Need help on recursion problem for discrete structure. First year in c++ and discrete structure class. Can only take 3 functions only. And can only use C++.

Lab 3:Recursion In this lab, yu implement the recursive algorithms you came up with in section 9.8. Program Specifications Each of these functions must be implemented recursively. If any function does not solve the task recursively, you will not get credit for this lab! 1. Write a recursive function to compute the sum of the cubes of the first n positive integers. For example, if n 4, your function should return 100 (1323343) 2. Write a recursive function takes as input two non-negative integers x and y and returns the product of x and y. The only arithmetic operations your algorithm can perform are addition or subtraction. Your algorithm should have no loops. 3. Write a recursive function that takes as input a non-negative integer n and returns a collection (array, vector, set, whatever you want) containing all binary strings of length n. Make sure every element in the collection is unique (sets will do this for you, and behave pretty much the same way as vectors do) http://www.cplusplus.com/reference/set/set/ Implement a menu to let the user choose which function to run. The program should loop until the user chooses to quit. Be sure to handle the case that the user inputs an invalid number as the menu choice. sample output given below Hints and Tips Submit a PDF containing a screen shot of your program running. Use the input from the . If yo u want to format your output, check out the iomanip header You may want to check out what methods are available for strings (http://www.cplusplus.com/reference, string, string/Tkw=string) Check list Your code must have a name header as described in the syllabus. Each of these items is worth two points of your grade. Your output must Have a titlein the output Include a short paragraph indicating the purpose of the application to the user and any directions the user needs. . Use complete and clear sentences - do not assume the user knows what you expect from him/her Have NO grammatical errors and/or spelling errors. Have NO typos this includes using capital letters at the beginning of a sentence and pune- tuation at the end of sentences