SquareSpiral

# https://www.reddit.com/r/dailyprogrammer/comments/3ggli3/20150810_challenge_227_easy_square_spirals/

import math


def spiral(*args):

    origin = [math.ceil(args[0]/2), math.ceil(args[0]/2)]
    if len(args) == 2:  # when the input is a single value in the square spiral
        x = math.sqrt(args[1])  # finding the value of the next lower odd number squared
        y = math.floor(x)
        if y % 2 == 1:
            if x != y:
                pass
            else:
                y -= 2  # when x is an odd number and when the input value is an odd number squared
        else:
            y -= 1  # when x is an even number

        # adding from the value of the next lower odd number sqaured, i.e. 25, 49, etc.
        # and going around the square
        if y**2 < args[1] and args[1] <= y**2 + y + 1:  # right side of square
            origin[0] = origin[0] + math.ceil(y/2)
            origin[1] = int(origin[1] + 0.5*(2*y**2 + y + 1) - args[1])

        elif y**2 + y + 1 < args[1] and args[1] <= y**2 + 2*y + 2:  # top
            origin[0] = int(origin[0] + 0.5*(2*y**2+3*y+3) - args[1])
            origin[1] = origin[1] - math.ceil(y/2)

        elif y**2 + 2*y + 2 < args[1] and args[1] <= y**2 + 3*y + 3:  # left
            origin[0] = origin[0] - math.ceil(y/2)
            origin[1] = int(origin[1] - 0.5*(2*y**2 + 5*y + 5) + args[1])

        elif y**2 + 3*y + 3 < args[1] and args[1] <= y**2 + 4*y + 4:  # bottom
            origin[0] = int(origin[0] - 0.5*(2*y**2+7*y+7) + args[1])
            origin[1] = origin[1] + math.ceil(y/2)

        print(origin)

    else:  # when the inputs are coordinates
        x = args[1]-origin[0]  # finding coordinates relative to center
        y = -args[2]+origin[1]
        z = max([abs(x), abs(y)])
        value = 2*z - 1
        value1 = value ** 2  # value of the next lower odd number squared
        value2 = value+2
        value3 = (value2**2-value**2)/4  # increment
        # print(x,y,z,value,value1,value2,value3)

        if abs(y) >= abs(x) and y > 0:  # top side of square
            answer = value1 + 1.5 * value3 - x

        elif abs(y) >= abs(x) and y < 0:  # bottom
            answer = value1 + 3.5 * value3 + x

        elif abs(y) < abs(x) and x > 0:  # right
            answer = value1 + 0.5 * value3 + y

        elif abs(y) < abs(x) and x < 0:  # left
            answer = value1 + 2.5 * value3 - y

        print(answer)

spiral(3, 8)
spiral(11, 50)
spiral(1024716039, 557614022)
print()
spiral(7, 1, 1)
spiral(9, 6, 8)
spiral(234653477, 11777272, 289722)