Assignment Instructions:

For this assignment you will be creating a number of recursive functions to solve the following problems. You can implement all of the functions in a single module.

Recursive Multiplication:

Implement a recursive algorithm to compute the product of two integers, m and n$,$ using only addition and subtraction.

Harmonic Calculation:

Implement a recursive algorithm to compute the nth Harmonic number defined as: Isabel's Technique for List Summing:

Isabel has an approach for summing up an array $($list$)$ of integers that had a number of elements $($n$)$ equal to some power of $2($i$.$e$.2,4,8,16,32,$ etc.$)$ by creating a new list $($B$)$ of half the size of the original $($A$)$ such that B$[$i$]=$ A$[2$i$]+$ A$[2$i$+1]$ for all values of i in the range $0...($n$/2)-1.$

Implement a recursive algorithm that will calculate the sum of a list of integers using Isabel's approach. Your function can assume that the list must have a number of elements equal to some power of $2.$

File Search:

Implement a recursive algorithm that will print out any files from a specified starting path $($directory$)$ that match a search term. Your algorithm should process all sub$-$directories within the specified starting path and should output any files that contain the search term, even if they are not an exact match.

Testing Your Program:

Write some additional code in a main method to test out each of your functions and demonstrate that they work. For the multiplication function, demonstrate all combinations of positive and negative arguments.