Looking for ideas how to refactor my algorithm

Question

I am trying to write my own Game of Life, with my own set of rules. First 'concept', which I would like to apply, is socialization (which basicaly means if the cell wants to be alone or in a group with other cells). Data structure is 2-dimensional array (for now).

In order to be able to move a cell to/away from a group of another cells, I need to determine where to move it. The idea is, that I evaluate all the cells in the area (neighbours) and get a vector, which tells me where to move the cell. Size of the vector is 0 or 1 (don't move or move) and the angle is array of directions (up, down, right, left).

This is a image with representation of forces to a cell, like I imagined it (but reach could be more than 5):

Let's for example take this picture:

Forces from lower left neighbour: down (0), up (2), right (2), left (0)
Forces from right neighbour     : down (0), up (0), right (0), left (2)
sum                             : down (0), up (2), right (0), left (0)

So the cell should go up.

I could write an algorithm with a lot of if statements and check all cells in the neighbourhood. Of course this algorithm would be easiest if the 'reach' parameter is set to 1 (first column on picture 1). But what if I change reach parameter to 10 for example? I would need to write an algorithm for each 'reach' parameter in advance... How can I avoid this (notice, that the force is growing potentialy (1, 2, 4, 8, 16, 32,...))? Can I use specific design pattern for this problem?

Also: the most important thing is not speed, but to be able to extend initial logic.

Things to take into consideration:

• reach should be passed as a parameter
• i would like to change function, which calculates force (potential, fibonacci)
• a cell can go to a new place only if this new place is not populated
• watch for corners (you can't evaluate right and top neighbours in top-right corner for example)

Answer 1

It should not be difficult to write your algorithm to search all of the cells within the reach distance of a particular cell C. Each cell that has an inhabitant would have a particular force of repulsion on cell C. This force of repulsion is based on the distance from the cell to cell C. In the example that you have given, that force of repulsion is based upon the L-1 distance and is 2^(reach-distance). Each repulsion force is then added together to create a cumulative force that dictates the direction in which to move the inhabitant in cell C.

You do not need to write an algorithm for each different reach. The magnitude of the force can be determined via a simple formula. If you change that formula to something else such as a Fibonacci number, you should still be able to calculate the magnitude as needed based upon the distance and the reach.

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Here is some rough code written in pseudo-Java showing the basic ideas: http://codepad.org/K6zxnOAx

enum Direction {Left, Right, Up, Down, None};

Direction push(boolean board[][], int testX, int testY, int reach)
{
    int xWeight = 0;
    int yWeight = 0;
    for (int xDist=-reach; xDist<=+reach; ++xDist)
    {
        for (int yDist=-reach; yDist<=+reach; ++yDist)
        {
            int normDist = abs(xDist) + abs(yDist);
            if (0<normDist && normDist<reach)
            {
                int x = testX + xDist;
                int y = testY + yDist;
                if (0<=x && x<board.length && 0<=y && y<board[0].length)
                {
                   if (board[x][y])
                   {
                       int force = getForceMagnitude(reach, normDist);
                       xWeight += sign(xDist) * force;
                       yWeight += sign(yDist) * force;
                   }
                }
            }
        }
    }
    if (xWeight==0 && yWeight==0) return Direction.None;
    if (abs(xWeight) > abs(yWeight))
    {
        return xWeight<0 ? Direction.Left : Direction.Right;
    }
    else
    {
        return yWeight<0 ? Direction.Up : Direction.Down;
    }
}

int getForceMagnitude(int reach, int distance)
{
    return 1<<(reach-distance);
}

Answer 2

Write a function to loop over the neighbors:

• Use min/max to clamp the bounds of the matrix.
• Use a for loop to loop over all neighbors.
• Modify the for loop bounds to represent reach.

:

def CalculateForceOnCell(x, y):
    force_on_x_y = [0,0,0,0]
    for i in range(max(0, x-reach), min(WIDTH, x+reach)+1):
        limited_reach = reach - abs(x-i)
        for j in range(max(0, y - limited_reach), min(HEIGHT, y + limited_reach + 1)):
            force_coefficient = limited_reach + 1
            AddNeighborForce(force_on_x_y, (x, y), (i, j), force_coefficient)
    return force_on_x_y