k12ish/knights_move_sympy.py

## knights_move_sympy.py
from sympy import symbols, solve, Eq


def knight_moves(x, y, board_size=8):
    moves = [
        (x + 1, y + 2),
        (x + 1, y - 2),
        (x - 1, y + 2),
        (x - 1, y - 2),
        (x + 2, y + 1),
        (x + 2, y - 1),
        (x - 2, y + 1),
        (x - 2, y - 1),
    ]
    return [(i, j) for i, j in moves if 0 <= i < board_size and 0 <= j < board_size]


squares = [symbols(f"{col}1:9") for col in "abcdefgh"]


def equations():
    for i in range(8):
        for j in range(i, 8):
            # symmetry condition along diagonal
            yield Eq(squares[i][j], squares[j][i])
            if (i, j) == (7, 7):
                # the final square is the destination, and is set to zero
                yield Eq(squares[-1][-1], 0)
            else:
                # every other square is equal to 1 + (∑ neighbour ) / len(neighbours)
                possible_moves = knight_moves(i, j)
                yield Eq(
                    squares[i][j],
                    1
                    + sum(squares[x][y] for x, y in possible_moves)
                    / len(possible_moves),
                )


print(solve(list(equations())))
	from sympy import symbols, solve, Eq


	def knight_moves(x, y, board_size=8):
	moves = [
	(x + 1, y + 2),
	(x + 1, y - 2),
	(x - 1, y + 2),
	(x - 1, y - 2),
	(x + 2, y + 1),
	(x + 2, y - 1),
	(x - 2, y + 1),
	(x - 2, y - 1),
	]
	return [(i, j) for i, j in moves if 0 <= i < board_size and 0 <= j < board_size]


	squares = [symbols(f"{col}1:9") for col in "abcdefgh"]


	def equations():
	for i in range(8):
	for j in range(i, 8):
	# symmetry condition along diagonal
	yield Eq(squares[i][j], squares[j][i])
	if (i, j) == (7, 7):
	# the final square is the destination, and is set to zero
	yield Eq(squares[-1][-1], 0)
	else:
	# every other square is equal to 1 + (∑ neighbour ) / len(neighbours)
	possible_moves = knight_moves(i, j)
	yield Eq(
	squares[i][j],
	1
	+ sum(squares[x][y] for x, y in possible_moves)
	/ len(possible_moves),
	)



	print(solve(list(equations())))