1. 
A famous mathematical problem is: given a graph, find out whether it is possible to color
its vertices using 3 colors (say R,G,B) so that no 2 adjacent vertices have the same
color. 

Design a **iterative brute-force** algorithm to solve this problem based on the given
definition.

What is the run-time complexity of your algorihm?

You may use the following pseudo-code constructs:
for each combinatorial object (permutations, tuples, etc
assume you have bool CheckColors() - returns true if assigned colors satisfy the constraint.


2.
Solve the above problem using a **backtracking** algorithm (recursive brute-force).

3. 
Your game uses sprites (2-D images), for simplicity it is just one color. Here is an
example ”car” sprite
    *********
   **********
********************
********************
***            ***
your graphics can display either 1x1 or 3x3 squares in one time unit. Problem -
write a backtracking algorithm that accepts a sprite and represents it in the smallest
number of 1x1 and 3x3 squares to optimize the time needed to display the sprite.

3x3 squares MAY overlap - overlapping does not change the color, so for example
***
****
****
 ***
is 2 3x3 squares
111
111*
111*
 ***
and
***
*222
*222
 222
Remember - it should be a high-level pseudo code. Anything longer than 10 lines will
go into unnecessary low-level details and will probably be incorrect.


4.
based on your solution of the previous problem: Explain how to design branch-and-bound
optimization. Make sure to specify how to calculate the bound, whether it is an upper or
lower bound and how branch termination condition works.

5. See problems in big-O notes.

6. What is minimal change ordering and how one can use it to optimize backtracking algorithms? 
Explain how it can be applied to N-queen problem.