mulDigits$($num$,$ fn$)(1$ pt$)$

Returns the multiplication of all digits in num for which fn returns True when receiving the digits

as argument. You can assume that fn will always be a function that takes one number as argument

and returns a boolean value. You are not allowed to use lists, tuples, strings or convert num to

string using str$($num$).$

Examples:

$>>>$ isTwo $=$ lambda num: num $==2$ # Simple anonymous function

$>>>$ mulDigits$(5724892472,$ isTwo$)$ # Only $2$ evaluates to True

$8$

$>>>$ def divByFour$($num$)$: # Conventional function definition

$...$ return not num$\%4$

$>>>$ mulDigits$(5724892472,$ divByFour$)$ # Only $4$ and $8$ evaluate to True

$128$

getCount$($x$)(1$ pt$)$

Takes in a positive integer and returns a function that takes in an integer num, returning how many

times x appears as a digit in num. You are not allowed to use lists, tuples, strings or convert num

to string using str$($num$).$ Note that num$//10$ does not behave the same when num is negative,

$562//10$ returns $56$ while $-562//10$ returns $-57.$

Examples:

$>>>$ digit $=$ getCount$(7)$

$>>>$ digit$(945784578457077076)$

$6$

$>>>$ getCount$(6)(-65062156)$

$3$

Dual$\_$Iterator $(3$ pts$)$

An iterator that can iterate through all the elements of some sequence $($list$,$ string$),$ and when

reaching the end of the sequence, it loops back to the beginning. The iterator also includes the

method reverse$()$ that allows us to traverse in the reverse order, so when we reach the first element

of the sequence, it should loop to the last element of the iterable. You will need to initialize the

iterator settings in the constructor of the Dual$\_$Iterator class. You are not allowed to use any built$-$

in reverse methods such as reverse$(),[$::$-1],$ etc.

The implementation of the $\_\_$iter$\_\_$ method has been provided in the starter code. Do not modify

it$.$ You should only implement the following methods:

$\_\_$init$\_\_$ method: iterator settings. Takes a sequence as argument. In lecture $9\mathrm{.}3$ and $9\mathrm{.}31,$

we presented examples of iterator implementations. Revise those examples so you can

determine any additional settings besides the sequence $($our solution uses only $2$ more

attributes$)$

$\_\_$next$\_\_$: returns the next value. It does not raise a StopIteration exception since this is an

infinite iterator $($loops back$)$

$$ reverse$()$: Takes no arguments and enables the change of direction in the iterator: from

forwards to backwards and vice versa

Examples:

$>>>$ it $=$ Dual$\_$Iterator$([2,4,6,8,10])$

$>>>$ next$($it$)$

$2$

$>>>$ next$($it$)$

$4$

$>>>$ next$($it$)$

$6$

$>>>$ it$.$reverse$()$ # it stopped at $6,$ change direction

$>>>$ next$($it$)$

$4$

$>>>$ next$($it$)$

$2$

$>>>$ next$($it$)$

$10$

$>>>$ it$.$reverse$()$ # it stopped at $10,$ change direction

$>>>$ next$($it$)$

$2$

$>>>$ next$($it$)$

$4$

$>>>$ next$($it$)$

$6$

$>>>$ it$.$reverse$()$ # it stopped at $6,$ change direction

$>>>$ next$($it$)$