Write a program that takes a value n as input; produces n random numbers with a uniform distribution between 1 and n and places them in a singly linked list in sorted order. Place them in the list in order, do not sort the array after placing them there. You must have the list source code in your program. You may not use a built-in list class or library. Write the program as efficiently as you can.

For the problem:

1. From an analysis of your code, give a function representing the running time of your code. Give a tight asymptotic bound for that function.

2. Run your code for various values of n and time it,

3. Create a chart showing the running times for various values of n,

4. Create a graph of the running times vs various values of n. Use a linear scale on the axes.

5. Describe how the running times support your analysis of the asymptotic running times.