squares_in_circle

import math

"""
This script calculates how many squares of length 1 fit in a circle.
The fitting squares are divided into partial and completely in the circle.
"""

def generate_squares(radius):
    """Generates all the squares possibly in the circle
       as 4 point tuples."""

    square_list  = []
    length = math.ceil(radius)

    for x in range(length):

        for y in range(length):
            square = ((x,y),(x+1,y),(x,y+1),(x+1,y+1))
            square_list.append(square)

    return square_list

def count_squares(radius):
    """ Counts all the full and partial squares in the circle by checking
    how many edges are in the circle"""

    square_list = generate_squares(radius)

    full_squares = 0
    partial_squares = 0

    for square in square_list:
        edges_in_circle = 0

        for (x,y) in square:
            if x**2 + y**2 <= radius**2:
                edges_in_circle += 1
        if(edges_in_circle == 4):
            full_squares += 1
        elif(edges_in_circle>0):
            partial_squares += 1

    return (full_squares*4,partial_squares*4)