Write a function to generate customized clusters. $(15\backslash \%)$

$-$ There are two clusters, both contain $\backslash ($ n $\backslash )$ samples.

$-$ One cluster is the frame of a square with size $\backslash (=2$ r $\backslash ).$

$-$ Another cluster is the frame of a rhombus with size $\backslash (=\backslash$sqrt$\{2\}$ r $\backslash ).$

Hint: In generating a square, you can obtain $2$ random numbers, in which the first random number determines one out of the four sides, while the second random number determines the location of the point on the side.

This problem is about clusters.

Note: In application, you can add some random noise to make the cluster thicker.

Code:

$```$

# Problem $5$

import random

def problem$\_5($n$=100,$ r$=1,$ output$="$q$5.$jpg$")$:

# write your logic here

random.seed$(4320)$ # for reproducibility

plt$.$savefig$($output$)$ # do not show the plt

$```$

Execution:

$>$ problem$\_5($n$=200,$ r$=5)$

q$5.$jpg: