Return the smallest circle in the from the list of circles

I am working with recursions in python. I have two functions r(coord) that returns the radius of a circle with the center at the given coordinates and inside(coord) that returns the set of centers of all circles directly inside the circle with the given center.

I want to calculate the surface of all circles and I want to return the center of the smallest circle. I have already written the function for surface:

def surface(coord):
        return sum([surface(x) for x in inside(coord)], r(coord) * r(coord) * pi)

Now I want to return the center of the smallest circle with recursion in one return. This is what I have written:

def smallest(coord):
    return min(inside(coord))

But this line of code outputs the different result then what I’m expecting.

Expected :(20, 10.625) <-- The one I get
Actual   :(16.25, 12.5) <-- The result I want the smallest circle

I’m stuck at this function and I’m not quite sure how to approach the problem or what the solution is.

This is my entire code

def r(coord):
    return {(0, 10): 7.5,
            (0, 6): 2.5,
            (3.75, 12.5): 2.5,
            (3.75, 11.25): 1.25,
            (-3.75, 12.5): 2.5,
            (-5, 12.5): 1.25,

            (20, 10): 7.5, (20, 6): 2.5,
            (23.75, 12.5): 2.5, (23.75, 11.25): 1.25,
            (16.25, 12.5): 2.5, (15, 12.5): 1.25,
            (20, 10.625): 0.625,

            (-2.5, -8.75): 8.75,
            (-8.125, -4.375): 0.625,
            (-1.875, -9.375): 6.875,
            (-1.25, -10): 5,
            (-1.25, -9.25): 3.75,
            (-0.625, -10.625): 1.875,

            (21.25, -16.25): 11.25,
            (21.25, -7.5): 2.5,
            (22.5, -7.5): 1.25,
            (25.625, -13.125): 3.125,
            (26.875, -11.875): 0.625,
            (26.25, -21.25): 3.75,
            (16.25, -21.25): 3.75,
            (16.25, -22.25): 2.5,
            (16.125, -22.875): 0.875,
            (16.25, -12.5): 3.75
            }[coord]



def inside(coord):
    inside1 = {(0, 10): [(0, 6), (3.75, 12.5), (-3.75, 12.5)],
             (0, 6): [],
             (3.75, 12.5): [(3.75, 11.25)],
             (3.75, 11.25): [],
             (-3.75, 12.5): [(-5, 12.5)],
             (-5, 12.5): [],

             (20, 10): [(20, 6), (23.75, 12.5), (16.25, 12.5), (20, 10.625)],
             (20, 6): [],
             (23.75, 12.5): [(23.75, 11.25)],
             (23.75, 11.25): [],
             (16.25, 12.5): [(15, 12.5)],
             (15, 12.5): [],
             (20, 10.625): [],

             (-2.5, -8.75): [(-8.125, -4.375), (-1.875, -9.375)],
             (-8.125, -4.375): [],
             (-1.875, -9.375): [(-1.25, -10)],
             (-1.25, -10): [(-1.25, -9.25)],
             (-1.25, -9.25): [(-0.625, -10.625)],
             (-0.625, -10.625): [],

             (21.25, -16.25): [(21.25, -7.5), (25.625, -13.125),
                               (26.25, -21.25), (16.25, -21.25),
                               (16.25, -12.5)],
             (21.25, -7.5): [(22.5, -7.5)],
             (22.5, -7.5): [],
             (25.625, -13.125): [(26.875, -11.875)],
             (26.875, -11.875): [],
             (26.25, -21.25): [],
             (16.25, -21.25): [(16.25, -22.25)],
             (16.25, -22.25): [(16.125, -22.875)],
             (16.125, -22.875): [],
             (16.25, -12.5): []}[coord]
    random.shuffle(inside1)
    return inside1

def surface(coord):
    return sum([surface(x) for x in inside(coord)], r(coord) * r(coord) * pi)


def smallest(coord):
    return min(inside(coord)) <-- wrong output

Answer

I found solution for my problem. It outputed the right coordinates. It loops through all the circles and finds the smallest and then stores them coord. This is the code:

return min([coord]+[smallest(x) for x in inside(coord)], key=r)

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Answer