$1\mathrm{.}1$

Given a list lst of integers with length $n.$ What is the worst$-$case time complexity when calling

$f(lst,n)?$ Explain how this worst$-$case runtime is derived from the individual operations and sub$-$

function calls.

Algorithm $1$: $f(lst,n)$

if $n1$ then

return lst;

end

mlarr$\frac{n}{\frac{?}{?}}2$;

llarrlst$[$:$m]$

rlarrlst$[m$:$]$;

llarrf$(l,m)$;

rlarrf$(r,n-m)$;

return $\frac{?}{\text{b}\text{a}\text{r}}(l,r)$;

Algorithm $2$: $\frac{?}{\text{b}\text{a}\text{r}}(l,r)$

result larrlist$()$;

ilarr$0$;

jlarr$0$;

while $l[i]r[j](l[i])ilarri+1r[j]jlarrj+1(l[i$:$])r[j$:$]jdo$

$ifl[i]r[j]$ then

result.append $(l[i])$;

ilarri$+1$;

end

else

result.append$(r[j])$;

jlarrj$+1$;

end

end

result.extend $(l[i$:$])$;

result.extend$(r[j$:$])$;

return result;i and $jdo$

$ifl[i]r[j]$ then

result.append $(l[i])$;

ilarri$+1$;

end

else

result.append$(r[j])$;

jlarrj$+1$;

end

end

result.extend $(l[i$:$])$;

result.extend$(r[j$:$])$;

return result;