N-Queens

def solve_n_queens(n):
    columns, down, up = set(), set(), set()
    placements, result = [], []
    def visit(row):
        if row == n:
            result.append(["." * col + "Q" + "." * (n - col - 1) for col in placements])
            return
        for col in range(n):
            if col in columns or row - col in down or row + col in up:
                continue
            columns.add(col)
            down.add(row - col)
            up.add(row + col)
            placements.append(col)
            visit(row + 1)
            placements.pop()
            columns.remove(col)
            down.remove(row - col)
            up.remove(row + col)
    visit(0)
    return result