$1)$ Write a function get$\_$continued$\_$fraction$($lst$)$ which given a list of numbers $[0,...,1]$

computes the continued fraction:

$10+11+12+1+11$

Your function should return a pair of integers $(,)$

where $!=0$

$.$

For example: get$\_$continued$\_$fraction$([1,2,2])$ should return $(5,7)$

Python code:

def get$\_$continued$\_$fraction$($lst$)$:

assert len$($lst$)>=1$

$($n$4,$ d$4)=$ get$\_$continued$\_$fraction$([5])$

print$($f$\text{'}$Test # $0$: $\{$n$4\}/\{$d$4\}\text{'})$

assert n$4==1$ and d$4==5$

$($n$1,$ d$1)=$ get$\_$continued$\_$fraction$([1,2,2])$

print$($f$\text{'}$Test # $1$: $\{$n$1\}/\{$d$1\}\text{'})$

assert n$1==5$ and d$1==7$

$($n$2,$ d$2)=$ get$\_$continued$\_$fraction$([1,2,1,2,1])$

print$($f$\text{'}$Test # $2$: $\{$n$2\}/\{$d$2\}\text{'})$

assert n$2==11$ and d$2==15$

$($n$3,$ d$3)=$ get$\_$continued$\_$fraction$([1,1,1,1,1,1])$

print$($f$\text{'}$Test # $3$: $\{$n$3\}/\{$d$3\}\text{'})$

assert n$3==8$ and d$3==13$

$2)$ Write a function make$\_$continued$\_$fraction$($a$,$ b$)$ given numerator a and denominator b wherein $0<<=$ that returns a list $[0,...,1]$ corresponding to the continued fraction representation of $$

$.$

Python code:

def make$\_$continued$\_$fraction$($a$,$ b$)$:

assert a $>0$

assert a $<=$ b

# your code here

continued$\_$fraction $=[]$

$$

while b $!=0$:

quotient $=$ b $//$ a

remainder $=$ b $\%$ a

continued$\_$fraction.append$($quotient$)$

a$,$ b $=$ remainder, a

$$

return continued$\_$fraction

f$1=$ make$\_$continued$\_$fraction$(197,1024)$

print$($f$\text{'}197/1024=$ ContinuedFraction$(\{$f$1\})\text{'})$

assert f$1==[5,5,19,2]$

$$

f$2=$ make$\_$continued$\_$fraction$(64,128)$

print$($f$\text{'}64/128=$ ContinuedFraction$(\{$f$2\})\text{'})$

assert f$2==[2]$

$$

$$

f$3=$ make$\_$continued$\_$fraction$(1,1)$

print$($f$\text{'}1/1=$ ContinuedFraction$(\{$f$3\})\text{'})$

assert f$3==[1]$

$$

f$4=$ make$\_$continued$\_$fraction$(314157,1000000)$

print$($f$\text{'}314157/1000000=$ ContinuedFraction$(\{$f$4\})\text{'})$

assert f$4==[3,5,2,5,1,7,1,2,3,2,1,15]$