Question $4()$:

Consider the following Java code fragment:

$//$ Print out all ordered pairs of numbers between $1$ and $n$

for$(i=0$;$in$;$i++\{$

for

System.out.println$(i+,+j$;

$\}$

$\}$

$($a$)(3$ points$)$ Use the statement counting approach to determine the exact number of statements that

are executed when we run this code fragment as a function of $n.$ Show all of your calculations.

$($b$)(1$ point$)$ Express the answer you obtained in part $($a$)$ in big$-$ notation $($since the best and worst

cases are the same $-$ there is only one path of execution through this loop$).$

Page $2$

Question $5()$:

Consider the following pseudocode:

Algorithm roundRobinTournament$($a$)$

This algorithm generates the list of matches that must be

played in a round$-$robin pirate$-$dueling tournament $($a tournament where

each pirate duels each other pirate exactly once$).$

a is an array of strings containing names of pirates in the tournament

$n=a*$ length

for $i=0$ to $n-1$

for $j=i+1$ to $n-1$

print $a[i]+$ duels $"+$ a$[$j$]+",$ Yarrr!"

Note: the pseudocode for $i=a$ to $b$ means that the loop runs for all values of i between a and $b,$ inclusive,

that is$,$ including the values a and $b.$

$($a$)(6$ points$)$ Use the statement counting approach to determine the exact number of statements that

are executed by this pseudocode as a function of $n.$ Show all of your calculations.

$($b$)(1$ point$)$ Express the answer you obtained in part a$)$ in big$-$ notation $($since$,$ again, the best and

worst cases are the same$).$

Question $6(3$ points$)$:

Using the active operation approach, determine the time complexity of the pseudocode in question

Show all your work and express your final answer in big$-$ notation.