How much time is required to compute f(x) = Eo a;x: a. Using a simple routine to perform exponentiation?
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![How much time is required to compute f(x) = Eo 4;x':
a. Using a simple routine to perform exponentiation?
b. Using the routine in Section 2.4.4?
2.13
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- Start with a pile of n stones and successively split a pile into two smaller piles until each pile has only one Each time a split happens, multiply the number of stones in each of the two smaller piles. (For example, if a pile has 15 stones and you split it into a pile of 7 and another pile of 8 stones, multiply 7 and 8.) The goal of this problem is to show that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2. Using strong mathematical induction, prove that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2.A matrix's trace is equal to its trace transposed. The diag method of Numpy may be used to extract the elements along the diagonal of a square matrix. Retrieving data from diagonals above or below the primary diagonal is possible using the optional parameter k. The call trace, just like in Python programming, may be used to get a matrix's trace.Maclaurin series are a type of Mathematic series expansion in which all terms are nonnegative real powers of the variable. The Maclaurin series expansion for sin(x) is given by the following formula that is valid for all real values of x such that x is in radians (Note that: radians(x) = x X 1/180): sin(x) = x - 3! 5! Implement a Java program to compute the value of Maclaurin series expansion for sin(x) where x is a nonnegative real value according to the following: a. Write a java method named Factorial that takes as an argument an integer value n and returns the mathematical factorial n! of n as a long value such that: n! = n x (n – 1) x (n – 2) ... × 2 x 1 b. In the main method: i. Ask the user to enter the value of the angle x to be calculate in the Maclaurin series expansion for sin(x) as given above. x Should be entered in degrees, i.e., 0° < x< 360° and then converted into radians using the formula: (radians(x) = x × 1/180). ii. Ask the user to enter the number of terms to be…
- Code in Matlab. Urgent Do itPlease solve this code.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…
- make a python code for this problem using jupyter notebookBottom: Given b, set the low-order b bits of x to 1; the others to 0. For example, if b is 3, x should be 7. Pay special attention to the edge cases: if b is 32 x should be −1; if b is 0 x should be 0. Do not use - in your solution. Write code in Java. Provided input(s): b Permitted: 40 operations (may use !, ~, +, <<, >>, &, ^, |) Hint: The obvious solution ~(0xFFFFFFFF << b) won’t work. Bit shifts always do a modulo on their right-hand operand, so a << b does the same thing as a << (b % (8*sizeof(a)). Thus, << 32 and << 0 do the same thing.Python problem: Replace of the ten Xs in the simple sum shown below with a digit drawn without-replacement from the set of 10 digits [ 1,1,2,2,4,4,7,7,8,9 ] (the duplicates are intended) so that the sum is correct. Each digit is used exactly one time in each candidate replacement. X5XX + XXX3 = XX6XX Note There are 10! = 3,628,800 candidate permutations to check and 96 of the candidate permutations qualify as solutions. Of those 96 solutions, only 96 ÷ (2!×2!×2!×2!) = 6 are unique soultions. Sample Output: 4524 + 8173 = 12697 4574 + 8123 = 12697 8524 + 4173 = 12697 8524 + 9123 = 17647 8574 + 4123 = 12697 9524 + 8123 = 17647
- PythonGiven an integer N and a base X, the task is to find the minimum number of operations required to represent N as a sum of the distinct powers of X. In each operation, you can either increment or decrement N. You are allowed to make the given operation any number of times Examples: Input: N = 7, X = 3 Output: 3.Problem: In this problem, we would like to implement the algorithm to calculate digit sum of a given natural number that can be used in detecting errors in message transmission or data storage.For example:N = 103509, the digit sum = 1 + 0 + 3 + 5 + 0 + 9 = 18.N = 9512, the digit sum = 9 + 5 + 1 + 2 = 17Exercise 1: Write a pseudo-code to solve the above problem using Iteration. Write a program from the pseudo-code and solve the Problem using Iteration. Calculate the complexity. Justify your answer. Exercise 2: Write a program to solve the Problem using Recursion (with Iteration if necessary). Calculate the complexity. Justify your answer. Exercise 3: Write a program to solve the Problem using a List data structure. Note: Elements in List data structure can be used to store a digit of the given natural number.
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