Consider a following algorithm and answer the questions below. ALGORITHM(X) INPUT: Integer X OUTPUT: Integer count 1 count = 0 2 conver X to bit string S 3 while S# 0 (A) 14 count = count + 1 5 S=SA (S - 1) 6 return count What is the time complexity of this algorithm in Theta(0) notation where the size of bit string S is n? Justify your answer. • Suppose that the following loop is inserted in (A). Does it affect the complexity? If so, find the complexity in Theta(0) notation. Justify your answer. for i = 0 to S.length - 1

Suppose that each row of an n × n array A consists of 1's and 0's such that in any row of A all the 1's come before any O's in that row. Assuming that A is already in memory, describe an algorithm running in O(n) time for finding the row that contains the most 1's. Write the algorithm following the style of your course-notes.

Give the time complexity for the following algorithm. You need to identify the basic operation first. F(int n) { if (n>1) Return F(n/3)+F(n/3)+5; else return 1; } 1) What is the basic operation? 2) Set up the recurrence. Let T(n) be the # of basic operations 3) Solve the recurrence using the Master theorem

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"