A sandpile is a grid of piles of sand ranging from 0 to some max integer value. For simplicity's sake, we'll look at a 3x3 grid containing 0, 1, 2, or 3 grains of sand.

An example of this sort of sandpile might look like this:

1 3 0     . ∴ 
1 2 1  =  . : .
3 2 2     ∴ : :

Sandpiles are a form of number, and as numbers, they support a single operation: addition. To add two sandpiles, simply add the number of grains of sand within each cell with the matching cell in the second value:

1 3 0   2 0 2   (1+2) (3+0) (0+2)   3 3 2
1 2 1 + 2 1 0 = (1+2) (2+1) (1+0) = 3 3 1
3 2 2   0 0 1   (3+0) (2+0) (2+1)   3 2 3

You probably already have wondered, what happens if the number of grains goes above our max value of 3? The answer is, that pile topples over. If the pile is in the middle, it dumps one grain of sand to each neighbor, keeping whatever is left over. If it's on the edge, it loses one grain to each direct neighbor and also loses one grain for any edges that are on the side, which just disappear. This means that, no matter what, the over-sized cell loses 4 grains of sand, while any neighboring cells gain 1 grain of sand.

This repeats until we've reached a state or equilibrium, like so:

                           *            *
1 3 0   3 0 2   4 3 2    * 0 5 2      2 1 3      2 1 3
1 2 1 + 2 3 0 = 3 5 1 =>   5 1 2 => * 1 3 2 =>   2 3 2 =>
3 2 2   0 0 1   3 2 3      3 3 3      4 3 3    * 0 4 3
                                                 *

                                                   *
                2 1 3    2 2 3      2 2 4      2 3 0 *
             => 2 4 2 => 3 0 4   => 3 1 0 * => 3 1 1
                1 0 4    1 2 0 *    1 2 1      1 2 1
                  *          *

So the final sum looks like this.

1 3 0   3 0 2   2 3 0
1 2 1 + 2 3 0 = 3 1 1
3 2 2   0 0 1   1 2 1

We want to create a class, Sandpile, that simulates the 3x3, max 3 sandpile. This class should have the following properties:

• The constructor optionally takes a string, which is 3 groups of 3 integers (0-9), separated by a newline. If any of the values of the integers are over 3, then immediately topple each pile until the Sandpile is at rest. If no argument is provided, initialize the piles with all zeros.
• There should be a toString method, which prints the sandpile the same way as the constructor. This will be used to validate your results.
• There should be an add method, which takes another Sandpile as an argument. This method returns a new Sandpile, with the sum of the previous Sandpiles.
• Sandpiles are immutable after creation
• The add function will only ever receive another Sandpile instance.

Tests

Add sp1 with sp2 (no topple):

let sp1 = new Sandpile('130\n121\n322');
let sp2 = new Sandpile('202\n210\n001');

Add sp1 with sp2 (with topple):

let sp1 = new Sandpile('333\n333\n333');
let sp2 = new Sandpile('000\n010\n000');

Good luck!

This challenge comes from OverZealous on CodeWars. Thank you to CodeWars, who has licensed redistribution of this challenge under the 2-Clause BSD License!

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