Recall the "better" algorithm to determine whether or not the input positive integer is a prime number that we discussed in the class. What is a running time of that algorithm with input ?n? Justify your answer

Design an algorithm to find the kth number such that the only prime factors are 3, 5, and 7. Note that 3, 5, and 7 do not have to be factors, but it should not have any other prime factors. For example, the first several multiples would be (in order) 1, 3, 5, 7, 9, 15, 21.

The following code is supposed to return nl, for positive n. An analysis of the code using our Three Question" approach reveals that: int factorial(int n)£ if (n -- e) return 1; else return (n - factoriel(n - 1)); it fails the smaller-caller question. it fails the general-case question. it passes on all three questions and is a valid algorithm. it fails the base-case question.

I needed the algorithm for G whose length is even. You can read it in the last line of the question. I don't know where the divisible by 5 part came from. Please solve the question again.

You want to design an algorithm, called minMax(A,p,r), that takes an array of integers and indexes of the first and last elements, and returns the minimum and maximum values in that range. Now write the pseudo code of a divide and conquer (and therefore, recursive) algorithm with the same time complexity (Θ(n)). You can assume that p ≤ r. Also, in your code, you can return two numbers by returning a pair, e.g. “return (a, b)”, and can save the output in a similar way, e.g. “(a, b) = minMax(parameters)”. (Short answer please)

Algorithm Prime2 (n: integer):{T,F};           prime = F; d=2; while d < n/2 and prime = F do    if n mod d = 0 then prime = T                           else d = d+1 return prime; How many times is the operation "n mod d" performed, when the input for Algorithm Prime 2 is n=123? Group of answer choices 1 4 3 2 None of these.

Are all of my answers correct?

Describe an algorithm using pseudocode that takes a list of n integers a1, a2, ..., an, and returns the product of the positive integers. Be sure to initialize the variables. I don't really have a good understanding of how to do this problem.

An unknown searching algorithm took a second to find an item in a list of 250 entries, two seconds to find an item in a list of 2,500 entries, and three seconds to find an item in a list of 25,000 entries. Estimate its runtime in big-? terms. How did you arrive at your answer?

Note that you can only use recursion to solve Q1  and you cannot use any loop. You are free to add helper methods, but you are not allowed to change the method header.Question 1: Crazy seriesIn this session, you need to implement the crazy series method. In the crazy series, you will be given a starting number. Then, you need to times 2 for each number until the number is greater than 100. After the number is greater than 100, you need to divide 3 until we reach the number is less than 5. Note that the input number must be greater than 0, and you are not allowed to use loop here.For example,crazySeries(10) should return ArrayList [10.0, 20.0, 40.0, 80.0, 160.0, 53.333333333333336, 17.77777777777778, 5.9259259259259265, 1.9753086419753088]crazySeries(5) should return ArrayList [5.0, 10.0, 20.0, 40.0, 80.0, 160.0, 53.333333333333336, 17.77777777777778, 5.9259259259259265, 1.9753086419753088]crazySeries(1) should return ArrayList [1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0,…