Moore Neighbourhood Moore Neighbourhood
Elementary+
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"Animals and plants can reproduce themselves, but it was only recently shown that machines can be made which also reproduce themselves... Other kinds of self-reproducing machines will be described, and one simple mechanical model, with no electrical or magnetic complications, will be there in working order for the audience to inspect and operate."

-- Edward Forrest Moore

In cellular automata, the Moore neighborhood comprises the eight cells surrounding a central cell on a two-dimensional square lattice. The neighborhood is named after Edward F. Moore, a pioneer of cellular automata theory. Many board games are played on a rectangular grid with squares as cells. For some games, it is important to know the conditions of neighbouring cells for chip (figure, draught, checker, etc) placement and strategy.

You are given a state for a rectangular board game grid with chips in a binary matrix, where 1 is a cell with a chip and 0 is an empty cell. You are also given the coordinates for a cell in the form of row and column numbers (starting from 0). You should determine how many chips are close to this cell. Every cell interacts with its eight neighbours; those cells that are horizontally, vertically, or diagonally adjacent.

example

The two examples shown use the same grid:

((1, 0, 0, 1, 0),
 (0, 1, 0, 0, 0),
 (0, 0, 1, 0, 1),
 (1, 0, 0, 0, 0),
 (0, 0, 1, 0, 0),)

For the first example, coordinates of the cell are (1, 2) and as we can see from the schema this cell has 3 neighbour chips. For the second example coordinates are (0, 0). This cell contains a chip, but we count only neighbours and the answer is 1.

Input: Three arguments:

  1. A grid as a tuple of tuples containing integers 1 or 0)
  2. A row number for a cell, as an integer
  3. A column number for a cell, as an integer

Output: The number of neighbouring cells that have chips, as an integer.

Example:

count_neighbours(((1, 0, 0, 1, 0),
                  (0, 1, 0, 0, 0),
                  (0, 0, 1, 0, 1),
                  (1, 0, 0, 0, 0),
                  (0, 0, 1, 0, 0),), 1, 2) == 3
count_neighbours(((1, 0, 0, 1, 0),
                  (0, 1, 0, 0, 0),
                  (0, 0, 1, 0, 1),
                  (1, 0, 0, 0, 0),
                  (0, 0, 1, 0, 0),), 0, 0) == 1

How it is used: As we mentioned in the beginning, this idea can be useful for developing board game algorithms. In addition, the same principles it can be useful for navigational software, or geographical surveying software.

Precondition:
3 ≤ len(grid) ≤ 10
all(len(grid[0]) == len(row) for row in grid)