Daily Algorithm - shapeArea

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.

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] 3 seconds (java)

• [input] integer n

  Guaranteed constraints:
  1 ≤ n < 104.

• [output] integer

  The area of the n-interesting polygon.

Solution

public class ShapeArea {
    static int shapeArea(int n) {
        if(n == 1)
            return 1;

        return shapeArea(n - 1) + 4 * (n - 1);
    }

    public static void main(String[] args) {
        System.out.println(shapeArea(2));
    }
}

문제 출처 : https://codefights.com/arcade/intro/level-2/yuGuHvcCaFCKk56rJ/