2. Write a program that paints the following checkerboard floor pattern. How long is your program in terms of number of commands? If the floor was of size n-by- n, give a big-e estimate for the length of the program needed to paint the same pattern. Explain how you derived your estimate. Hints: For a lower bound, what is the number of "P" commands that you will need in terms of n? For the upper bound, overestimate how many times you will need each command separately in terms of n and then add your estimates together. 2 Introduction Objective: In this project we will explore the concept of big- and give some big- estimates for different algorithms. Suppose you have a robot that you are trying to program to paint floor patterns for you on a square grid in a square room. This robot can only understand a few simple commands: 1. F move forward one square 2. R-rotate 90 to the right 3. L rotate 90 to the left 4. P- paint the floor square underneath Assume that the robot always begins in the bottom leftmost square in the room facing upwards.