Suppose we have an array $A=[k,d,c,i,t,e,s,n,o,p,j,u,x,a,q,y,l,b,g,m,h,r,v,f,w]$ which

includes $25$ integers and we are trying to find the median of $A.$ You can assume that variables

that are lexicographically greater have greater values.

$($a$)$ Utilize the median of medians algorithm to find the "true" median of $A.$ Please use sub$-$

arrays of size $5.$ If the length of the array is not a multiple of $5,$ the last sub$-$array can be

incomplete. Note that you do not have to show work when sorting sub$-$arrays or ordering

the medians of sub$-$arrays.

$($b$)$ In the first iteration, what values are guaranteed to be less than the median of medians?

What values are guaranteed to be greater than the median of medians?

$($c$)$ What would be the time complexity of this algorithm if our sub$-$arrays were of size $10?$