Write a module of utility functions called util. py for manipulating $2-$dimensional arrays of size

$44.($These functions will be used in Question $3.)$

The functions you need to write are as follows:

def create$\_$grid$($grid$)$:

$"""$create a $4\backslash$times$4$ array of zeroes within grid"""

def print$\_$grid $($grid$)$:

$"""$print out a $4$x$4$ grid in $5-$width columns within a box"""

def check$\_$lost $($grid$)$:

$"""$return True if there are no $0$ values and there are no

adjacent values that are equal; otherwise False"""

def check$\_$won $($grid$)$:

$"""$return True if a value$>=32$ is found in the grid; otherwise

False"""

def copy$\_$grid $($grid$)$:

$"""$return a copy of the given grid"""

def grid$\_$equal $($grid$1,$ grid$2)$:

$"""$check if $2$ grids are equal $-$ return boolean value"""

Version $11/09/202413$:$53$

Note: these functions are described using docstrings.

Use the

testutil.py test program to test your functions. This program takes a single integer

input value and runs the corresponding test on your module. This is a variant of unit testing, where

test cases are written in the form of a program that tests your program. You will learn more about

unit testing in future CS courses.

Sample IO $($The input from the user is shown in bold font $-$ do not program this$)$:

Sample IO $($The input from the user is shown in bold font $-$ do not program this$)$:

$7$

True

Sample IO $($The input from the user is shown in bold font $-$ do not program this$)$:

$17$

$4$

$1616$

$2\}$

$644$

$6416$

$642$

Sample IO $($The input from the user is shown in bold font $-$ do not program this$)$:

$9$

True

Sample IO $($The input from the user is shown in bold font $-$ do not program this$)$: