Prove or disprove

a$.5$n$^2+40$n $+100=$ O$($n$^2).$

b$.$ n$^3/1000=$ O$($n$^2).$

c$.$ f$($n$)==1$ i $2.$ is f$($n$)=$Q$1$: Use Compiler $($ex: $C++$ to create $2(n**n)$ matrices $A*$

$[B]=[C].$ Generate A and $B$ randomly as follows:

$[A]**[B]$

Execution Time

Q$2$: A$)$ Use Compiler $($in: $C++)$ to create array $A=[dots..n],$

Generate A randomly as follows, then apply insertion and

selection sort for the same generated array:

$A=[1$dots..$n]$ Insertion sort time Selection sort time

B$)$ Apply insertion sort to sort the string "algorithm" in alphabetical

order

Show each iteration of insertion sort on the string. Find the number

of comparisons $($n$^3)?$

d$.$ n$^$k$=(2^$n$)$

e$.$ E$=1$ logi $=($nlogn$)$

f$.7"=\backslash$Omega $(9")$