OBJECTIVE: The point of this exercise is to give you more practice with creating classes, creating methods inside these classes, and performing recursion.

OVERVIEW: Create a class named RecursionManager that contains the following:

METHOD: void triangleSum(int[] nums, int k) - this method will take as input a list of integers and calculate the sums for each window of size k starting from the end of the array and going to the front. It will store all the sums in an array, format a string of the array's contents using the printFormattedArray() method you will also write, and print the returned string from the printFormattedArray() method. This process will repeat again using the sum array as input for the next triangleSum() call, and repeat over again until an array of size < k is used as input for a triangleSum() call. Use recursion to write this method. PLEASE READ THE EXAMPLE BELOW BEFORE CODING!!!

METHOD: String printFormattedArray(int[] nums) - this method will take as input a list of integers and format a string that starts with an '_', contains an '_' between each number, and ends with an '_'. For example an input array of {1, 2, 3} should result in a string that is "_1_2_3_".

INSTANCE VARIABLE: int k - this k will be used as the argument when calling triangleSum()

CONSTRUCTOR: RecursionManager(int k) - this constructor will set the instance variable k to the parameter k's value.
Example:

Input array = {1, 2, 3, 4, 5, 6}

Input k = 2

What gets printed:

_11_9_7_5_3_

_8_12_16_20_

_36_28_20_

_48_64_

_112_

Explanation of results:

_11_9_7_5_3_ 

Since input array is {1, 2, 3, 4, 5, 6}, the sums of windows of size 2 going backwards is 6 + 5, 5 + 4, 4 + 3, 3 + 2, 2 + 1. This is 11, 9, 7, 5, 3. Pass these numbers as an integer array into printFormattedArray() to be formatted.

_8_12_16_20_

Since input array is {11, 9, 7, 5, 3}, the sums of windows of size 2 going backwards is 3 + 5, 5 + 7, 7 + 9, 9 + 11. This is 8, 12, 16, 20. Pass these numbers as an integer array into printFormattedArray() to be formatted.

_36_28_20_

Since input array is {8, 12, 16, 20}, the sums of windows of size 2 going backwards is 20 + 16, 16 + 12, 12 + 8. This is 36, 28, 20. Pass these numbers as an integer array into printFormattedArray() to be formatted. _48_64_ Since input array is {36, 28, 20}, the sums of windows of size 2 going backwards is 20 + 28, 28 + 36. This is 48, 64. Pass these numbers as an integer array into printFormattedArray() to be formatted. _112_ Since input array is {48, 64}, the sums of windows of size 2 going backwards is 64 + 48. This is 112. Pass these numbers as an integer array into printFormattedArray() to be formatted.