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- # Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):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.Please complete the following Java program using the math.random function. USE THE Math.random() class. DO NOT use arrays, the Random function. (i.e keep the program simple using while loops, if/else, for loops, etc)
- : In the classic problem FizzBuzz, you are told to print the numbers from 1 to n. However,when the number is divisible by 3, print "Fizz''. When it is divisible by 5, print "Buzz''. When it isdivisible by 3 and 5, print"FizzBuzz''. In this problem, you are asked to do this in a multithreaded way.Implement a multithreaded version of FizzBuzz with four threads. One thread checks for divisibilityof 3 and prints"Fizz''. Another thread is responsible for divisibility of 5 and prints"Buzz''. A third threadis responsible for divisibility of 3 and 5 and prints "FizzBuzz''. A fourth thread does the numbers.The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × A
- Q3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…write legibly.Please complete the following Java program using the math.random function. DO NOT USE arrays, random function. (i.e keep the program simple using while loops, if/else, for loops, etc)
- WATERSORT PROGRAM - JAVA •The aim of Part 2 is to set up the puzzle for the player to solve in Part 3. IMPORTANT NOTE: We are not going to start with 2 empty bottles, but rather with 8 empty slots spread over the 5 bottles as explained in the intro video. Start with 5 empty bottles. Use a random number generator to fill bottles one slot at a time with the colours while keeping 8 slots empty – there is a total of 5*4 = 20 slots – so if we will 12 slots, 8 are free. •Advantage: Easy to create a puzzle with a good mix •Disadvantage: With more colours and bottles and only 2 open bottles for more advanced versions of the game, the result might not be solvable. Start with three sorted bottles. In the strategy the idea is to load three bottles with uniform colour and then move ink around for a number of moves until the bottles are mixed up. •Advantage: Result is always solvable since the bottles are created in a reversed-game strategy. •Disadvantage: It is hard to develop an algorithm which…Correct answer will be upvoted else downvoted. number is called 2050-number if it is 2050, 20500, ..., (2050⋅10k for integer k≥0). Given a number n, you are asked to represent n as the sum of some (not necessarily distinct) 2050-numbers. Compute the minimum number of 2050-numbers required for that. Input The first line contains a single integer T (1≤T≤1000) denoting the number of test cases. The only line of each test case contains a single integer n (1≤n≤1018) denoting the number to be represented. Output For each test case, output the minimum number of 2050-numbers in one line. If n cannot be represented as the sum of 2050-numbers, output −1 instead.Correct answer will be upvoted else downvoted. Computer science. You are given an integer n. Check if n has an odd divisor, more noteworthy than one (does there exist such a number x (x>1) that n is separable by x and x is odd). For instance, assuming n=6, there is x=3. Assuming n=4, such a number doesn't exist. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t experiments follow. Each experiment contains one integer n (2≤n≤1014). If it's not too much trouble, note, that the input for some experiments will not squeeze into 32-cycle integer type, so you should use no less than 64-digit integer type in your programming language. Output For each experiment, output on a different line: "Indeed" if n has an odd divisor, more noteworthy than one; "NO" in any case. You can output "YES" and "NO" regardless (for instance, the strings yEs, indeed, Yes and YES will be perceived as certain).