Assistance: C++ Do the Project and Explain.

For all the following problems, make sure you devise testing of the algorithms that prove that what you programmed worked as intended. I want a menu that runs the programs and returns to the menu for further choices. See the menu program sent with this midterm. I want you to do any 4 or 5 of the following programs but there must be one of each type Vector, List, and Recursion. Yes, these are easy problems. Make sure you total the points when you are done. 100 is the maximum score. Put your problems and point count in a menu program. Here are the points for each problem 1 - 15 pts 2 - 20 pts 3 - 25 pts 4 - 15 pts 5 - 20 pts 6 - 25 pts 7 - 25 pts 8 - 15 pts 9 - 25 pts 1) Vector - Fill a vector with random inputs. Write a function vector *top(vector x,int p) that returns in a vector the top p elements of the x input vector. 2) Vector - Fill a vector with random inputs. Write a function vector *mode(vector x) that returns a vector that represents the mode of vector x. Note: Make sure there is more than one mode. 3) Vector - Fill a vector with random inputs. Write a function statClass *stat(vector x) that returns a class that contains the min,max and average of the x vector but also uses a map to solve the mode problem and returns the important elements for the mode. 4) List - Try using a list that does 1) 5) List - Try using a list that implements 2) 6) List - Try using a list that implements 3) 7) List - A self-organizing list is a list that moves each element to the front of the list whenever it is accessed. This modification improves the efficiency of the standard implementation if the list is used mostly for look-up. Use inheritance to define a SelfOrganizingList class template. Add a single function that tests if the list contains the element by returning a boolean then putting the element at the front of the list. 8) Recursion - Implement the tangent function recursively using the formulas tan(2x)=(2 tan(x))/(1-(tan(x))^2) |tan(x) ~ x + x^3/3| < epsilon Accuracy to 2 decimal places is good enough. 9) Recursion - Use mutual recursion to implement the following functions h(2x)=2h(x)g(x) g(2x)=1+2(h(x)^2) h(x) ~ x + x^3/6 just test if |x| < epsilon g(x) ~ 1 + x^2/2 just test if |x| < epsilon Epsilon -> accuracy to 6 decimal places is good enough.