An algorithm was introduced for finding integers a, b for any m, n where m, n are positive such that am+bn = gcd(m, n). Implement this algorithm as a Python program

given %matplotlib inline import numpy as np from matplotlib import pyplot as plt from math import sin, cos, exp, pi, sqrt import math   answer in python

Write an efficient algorithm for the following problem (either pseudocode or java), and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem will be on repeat numbers input will be ARRAY[1,2, ... , n] number of positive numbes. Output will any one number that is repeated more than n/3 times. for example, if you have [1,1,2,2,2,1], since n = 6 and n/3 = 2, both 1 and 2 showed up more than n/3 times. the output will be either 1 or 2 (just one of the values are required)   if you have [1,1,3,4,5,6,7,8,9], since 1 is only repeated twice, and n/3 = 3, output will be "none"

Prove that the time complexity of the pseudocode below is O(Log n). for (int i = 1; i <=n; i *= c) {// some O(1) expressions}for (int i = n; i > 0; i /= c) {// some O(1) expressions}

If it takes 10ms to run program (A) for n=100, how large a problem can be solved in 40ms? Explain

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Computer Algorithms Obtain the complexity of the program fragment below   for i <-- 1 to n do k <-- n while K > 1 do K <-- k/2 while (k) end-while end-for

For any positive m, n, a method was created to find integers a, b such that am+bn = gcd(m, n). Python-program this algorithm.

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