In this assignment, you will create two decorators. I suggest you follow $2$ steps.

Step $1$

Refer to the trace decorator from Professor Allison's Chapter $9$ slide set. It counts the number of times a decorated function is executed. Modify trace $($and rename it as track$)$ so that it

$1)$ caches the result of all function calls, so that the decorated function is never called twice with the same arguments,

def track$($f$)$:

cache $=\{\}$

def wrapper$(*$args$,**$kwargs$)$:

$2)$ counts the total number of function calls. Tracking the count of calls is accomplished by using a function attribute. To illustrate how this works, consider the recursive function that computes the nth Fibonacci number.

def fib$($n$)$:

return n if n in $(0,1)$ else fib$($n$-1)+$ fib$($n$-2)$

This implementation makes many repeated function calls on the same argument. If we decorate it as follows:

@track

def fib$($n$)$:

return n if n in $(0,1)$ else fib$($n$-1)+$ fib$($n$-2)$

then calling print$($fib$(10),$ 'count $=\text{'},$fib.count$)$ yields the following:

$55,$ calls $=177$

Very wasteful! Your modified track decorator should print the following:

$(1,)\{\}$ found in cache

$(2,)\{\}$ found in cache

$(3,)\{\}$ found in cache

$(4,)\{\}$ found in cache

$(5,)\{\}$ found in cache

$(6,)\{\}$ found in cache

$(7,)\{\}$ found in cache

$(8,)\{\}$ found in cache

The eight trace statements are printed whenever a repeated call is attempted on the arguments shown. Note that both positional and keyword arguments function as the cache dictionary key. This is done with the following statement:

key $=$ str$($args$)+$ str$($kwargs$)$

using the customary parameter names for decorators.

Step $2$

Write a separate logging decorator that saves all function calls and their results in the file "log.txt$".$ This requires opening the file for appending:

logfile $=$ open$(\text{'}$log$.$txt$\text{'},\text{'}$a$\text{'})$

You will need the wrapper function to open the file for each function call, write the information, and close the file.

When you decorate fib with only the log decorator, log$.$txt should contain the output below:

@log

def fib$($n$)$:

return n if n in $(0,1)$ else fib$($n$-1)+$ fib$($n$-2)$

print$($fib$(10))$ # Prints $55$

Now decorate fib with both track and log:

@track

@log

def fib$($n$)$:

return n if n in $(0,1)$ else fib$($n$-1)+$ fib$($n$-2)$

print$($fib$(10),$ 'calls $=\text{'},$ fib.count$)$

The output should then be

$(1,)\{\}$ found in cache

$(2,)\{\}$ found in cache

$(3,)\{\}$ found in cache

$(4,)\{\}$ found in cache

$(5,)\{\}$ found in cache

$(6,)\{\}$ found in cache

$(7,)\{\}$ found in cache

$(8,)\{\}$ found in cache

$55,$ calls $=11$

from the trace decorator, and log$.$txt should contain:

fib$((1,)\{\})=1$

fib$((0,)\{\})=0$

fib$((2,)\{\})=1$

fib$((3,)\{\})=2$

fib$((4,)\{\})=3$

fib$((5,)\{\})=5$

fib$((6,)\{\})=8$

fib$((7,)\{\})=13$

fib$((8,)\{\})=21$

fib$((9,)\{\})=34$

fib$((10,)\{\})=55$