fun with n-queen

queens.py

#!/usr/bin/python3

def make_solution(size):
    def exception_queen(i, half):
        return 2 * i + half - 3

    def simple_queen(i, half):
        return 2 * i - 1

    table  = [0] * size
    half   = int(size / 2)
    n      = half * 2
    solver = exception_queen if (half - 1) % 3 == 0 else simple_queen

    for i in range(1, half + 1):
        queen = solver(i, half)

        table[i - 1] = 1 + queen % n
        table[n - i] = n - queen % n

    if size % 2 == 1:
        table[size - 1] = size

    return table


def verify_solution(array):
    def step(table):
        if not table:
            return True

        (x1, y1), *tail = table

        for (x2, y2) in tail:
            if y1 == y2:
                return False
            if abs(y2 - y1) == abs(x1 - x2):
                return False

        return step(tail)

    return step(enumerate(array))


def print_table(table):
    n = len(table)
    for queen in table:
        print("{}Q {}".format(". " * (queen - 1), ". " * (n - queen)))


for n in range(4, 40):
    table    = make_solution(n)
    verified = verify_solution(table)

    print("n {} is {}".format(n, "valid" if verified else "invalid"))
    print_table(table)
    print()