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Question 8 (10%) Below we will define an $n$-interesting polygon. 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. (a) Write an efficient algorithm to find the area of a polygon for a given $n$. (5 points) • For $n = 2$, the output should be $SHAPEAREA(2) = 5$ • For $n = 3$, the output should be $SHAPEAREA(3) = 13$ (b) What is the running time of your algorithm? (5 points) n=1 n=2 n=3 n=4

          Question 8 (10%)
Below we will define an $n$-interesting polygon.
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.
(a) Write an efficient algorithm to find the area of a polygon for a given $n$. (5
points)
• For $n = 2$, the output should be $SHAPEAREA(2) = 5$
• For $n = 3$, the output should be $SHAPEAREA(3) = 13$
(b) What is the running time of your algorithm? (5 points)
n=1
n=2
n=3
n=4

Question 8 (10%)
Below we will define an n-interesting polygon.
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.
(a) Write an efficient algorithm to find the area of a polygon for a given n. (5
points)
• For n = 2, the output should be SHAPEAREA(2) = 5
• For n = 3, the output should be SHAPEAREA(3) = 13
(b) What is the running time of your algorithm? (5 points)
n=1
n=2
n=3
n=4

Added by Julian B.

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