shapeArea.py

"""
Below we will define an n-interesting polygon. Your task is to find the area of a polygon for a given n.

A 1-interesting polygon is just a square with a side of length 1. 
An n-interesting polygon is obtained by taking the n - 1-interesting polygon and 
appending 1-interesting polygons to its rim, side by side. 
You can see the 1-, 2-, 3- and 4-interesting polygons in the picture below.
                            
                             X
                X           XXX
    X          XXX         XXXXX       
                X           XXX
                             X

  n=1          n=2          n=3
Example

For n = 2, the output should be
shapeArea(n) = 5;
For n = 3, the output should be
shapeArea(n) = 13.
Input/Output

[execution time limit] 4 seconds (py3)

[input] integer n

Guaranteed constraints:
1 ≤ n < 104.

[output] integer

The area of the n-interesting polygon.
"""


def shapeArea(n):

    if n == 1:
        return 1

    area = 0
    start = n
    for i in range(n, 2, -1):
        area += 4+(start-2)*4
        start -= 1

    area += 5
    return area
    #
    # def helper(n):
    #     if n == 1:
    #         return 1
    #
    #     if n == 2:
    #         return 5
    #     return 4+(n-2)*4 + helper(n-1)
    #
    # return helper(n)


def shapeArea_redux(n):
        return n ** 2 + (n - 1) ** 2


if __name__ == '__main__':
    print(shapeArea(1))
    print(shapeArea(2))
    print(shapeArea(3))
    print(shapeArea(4))