Possible points: $60$

Big$-$Oh: Determine the Big$-$Oh of the growth functions below: $20$ points

I. $5N+4$

II$.9N^2+8N-7$

III. $2logN$

IV$.3$Nlog$4N$

V$.6^{*}{2}^{7N}$

VI$.,3N!+\frac{1}{2^{*}}{N}^3$

VII. $42$

VIII. $,2^{*}{N}^3+999*N^2+123456789*N$

Stuck? Plug in some numbers to get a better idea.

What does the following algorithm do$?$ Analyze $($provide detail explanation$)$ its worst$-$case running

time, and express it using "Big$-$Oh$"$ notation. $20$ points

Algorithm Foo $($a$,$n$)$:

Input: two integers, a and n

Output: $?$

k$\}\backslash$leftarrow

b$\}\backslash$leftarrow

k$\backslash$leftarrowk$+1$

b$\backslash$leftarrowb$*$a

return b

What does the following algorithm do$?$ Analyze $($provide detail explanation$)$ its worst$-$case running

time, and express it using "Big$-$Oh$"$ notation. $20$ points

Algorithm Bar $($a$,$ n$)$:

Input: two integers, a and n

Output:?

k$\}\backslash$mp@subsup$\{\backslash$mathrm$\{$ n$\}\}\{\}\{2$

b$\}\backslash$leftarrow

c &

while k$>0$ do

k$\}\backslash$leftarrowk$/$

c $\backslash$leftarrowc$*$c

b $\backslash$leftarrowb$*$c

return b

Submission: Please submit a single PDF containing all the answers.