In this project, we want to solve a customized sudoku game by traversing our search tree recursively.
We call this algorithm Backtracking and also we use MRV and Degree methods as heuristics.

In this game, we have a board that we want to fill with the correct number and also Colors.
Despite the original sudoku here we have a color besides the number for each block that we want to put them on.
Now let's review sudoku's original rules:

• We must use all numbers in each row
• A number must be unique in each row
• A number must be unique in each column

But as mentioned earlier we added color to each block.
So we have new rules now:

• A block must have a different color from its adjacent blocks
• Our colors are prioritized, so if the color of a specific block has a higher priority than each adjacent block, the number of that block must be higher than that adjacent block

And we want to solve each sample of this game with a backtracking algorithm.

We have a Block class that we store number, color, a list of possible colors, and a list of possible numbers for that block in this class.
And also in a class named State, we store a two-dimensional array of blocks that represents each of the possible states.
When making each state, after selecting one of the possible numbers and colors, we amend possible numbers and colors of other blocks using Forward checking.
And when we reach a state that is recognized as a possible target, we finish our algorithm and print that state.

As input in the first line, we get our colors count and then our board size. (our board is square)
After that in the second line, we get colors in prioritized order which the first one has the highest priority.
Then at each row, we get the blocks. Each block is represented with two characters, the first is its number and the second is its color. (if the number is unknown we use * and if the color is unknown we using #)

5 3
r g b y p
1# *b *#
*# 3r *#
*g 1# *#

::::::::::::::::::
1p|2b|3g|
2y|3r|1p|
3g|1p|2y|
::::::::::::::::::