I. Write two functions, to evaluate the following function based on user's input.

          Let x be a non negative integer.
             F(0) = 0 and
             F(x) = 2 * F( x - 1) + x2,  when x > 0.

II Write the main function to show a menu of paragraph on screen as below:
Which of the following methods would you like to do?
 1. None Recursive Function
 2. Recursive Function
Enter your selection ( 1 or 2 ):
According to user's selection, you call one of the functions on step I.

III. Analyze the time of your both programs in terms of Big-Oh notation.

Note:
        You may check your programs by entering the following data:
 
 
x
F(x)
0
0
1
1
2
6
3
21
4
58
5
141

IV. Use a computer to get the excution time of program.
Use the following code to count program time

// clock_t is pre-defined type in time.h

clock_t Begin_time, End_time;
int time;
Begin_time = clock();
//......
//.....
//....
End_time = clock();
time = End_time - Begin_time; //duration time

OR
#include <time.h>
// clock_t is pre-defined type.
// CLOCKS_PER_SEC is a pre-defined constant in time.h

clock_t Begin_time, End_time;
double time;
Begin_time = clock();
//......
//.....
//....
End_time = clock();
time = (double)(End_time - Begin_time) / CLOCKS_PER_SEC; //duration time

V. Research deeper in these two topics.  Summarize your reading and your computer work.
     Write a formal paper including all references.
VI. Make a PowerPoint presentation about your topic and present to class.