), weight(j)+ OPT(P(j))} to fill in the OPT value for each j. (The…Q1 The periodic function sin(2x) has multiple roots between x values of -5π and 5π. If xL = -15 and xU = 15, which of the following statements is true using a bracketed method? Select one: a. All roots will be returned b. The middle root will be returned c. The chosen bracket is invalid for bracketed methods d. A single root will be returned e. The algorithm will be stuck in an infinite loop Q2 Consider x and y to represent data points (xi,yi), where i = 1, 2, 3, … n. What is the length of pafter running the following command? p = polyval(x,y) Select one: a. n b. n - 1 c. n + 1 d. Empty variable e. 1 Q3 Consider a system of linear equations in the form of AX = B, where X is the unknown vector. Which of the following can be used to solve for X? Select one: a. X = A\B b. X = B./A c. X = inv(B)*A d. X = inv(A)./B e. X = B\AOverview One of the oldest methods for computing the square root e of a number is the Babylonian Method e. The Babylonian Method uses an iterative algorithm to make successively more accurate estimates of a number's square root. The algorithm stops iterating when the estimate shows no further sign of improvement, or when the estimate is within some acceptable margin of error. The acceptable margin of error is often called an epsilon. Assuming that you need to solve for the square root of x, the algorithm works as follows. 1. Choose an epsilon value that determines how close your solution should be to the actual square root value before you decide it is "good enough." Because this assignment asks you to solve for the square root to three decimal places, we can safely set the epsilon value to 0.0001 (four decimal places). This guarantees that our solution will be accurate to the precision we need to display to the screen. 2. Choose an initial estimate e for the square root of x. An easy…
- Q2. The following algorithm returns the product of two numbers, a and b. The parameters x and y are natural numbers. First, prove the correctness of the algorithm. Then, analyze the time complexity of the algorithm in the worst case scenario. function mult (a, b) if b = 0: return 0 else if b is odd: return (mult (2a, b/2 ) +a) else: return (mult (2a, b/2 ) )Quadratic Root Solver For a general quadratic equation y = ax? + bx + c, the roots can be classified into three categories depending upon the value of the discriminant which is given by b2 - 4ac First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant is a positive value, there are two roots which are real and unequal. The roots can be computed as follows: -b+ Vb? – 4ac 2a Further, if the discriminant is a negative value, then there are two imaginary roots. In this case, the roots are given by b ь? - 4ас 2a 2a Programming tasks: A text file, coeff.txt has the following information: coeff.txt 3 4 4 4 1 4 Each line represents the values of a, b and c, for a quadratic equation. Write a program that read these coefficient values, calculate the roots of each quadratic equation, and display the results. Your program should perform the following tasks: • Check if the file is successfully opened before reading • Use loop to read the file from main…True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).
- Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You have a knapsack with the limit of W. There are likewise n things, the I-th one has weight wi. You need to place a portion of these things into the knapsack so that their all out weight C is half of its size, however (clearly) doesn't surpass it. Officially, C ought to fulfill: ⌈W2⌉≤C≤W. Output the rundown of things you will place into the knapsack or establish that satisfying the conditions is unimaginable. In case there are a few potential arrangements of things fulfilling the conditions, you can output any. Note that you don't need to expand the amount of loads of things in the knapsack. Input Each test contains various experiments. The principal line contains the number of experiments t (1≤t≤104). Depiction of the experiments follows. The main line of each experiment contains integers n and W (1≤n≤200000, 1≤W≤1018). The second line of each experiment…Please solve max 30 minutes thank u Boolean Satisfaction Problem Boolean Satisfiability Problem (SAT) (https://en.wikipedia.org/wiki/Boolean_satisfiability_problem) is one of the most important problems in Computer Science. SAT is a problem that has NP-Complete complexity, where the only way to solve the problem is to try all the possibilities and check which one is correct. [LO 1, LO 2, LO 3 & LO 4,] Briefly explain how you use Strongly Connected Component (SCC) to solve the special case of the Boolean Satisfiability Problem, namely 2-SAT (https://en.wikipedia. org/wiki/2-SAT) . This solution has linear complexity. NOTE LO1: Explain fundamental concept of analysis arithms. LO2: Apply algorithm techniques and methods. LO3: Solve a problem using specific algorithm. LO4: Compare several algorithm design methodsDesign a top-down algorithm (based on dynamic programming and recursion; i.e. memory function) for checking the existence of a winning strategy for the “Rocks” game. Hints: • Give it the name: RocksMF(n,m) where n,m are the number of rocks on the two piles • Use recursion to call the algorithm itself to solve smaller subproblems • Use a global variable for the two-dimensional table
- 9. Voting Suppose that the votes of n people for different candidates (where there can be more than two candidates) for a particular office are the elements of a sequence. A person wins the election if this person receives a majority of the votes. * Devise a divide-and-conquer algorithm that determines whether the two candidates who received the most votes each received at least n/4 votes and, if so, determine who these two candidates are. (NOTE: Please elaborate and explain briefly and please do not provide or copy answer from the internet or from chegg.)Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given an arrangement an of length n comprising of integers from 1 to n. The grouping may contain duplicates (for example a few components can be equal). Track down the number of tuples of m=3 components with the end goal that the maximum number in the tuple varies from the base by close to k=2. Formally, you want to view as the number of triples of lists i<j<z with the end goal that max(ai,aj,az)−min(ai,aj,az)≤2. For example, on the off chance that n=4 and a=[1,2,4,3], there are two such triples (i=1,j=2,z=4 and i=2,j=3,z=4). In the event that n=4 and a=[1,1,1,1], all four potential triples are suitable. Input The principal line contains a solitary integer t (1≤t≤2⋅105) — the number of experiments. Then, at that point, t experiments follow. The principal line of each experiment contains an integer n (1≤n≤2⋅105) — the length of the succession a. The following line contains n…Question 9 Evaluate and calculate the worst case running time for the following algorithm, show the steps Full explain this question