What is the complexity of the given code as a function of the problem size n$?$ Show the $($complete$)$ details of your analysis. This is a Complexity Analysis, not a Complexity Estimation. You must follow the process presented in the Week$-2$B lecture, considering the Best Case, Worst Case and Average Case.

Note: a$[$i$]$ is an array with n elements.

for $($int i $=0$; i $<$ n; i$++)\{$

if $($Math$.$random$()>0\mathrm{.}75)$

if $($i$\%2==0)$

BubbleSort $($a$[$i$])$;

else

QuickSort $($a$[$i$])$;

else

for $($int j $=$ i; j $<$ n; j$++)$

for $($int k $=0$; k $<$ i; k$++)$

BinarySearch $($i$,$a$[$i$])$;

$\}$

Best Worst Average

BubbleSort

Best: O$($n$)$

Worst: O$($n$^2)$

Average: O$($n$^2)$

QuickSort

Best: O$($nlog$^2$n$)$

Worst: O$($n$^2)$

Average: O$($nlog$^2$n$)$

BinarySearch

Best: O$(1)$

Worst: O$($log$^2$n$)$

Average: O$($log$^2$n$)$