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

Using a Java program solve the following problem using arrays: Past A: Coupon collector is a classic statistic problem with many practical applications. The problem is to pick objects from a set of objects repeatedly and determine how many picks are needed for all the objects to be picked at least once. A variation of the problem is to pick cards from a shuffled deck of 52 cards repeatedly and find out how many picks are needed before you see one of each suit. Assume a picked card is placed back in the deck before picking another. Write a program to simulate the number of picks needed to get total of four cards from each different suit and display the four cards picked (it is possible that a card may be picked twice). Here is a sample run of the program: Queen of Spades 5 of Clubs Queen of Hearts 4 of Diamonds Number of picks: 12 Sample run explanation: As you see in the above run, 12 picks are made to get the four cards from different suits. The other 8 picks (12-4-8) were from the…

1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…

1. Both mergesort and quicksort uses divide and conquer paradigm to sort unsorted list. (a) Imagine you want to write the quicksort algorithm to sort an array into non-increasing order. Write down the partition algorithm that is used in the divide phase in the quicksort algorithm. Show that the time complexity of this algorithm is 0(n). (b) Identify the worst case situation in the naive quicksort algorithm and show that in the worst case situation its time complexity is O(n2)