1. Let product(n,m) be a recursive method that computes the product of two positive integers, using only addition and subtraction. To make this method a recursive one, you are to make a) a base case when m = 1, b) a general case when m ≠ 1. For a general case, the return value should be n plus the result of a recursive call to the method product() with parameters n and m - 1. Write a short Java code for this method, along with a test program.

The 4th problem mimics the situation where eagles flying in the sky can be spotted and counted.FindEagles: a recursive function that examines and counts the number of objects (eagles) in aphotograph. The data is in a two-dimensional grid of cells, each of which may be empty (value 0) orfilled (value 1 to 9). Maximum grid size is 50 x 50. The filled cells that are connected form an object(eagle). Two cells are connected if they are vertically, horizontally, or diagonally adjacent. Thefollowing figure shows 3 x 4 grids with 3 eagles. 0 0 1 21 0 0 01 0 3 1 FindEagle function takes as parameters the 2-D array and the x-y coordinates of a cell that is a part ofan eagle (non-zero value) and erases (change to 0) the image of an eagle. The function FindEagleshould return an integer value that counts how many cells has been counted as part of an eagle and havebeen erased. The following sample data has two pictures, the first one is 3 x 4, and the second one is 5 x 5 grids. Notethat your program…

The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…

For each of the following recursive methods, identify the base case, the general case, and the constraints on the argument values, and explain what the method does. (images below)

Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.

The solution can be handwritten b) Trace the following recursive method for the function call “isPalindrome(rotator)” and show the output result.

Java - Write an iterative method that calculates the SUM of all integers between 1 and a given integer N (input into the method). Write a corresponding recursive solution. (return answer, don’t print)

Beeblebrox question help

Write a Non tail recursion and a tail recursion method in Java with a test class that does the following: The factorial of a positive integer n —which we denote as n!—is the product of n and the factorial of n 1. The factorial of 0 is 1. Write two different recursive methods in Java that each return the factorial of n. Please and Thank you

The factorial of a positive integer n —which we denote as n!—is the product of n and the factorial of n 1. The factorial of 0 is 1. Write two different recursive methods in Java that each return the factorial of n. Analyze your algorithm in Big-Oh notation and provide the appropriate analysis, ensuring that your program has a test class.